
Effect of Hydrophobic Coating on HagenPoiseuille Flows


Pages :
10351040


Authors :
A. RíosRodríguez,
C. A. PalaciosMorales,
E. Bernal,
G. Ascanio ,
J. P. AguayoVallejo,
The effect of a hydrophobic coating on the flow through circular pipes with Newtonian fluids has been investigated. Velocity fields inside a pipe were experimentally determined by the particle image velocimetry (PIV) technique. The test fluid presented a viscosity of about sixty times higher than water viscosity. Two glass pipe configurations were used: one uncoated and another covered with an extremely hydrophobic commercial product. Comparisons between coated and uncoated pipes were made at similar Reynolds (Re) numbers, all in the laminar regime (70250). Results show that the hydrophobic effect consists in an observable slip velocity at the wall, with a reduction in shear rate near the pipe boundary. Pressure drop values were estimated from a modified HagenPoiseuille equation, taking into consideration the nonzero velocity at the boundary for both set of experiments, and the results show a 20% reduction in the pressure drop for the hydrophobic wall compared with the uncoated pipe case.





Investigating the Drag Reduction Performance of Rigid Polymer–Carbon Nanotubes Complexes


Pages :
10411049


Authors :
E. O. Akindoyo,
H. A. Abdulbari,
Transporting liquids in commercial Pipeline is very expensive due to cost incurred in the installation of pumping stations. This cost can be reduced by polymeric additives. However, these polymeric additives degrade over time as a result of mechanical stress the fluids are subjected to. Previous efforts to address these problems have not been successful. It is thus inevitable to find alternative means of reducing the frictional drag in fluid flow. In this present work, the experimental study of rigid polymer, Carbon Nanotubes (CNT) Nanofluids and the complex mixtures for drag reduction in a rotating disk apparatus. The finding shows that, about 50% drag reduction was achieved; a comparative study was made on the drag reduction of both complex and nanofluids, where both were able to reduce drag, however at different concentrations. It could thus be concluded that combination of xanthan gum and Carbon nanotubes could reduce drag at a particular concentration





Gravity Currents in a Vegetated Valley of Trapezoidal Shape


Pages :
10511156


Authors :
E. Keramaris,
P. Prinos,
In this study lockexchange experiments are performed in a tank of rectangular upper cross section and a lower vegetated valley of trapezoidal shape to study the effect of drag resistance, due to vegetation, on gravity currents. Many natural and manmade channels are approximately trapezoidal. For the simulation of the vegetation the bed is covered by flexible grass vegetation (height of vegetation, hv=2.0cm) of different submergence ratio hν/H (hν=height of vegetation, H=water depth). The motion of the gravity current is monitored with a digital video of high definition, the front velocity is measured and the height of the front is captured. Twenty four experiments are performed, twelve inside the trapezoidal section (H/Htr=0.4, 0.6 or 0.8) and twelve over the trapezoidal section (H/Htr=1.2, 1.4 or 1.6). The initial Reynolds number, based on the height of the valley and the reduced gravity, is greater than 10000 for all cases indicating that the gravity currents are turbulent. Results are compared with those of similar experiments without vegetation (Keramaris and Prinos, 2010) and hence the effect of the vegetation drag resistance on the motion of the current is investigated. The main conclusion of this study is that the shape of the tank plays a significant role in the propagation of gravity currents. The presence of trapezoidal increases the velocity of gravity currents in comparison with triangular or orthogonal shape.





Numerical Investigation of the Water Droplet Transport in a PEM Fuel Cell with Serpentine Flow Channel


Pages :
10571071


Authors :
B. Mondal,
D. Chatterjee,
The serpentine flow channel can be considered as one of the most common and practical channel layouts for a polymer electrolyte membrane fuel cell (PEMFC) since it ensures an effective and efficient removal of water produced in a cell with acceptable parasitic load. Water management is one of the key issues to improve the cell performance since at low operating temperatures in PEMFC, water vapor condensation starts easily and accumulates the liquid water droplet within the flow channels, thus affecting the chemical reactions and reducing the fuel cell performance. In this article, a comprehensive three dimensional numerical simulation is carried out to understand the water droplet mobility in a serpentine gas flow channel for a wide range of surface properties, inlet air velocities, droplet positions (center or offcenter, bottom or top) and droplet sizes by deploying a finite volume based methodology. The liquidgas interface is tracked following the volumeoffluid (VOF) method. The droplet transport is found to be greatly influenced by the surface wettability properties, inlet velocities, number of droplets emerged and initial droplet positions. Super hydrophobic surface property is not always preferable for designing the gas flow channels. It depends upon the inlet velocity conditions, droplet positions, number of droplets and surface properties.





MHD HomogeneousHeterogeneous Reactions in a Nanofluid due to a Permeable Shrinking Surface


Pages :
10731079


Authors :
S. Mansur,
A. Ishak,
I. Pop,
The MHD homogeneousheterogeneous reaction in a nanofluid flow due to a permeable shrinking surface is studied. The bvp4c program in MATLAB is used to obtain the numerical solutions for several values of parameters such as suction parameter, magnetic parameter, nanoparticle volume fraction, heterogeneous reaction and homogeneous reaction rates. The results show that dual solutions exist and the magnetic parameter and the nanoparticle volume fraction widen the range of the solution domain. Suction parameter, magnetic parameter and nanoparticle volume fraction cause the skin friction coefficient to increase and the velocity to decrease. The concentration increases as the nanoparticle volume fraction increases but decrease as the homogeneous reaction rate and heterogeneous reaction rate increase.





Electrothermo Convection in a Porous Medium Saturated by Nanofluid


Pages :
10811088


Authors :
R. Chand,
G. C. Rana,
D. Yadav,
Thermal instability in a horizontal layer of nanofluid with vertical AC electric field in a porous medium is investigated. The flux of volume fraction of nanoparticles is taken to be zero on the isothermal boundaries and the eigenvalue problem is solved using the Galerkin method. Darcy model is used for the momentum equation. The model used for nanofluid incorporates the effect of Brownian diffusion and thermophoresis. Linear stability theory based upon normal mode technique is employed to find the expressions for Rayleigh number for stationary and oscillatory convection. Graphs have been plotted to study the effects of Lewis number, modified diffusivity ratio, concentration Rayleigh number, AC electric Rayleigh number and porosity on stationary convection.





A Study on Inviscid Flow with a Free Surface over an Undulating Bottom


Pages :
10891096


Authors :
S. Panda,
In this paper, the problem involving inviscid flow with a free surface over an undulating bottom is
studied within the framework of linear theory. Applying perturbation analysis in conjunction with
the Fourier transform technique, the boundary value problem arising from the flow problem is solved
analytically. Behaviour of both interface and freesurface profiles, which are unknown at the outset,
are analyzed. It is found that each profile (interface and freesurface) possesses a wave free region at
the far upstream, followed by a modulated downstream wave. It also observed, for the first time, that
the amplitude of the downstream wave is varying. Further, the effects of various system parameters
are analyzed and demonstrated in graphical forms.





Experimental Study of the LaminarTurbulent Transition in a Tilted TaylorCouette System Subject to Free Surface Effect


Pages :
10971104


Authors :
E. Adnane,
A. Lalaoua,
A. Bouabdallah,
An experimental study of the laminarturbulent transition between two coaxial rotating cylinders with the inner cylinder rotates and outer one stationary is presented in this paper. Special attention is given to the onset of various flow modes in tilted and partially filled system. The effect of the inclination angle was investigated on the different flow regimes occurring at fully and/ or partially filled space between two rotating cylinders. The flow behavior, the transitional phenomena and the features of various flow modes are discussed for different inclination angles, filling ratio and Taylor numbers. It is established that the different filling ratio and inclination angles of the TaylorCouette system deeply affect the flow patterns. Furthermore, the most significant result concerns the relaminarization of the flow when the aspect ratio is decreased and inclination angle is increased for a given value of Taylor number.





Throughflow and Gravity Modulation Effects on Heat Transport in a Porous Medium


Pages :
11051113


Authors :
P. Kiran,
The effect of vertical throughflow and timeperiodic gravity field has been investigated on Darcy convection. The amplitude of gravity modulation is considered to be very small and the disturbances are expanded in terms of power series of amplitude of convection. A weak nonlinear stability analysis has been performed for the stationary mode of convection. As a consequence heat transport evaluated in terms of the Nusselt number, which is governed by the nonautonomous GinzburgLandau equation. Throughflow can stabilize or destabilize the system for stress free and isothermal boundary conditions. The amplitude and frequency of modulation, Prandtl Darcy number on heat transport have been analyzed and depicted graphically. Further, the study establishes that the heat transport can be controlled effectively by a mechanism that is external to the system. Finally flow patterns are presented in terms of streamlines and isotherms.





Casson Fluid Flow near the Stagnation Point over a Stretching Sheet with Variable Thickness and Radiation


Pages :
11151022


Authors :
G. K. Ramesh,
B. C. Prasannakumara,
B. J. Gireesha,
M. M. Rashidi,
The stagnationpoint flow of an incompressible nonNewtonian fluid over a nonisothermal stretching sheet is investigated. Mathematical analysis is presented for a Casson fluid by taking into the account of variable thickness and thermal radiation. The coupled partial differential equations governing the flow and heat transfer are transformed into nonlinear coupled ordinary differential equations by a similarity transformation. The transformed equations are then solved numerically by RungeKuttaFehlberg method along with shooting technique. The effects of pertinent parameters such as the Casson fluid parameter, wall thickness parameter, velocity power index, velocity ratio parameter, Prandtl number and radiation parameter have been discussed. Comparison of the present results with known numerical results is shown and a good agreement is observed.





Entropy Generation Analysis for Variable Thermal Conductivity MHD Radiative Nanofluid Flow through Channel


Pages :
11231134


Authors :
Md. S. Alam,
M. A. Alim,
M. A. H. Khan,
The present work inspects the entropy generation on radiative heat transfer in the flow of variable thermal conductivity optically thin viscous Cu–water nanofluid with an external magnetic field through a parallel isothermal plate channel. Our approach uses the power series from the governing nonlinear differential equations for small values of thermal conductivity variation parameter which are then analysed by various generalizations of Hermite Padé approximation method. The influences of the pertinent flow parameters on velocity, temperature, thermal conductivity criticality conditions and entropy generation are discussed quantitatively both numerically and graphically. A stability analysis has been performed for the rate of heat transfer which signifies that the lower solution branch is stable and physically acceptable, whereas the upper solution branch is unstable.





A Novel Multidimensional Characteristic Modeling of Incompressible Convective Heat Transfer


Pages :
11351146


Authors :
S. E. Razavi,
T. Adibi,
A characteristicbased approach is developed for thermoflow with finite volume methodology (FVM) in which multidimensional characteristic (MC) scheme is applied for convective fluxes. Artificial compressibility (AC) is used, and as a result governing equations take the hyperbolic nature. To obtain compatibility equations and pseudo characteristics, energy equation is taken into account in the MC scheme. With MC scheme for convective ﬂuxes, no artiﬁcial viscosity is required even at high Reynolds numbers. As benchmarks, forced convection between parallel plates and forced and mixed convection in a cavity are examined for a wide range of Reynolds, Grashof and Prandtl numbers. Firstorder MC and secondorder averaging schemes are used for simulate them. Results show the better performance of MC scheme in force convection as well as mixed convection. Results confirm the robustness of MC scheme in terms of accuracy and convergence, and are in good agreement with the standard benchmark solutions in the literature.





CFD Simulation of InCylinder Flow on Different Piston Bowl Geometries in a DI Diesel Engine


Pages :
11471155


Authors :
S. K. Gugulothu,
K. H. C. Reddy,
The combustion process in the diesel engine should be controlled to avoid both excessive maximum cylinder pressure and an excessive rate of pressure rise, in terms of crank angle. At the same time, the process should be so rapid that substantially all the fuel is burned early in the expansion stroke. In this direction, piston configuration plays a crucial role. Four configurations i.e., flat, inclined, central bowl, and inclined offset bowl piston have been studied. This study is concerned with the CFD analysis has been carried out on two valve four stroke diesel engine to analyze the incylinder air motion during suction stroke, pressure and temperature variation inside the cylinder during the compression stroke for various configurations. The engine specifications are considered from the literature. For numerical analysis, Ansys15 CFD software has been used, for meshing polyhedral trimmed cells were adopted. Incylinder flows were analyzed by solving mass, momentum and energy equation. From this study, it is concluded that analysis has been carried out for each crank angle degree during suction and compression stroke for all the piston configurations, tumble ratio varies mainly with crank angle position. At the end of the compression stroke fuel is injected and the performance of different piston bowls are analyzed.





Time Response of Natural Convection of Nanofluid CuOH2O in Enclosure Submitted to a Sinusoidal Thermal Boundary Condition


Pages :
11571166


Authors :
M. Bouhalleb,
H. Abbassi,
A twodimensional steady laminar natural convection in rectangular enclosure filled with CuOwater nanofluid is numerically investigated. The horizontal walls are thermally insulated and the left vertical side one is heated by a temporal sinusoidal temperature variation, whereas the right wall is kept at cold temperature. Mass Conservation, momentum, and energy equations are numerically solved by the finite volume element method using the SIMPLER algorithm for pressurevelocity coupling. This study has been carried out for four parameters: the volumetric fraction of nanoparticles (0%≤≤4%), aspect ratio Ar (0.25≤Ar≤1), amplitude of temperature a (0.2≤a≤0.8) and its period (0.2≤Θ≤0.8). These simulations are performed at constant Rayleigh and Prandtl numbers (Ra=105and Pr=7.02). Numerical results show that the addition of nanoparticules into the basic fluid has a double role, increasing heat transfer and reducing the response time of the system. The decreasing of aspect ratio shows an increasing trend of the heat transfer and increases the amplitude of Nusselt number. We also see that after a time period the system does not return to its initial state (hysteresis phenomenon) because of the system inertia.





Radiation Effect on Mixed Convection Boundary Layer Flow of a Viscoelastic Fluid over a Horizontal Circular Cylinder with Constant Heat Flux


Pages :
11671174


Authors :
H. Ahmad,
T. Javed,
A. Ghaffari,
In the present article, radiation effect on mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder with constant heat flux has been numerically analyzed. The governing boundary layer equations are transformed to dimensionless nonlinear partial differential equations. The equations are solved numerically by using Kellerbox method. The computed results are in excellent agreement with the previous studies. Skin friction coefficient and Nusselt number are emphasized specifically. These quantities are displayed against the curvature parameter. The effects of pertinent parameters involved in the problem namely effective Prandtl number and mixed convection parameter on skin friction coefficient and Nusselt number are shown through graphs and table. Boundary layer separation points are also calculated with and without radiation and a comparison is shown. The presence of radiation helps to decrease or increase the skin friction coefficient for the negative or positive values of the mixed convection parameter accordingly. The decrease in value of effective Prandtl number helps to increase the value of skin friction coefficient and Nusselt number for viscoelastic fluids.





Analysis of Magnetic Field Effects on Distributed Heat Sources in a NanofluidFilled Enclosure by Natural Convection


Pages :
11751187


Authors :
A. Aghaei,
A. A. Abbasian Arani,
F. Abedi,
This paper studies the effect of magnetic field on the flow field and heat transfer of nanofluid with variable properties in the square enclosure with two arrangements of heat sources. Based upon numerical predictions, the effects of pertinent parameters such as the Rayleigh number (103, 104 and 105), the Hartmann number (0, 25, 50, 75 and 100) and the solid volume fraction (0 to 4%) on the flow and temperature fields and the heat transfer performance of the enclosure are examined. For the numerical solution of conservation equations, finite volume method and SIMPLER algorithm was used. The results show that the heat transfer rate influenced by district heat sources and it increases with distributing heat sources on the side walls and it increases with an increase of the Rayleigh number and volume fraction, but decreases with an increase of Hartmann number.





Numerical Analysis and Prediction of Unsteady Forced Convection over a Sharp and Rounded Edged Square Cylinder


Pages :
11891199


Authors :
P. Dey,
A. Das,
An unsteady twodimensional forced convection over a square cylinder with sharp and rounded corner edge is numerically analyzed for the low Reynolds number laminar flow regime. In this study, the analysis is carried out for Reynolds number (Re) in the range of 80 to 180 with Prandtl number (Pr) variation from 0.01 to 1000 for various corner radius (r=0.50, 0.51, 0.54, 0.59, 0.64 and 0.71). The lateral sides of the computational domain are kept constant to maintain the blockage as 5%. Heat transfer due to unsteady forced convection has been predicted by Artificial Neural network (ANN). The present ANN is trained by the input and output data which has been acquired from the numerical simulation, performed in finite volume based Computational Fluid Dynamics (CFD) commercial software FLUENT. The heat transfer characteristics over the sharp and rounded corner square cylinder are evaluated by analyzing the local Nusselt number (Nulocal), average Nusselt number (Nuavg) at various Reynolds number, Prandtl numbers and for various corner radii. It is found that the heat transfer rate of a circular cylinder can be enhanced by 12% when Re is varying and 14% when Prandtl number is varying by introducing a new cylinder geometry of corner radius r=0.51. It is found that the unsteady forced convection heat transfer over a cylinder can be predicted appropriately by ANN. It is also observed that the back propagation ANN can predict the heat transfer characteristics of forced convection very quickly compared to a standard CFD method.





A Double MultiRelaxationTime Lattice Boltzmann Method for Simulation of Magneto Hydrodynamics Natural Convection of Nanofluid in a Square Cavity


Pages :
12011214


Authors :
A. R. Rahmati,
A. Najjarnezami,
In this work, for the first time, a double multirelaxationtime lattice Boltzmann method (2MRTLBM) is proposed to simulate MHD natural convection of nanofluid in a twodimensional square cavity. The cavity is filled with TiO2water nanofluid and is get under a uniform magnetic field at different angles ϕ with respect to horizontal plane. The proposed numerical scheme is solved the flow field and the temperature field using MRTD2Q9 and MRTD2Q5 lattice model, respectively. So, the main objective of this work is to show the effectiveness of this model to predict the effects of pertinent parameters such as the Rayleigh number (103 < Ra < 107), the solid volume fraction (0 % < < 5 %), the Hartmann number (0 < Ha < 60) and the magnetic field angle (0 < ϕ < 90) on the flow field and temperature field and the heat transfer performance of the cavity. The obtained results indicate that the proposed method is a powerful approach to simulate the MHD natural convection of nanofluids in a square cavity. Also the numerical results show that for Ra = 105 and for the range of Hartmann number of this study, the heat transfer and fluid flow depend strongly upon the direction of magnetic field. Furthermore, the magnetic field influence on the effect of nanoparticles on the heat transfer enhancement is not significant.





Numerical Investigation on HydrogenFueled Scramjet Combustor with Parallel Strut Fuel Injector at a Flight Mach Number of 6


Pages :
12151220


Authors :
K. M. Pandey,
S. Roga,
G. Choubey,
A numerical analysis of the inletcombustor interaction and flow structure through a scramjet engine at a flight Mach number M = 6 with parallel injection (Strut with circular inlet) is presented in the present research article. Three different angles of attack (α=4°, α=0°, α=4°) have been studied for parallel injection. The scramjet configuration used here is a modified version of DLR scramjet model. Fuel is injected at supersonic speed (M=2) through a parallel strut injector. For parallel injection, the shape of the strut is chosen in a way to produce strong stream wise vorticity and thus to enhance the hydrogen/air mixing inside the combustor. These numerical simulations are aimed to study the flow structure, supersonic mixing, and combustion phenomena for the three different types of geometries along with circular shaped strut configuration.





MHD Mixed Convection Oscillatory Flow over a Vertical Surface in a Porous Medium with Chemical Reaction and Thermal Radiation


Pages :
12211229


Authors :
G. V. Ramana Reddy,
N. Bhaskar Reddy,
A. J. Chamkha,
The present paper concerns with the study of thermal radiation and magnetohydrodynamic effects on mixed convection flow of a viscous incompressible electricallyconducting fluid through a porous medium with variable permeability in the presence of oscillatory suction. The influence of a firstorder homogeneous chemical reaction, heat source and Soret effects are analyzed. The resultant governing boundary layer equations are highly nonlinear and coupled form of partial differential equations which are solved analytically using twoterm harmonic and nonharmonic functions. The effects of different physical parameters on the velocity, temperature and concentration fields are discussed in detail. The results are presented graphically and discussed qualitatively.





Head Discharge Relationship of Thin Plated Rectangular Lab Fabricated Sharp Crested Weirs


Pages :
12311235


Authors :
S. A. Tekade,
A. D. Vasudeo,
Measuring open channel flows has been a major challenge at the field level. Because of the fact that the measuring devices are to be made from procedures and materials prescribed in standard codes. Weirs over a period of time had been used to measure discharges in open channel systems. But nonavailability of standard material at village level proves to be a major bottleneck in implementing weirs as field measurement devices. The present experimental study is an attempt to prove the good hydraulic performance of weirs made of locally available metal sheets. That use of complicated material and machining is not necessary in the fabrication of rectangular weir. A discharge formula for the rectangular weir of different sizes is extensively studied. From the experimental study it is concluded that the Cd value for each weir is nearly same. Also material and slight variation in thickness has no effect on the Cd value in case of rectangular sharp crested weir.





CAD Modeling of Store Carrying Rack9 / Store Carrying Rack9A, Their Aerodynamic Analysis and Validation through Wind Tunnel Test


Pages :
12371246


Authors :
A. Bilal,
S. S. Shah,
Purpose of this research work is to model and analyze the Store Carrying Rack (SCR) of a fighter aircraft with an objective to improve its aerodynamic performance. Refined and grid independent mesh is generated with a technique used for symmetric bodies. The different CFD technique, to capture the flow physics parallel and perpendicular to the wall of the rack, is implemented. It includes capturing the boundary layer, flow separation, vortices formation etc. Results, for the actual flight conditions of the aircraft, are acquired. The results were compared to identify the reason of modification in model. CFD results of racks were validated through Wind Tunnel Test of a scaled down model in a subsonic Wind Tunnel. A new model is proposed having least drag among all the three models. SearsHacck volume distribution is the datum for modification in shape. The new proposed model SCR9AB is recommended for the future shape modification of SCR.





Stability of Two Axially Superposed Fluids of Different Viscosities between Two Rotating Cylinders


Pages :
12471253


Authors :
V. R. K. Raju,
The linear stability of two axially superposed immiscible fluids between two rotating coaxial cylinders is studied. The fluids are assumed to have equal density but different viscosities. The effect of viscosity ratio of the two fluids on the condition for onset of instability is studied. The critical Taylor number in the less viscous fluid for onset of instability is obtained as a function of the viscosity ratio. The two limiting values of this curve correspond to critical Taylor numbers of the one fluid configuration with height of fluid column either equal to that of the less viscous fluid or equal to the sum of those for both liquids. It is found that the variation of the critical Taylor number with viscosity ratio is small when the heights of the fluid columns are large compared to the gap between the cylinders but is significant when the heights are comparable with the gap. The marginal state is found to be stationary.





A Local Nonlinear Stability Analysis of Modulated Double Diffusive Stationary Convection in a Couple Stress Liquid


Pages :
12551264


Authors :
B. S. Bhadauria,
P. G. Siddheshwar,
A. K. Singh,
Vinod K. Gupta,
The nonautonomous GinzburgLandau equation with timeperiodic coefficients is derived for two
modulated doublediffusive stationary convection involving couple stress liquid. The heat and mass
transports are quantified in terms of Nusselt and Sherwood numbers, which are obtained as functions
of the slow time scale. Effects of Prandtl number, Lewis number, solute Rayleigh number and couple
stress parameter have been discuused in detail.





Effect of Rotation on Natural Convection in Differentially Heated Rotating Enclosure by Numerical Simulation


Pages :
12651272


Authors :
M. Narendra Kumar,
G. Pundrika,
K. Rama Narasimha,
K. N. Seetharamu,
Natural convection heat transfer in a two dimensional unsteady rotating differentially heated enclosure is studied numerically in this paper. The enclosure is filled with air and executes a steady counterclockwise rotation about the centre of the enclosure. A finite volume code on a staggered grid arrangement with TDMA algorithm is developed and employed to solve the governing equations subject to Boussinesq approximation. The numerical investigation is carried out for fixed Prandtl number equal to 0.71, Rayleigh number equal to1.1×〖10〗^5 while Taylors number vary from5.2×〖10〗^4 to 3.3×〖10〗^5and Rotational Rayleigh number from 4.9×〖10〗^2 to 3.1×〖10〗^3.Results reveal that there are considerable change in heat transfer rates beyond 15 rpm. The effect of rotation on the Nusselt number for a given Rayleigh number is shown in the present work which is not normally indicated and discussed in the available literature





Mean Velocity Predictions in Vegetated Flows


Pages :
12731283


Authors :
M. Morri,
A. Soualmia,
P. Belleudy,
Vegetation plays an important role in influencing the hydrodynamic behavior, ecological equilibrium and environmental characteristics of water bodies. Several previous models have been developed, to predict hydraulic conditions in vegetated rivers, but only few are actually used in practice. In This paper six analytic model derived for submerged vegetation are compared and evaluate: Klopstra et al. (1997); Stone and Shen (2002); Van velzen (2003); Baptist et al. (2007); Huthoff et al. (2007) and Yang and Choi (2010). The evaluation of the flow formulas is based on the comparison with experimental data from literature using the criteria of deviation. Most descriptors show a good performance for predicting the mean velocity for rigid vegetation. However, the flow formulas proposed by Klopstra et al. (1997) and Huthoff et al. (2007) show the best fit to experimental data. Only for experiments with law density, these models indicate an underestimation. Velocity predicted for flexible vegetation by the six models is less accurate than the prediction in the case of rigid vegetation.





The Mixed Finite Element Multigrid Preconditioned MINRES Method for Stokes Equations


Pages :
12851296


Authors :
K. Muzhinji,
S. Shateyi,
S. S. Motsa,
The study considers the saddle point problem arising from the mixed finite element discretization
of the steady state Stokes equations. The saddle point problem is an indefinite system of linear
equations, a feature that degrades the performance of any iterative solver. The heart of the study is
the construction of fast, robust and effective iterative solution methods for such systems. Specific
attention is given to the preconditioned MINRES solver PMINRES which is carefully treated for
the solution of the Stokes equations. The study concentrates on the block preconditioner applied
to the MINRES to effectively solve the whole coupled system. We combine iterative techniques
with the MINRES as preconditioner approximations to produce an efficient solver for indefinite
system of equations. We consider different preconditioner approximations of the building blocks
of the preconditioner and compare their effects in accelerating the MINRES iterative scheme. We
give a detailed overview of the algorithmic aspects and the theoretical convergence analysis of our
solver. We study the MINRES method with the following preconditioner approximations: diagonal, multigrid vcycle, preconditioned conjugate gradient and Chebyshev semi iteration methods. A
comparative analysis of the preconditioner approximations show that the multigrid method is a suitable accelerator for the MINRES method. The application of the preconditioner becomes mandatory
as evidenced by poor performance of the MINRES as compared to PMINRES. We study the problem in a two dimensional setting using the HoodTaylor Q2 − Q1 stable pair of finite elements. The
incompressible flow iterative solution software(IFISS) matlab toolbox is used to assemble the matrices. We present the numerical results to illustrate the efficiency and robustness of the MINRES
scheme with the multigrid preconditioner.





Mathematical Study of Laminar Boundary Layer Flow and Heat Transfer of Tangenthyperbolic Fluid Pasta Vertical Porous Plate with Biot Number Effects


Pages :
12971307


Authors :
V. Ramachandra Prasad,
S. Abdul Gaffar,
O. Anwar Beg,
In this article, we investigate the nonlinear steady boundary layer flow and heat transfer of an incompressible Tangent HyperbolicnonNewtonian fluid from a vertical porous plate. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a secondorder accurate implicit finitedifference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging nondimensional parameters, namely the Weissenberg number (We), the power law index (n), Prandtl number (Pr), Biot number (), and dimensionless local suction parameter()on velocity and temperature evolution in the boundary layer regime are examined in detail. Furthermore the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. Validation with earlier Newtonian studies is presented and excellent correlation achieved. It is found that velocity, Skin friction and Nusselt number (heat transfer rate) are reduced with increasing Weissenberg number (We), whereas, temperature is enhanced. Increasing power law index (n) enhances velocity and Nusselt number (heat transfer rate) but temperature and Skin friction decrease. An increase in the Biot number () is observed to enhance velocity, temperature, local skin friction and Nusselt number. An increasing Prandtl number, Pr, is found to decrease both velocity, temperature and skin friction but elevates heat transfer rate (Nusselt number). The study is relevant to chemical materials processing applications.





Spatial Resolution Correction for Electrochemical Wallshear Stress Measurements using Rectangular Sensors


Pages :
13091319


Authors :
F. Fadla,
R. Chovet,
D. Cornu,
M. Lippert,
Fethi Aloui,
L. Keirsbulck,
This article is mainly motivated by the growing needs for highly resolved measurements for
wallbounded turbulent flows and aims to proposes a spatial correction coefficient in order to
increase the wallshear stress sensors accuracy. As it well known for the hot wire anemometry, the
fluctuating streamwise velocity measurement attenuation is mainly due to the spatial resolution and
the frequency response of the sensing element. The present work agrees well with this conclusion
and expands it to the wallshear stress fluctuations measurements using electrochemical sensors and
suggested a correction method based on the spanwise correlation coefficient to take into account
the spatial filtering effects on unresolved wallshear stress measurements due to too large sensor
spanwise size.





Viscoelastic Flow and Heat Transfer over a NonLinearly Stretching Sheet: OHAM Solution


Pages :
13211328


Authors :
M. Mustafa,
In this paper the viscoelastic flow and heat transfer over a nonlinearly stretching sheet with the power law velocity of the form is investigated for the first time. A prescribed powerlaw surface temperature distribution of the form is considered. Mathematical model is constructed through the constitutive equations of second grade fluid. The arising nonlinear boundary value problem has been treated analytically by a powerful optimal homotopy analysis method (OHAM). The solutions are found in excellent agreement with the obtained numerical solutions in the case of Newtonian fluid. The results show that velocity and skin friction coefficient have direct relationship with the powerlaw index . Further the thermal boundary layer becomes thinner when larger values of are taken into account.





Flow of an OldroydB Fluid past an Unsteady Bidirectional Stretching Sheet with Constant Temperature and Constant Heat Flux


Pages :
13291337


Authors :
M. Ahmad,
I. Ahmad,
M. Sajid,
A. Abbasi,
This article describes the time dependent flow of a nonNewtonian fluid with heat transfer. We consider three dimensional unsteady flow and heat transfer of an OldroydB fluid for constant temperature (CT) and constant heat flux (CH) cases over an unsteady bidirectional stretching surface. Homotopic solutions of the governing boundary value problems have been computed. Convergence for both velocity and temperature profiles is explored. The effects of emerging parameters on the velocity and temperature fields are investigated with the help of graphs and tabular data. It is observed that due to unsteadiness temperature in both the constant temperature and constant heat flux cases decrease significantly. Comparison of obtained and previously published results is found in excellent agreement.





Simulation of Flow and Heat Transfer of Mist/Air Impinging Jet on Grinding WorkPiece


Pages :
13391348


Authors :
F. Jiang,
H. Wang,
Y. Wang,
J. Xiang,
The numerical investigation is presented for flow and heat transfer on grinding workpiece with mist/air impinging jet by using DPM (discrete phase model) model. The tracks of the mist droplets show most of them are accumulated on the right surface of grinding zone, and can be influenced by the rotating speed of the grinding wheel, the position and the number of the jet nozzle. The mechanism model of enhance cooling by mist/air impinging jet is developed, which indicated the mist droplet is an key factor of affecting the heat transfer coefficient, and the increasing of mist droplet leads to significant enhancement of the cooling effect. The effects of the jet nozzle location, the nozzle diameter, and the nozzle number on flow and heat transfer coefficient are studied. The results show that the less nozzle distance and inclination angle, the greater nozzle diameter and number lead to greater heat transfer coefficient.





Investigation of Particles Statistics in large Eddy Simulated Turbulent Channel Flow using Generalized lattice Boltzmann Method


Pages :
13491357


Authors :
M. Samari Kermani,
S. Jafari,
M. Salmanzadeh,
M. Rahnama,
The interaction of spherical solid particles with turbulent eddies in a 3D turbulent channel flow with friction Reynolds number was studied. A generalized lattice Boltzmann equation (GLBE) was used for computation of instantaneous turbulent flow field for which large eddy simulation (LES) was employed. The subgridscale (SGS) turbulence effects were simulated through a shearimproved Smagorinsky model (SISM), which can predict turbulent near wall region without any wall function. Statistical properties of particles behavior such as root mean square (RMS) velocities were studied as a function of dimensionless particle relaxation time ( ) by using a Lagrangian approach. Combination of SISM in GLBE with particle tracking analysis in turbulent channel flow is novelty of the present work. Both GLBE and SISM solve the flow field equations locally. This is an advantage of this method and makes it easy implementing. Comparison of the present results with previous available data indicated that SISM in GLBE is a reliable method for simulation of turbulent flows which is a key point to predict particles behavior correctly.





NonAligned EthyleneGlycol 30% Based Stagnation Point Fluid over a Stretching Surface with Hematite Nano Particles


Pages :
13591366


Authors :
R. Mehmood,
S. Nadeem,
N. Sher Akbar,
This article examines the nonaligned stagnation point flow and heat transfer of an EthyleneGlycol and water based Nano fluid towards a stretching surface utilizing hematite (Fe3O4) as a heat enhancing agent. Resulting differential equations of the physical problem are solved numerically using Midpoint integration as a basic scheme along with Richardson extrapolation as an enhancement scheme. Influence of the flow governing parameters on the dimensionless velocity and temperature profile are expressed through graphs. Skin frictions coefficient and Nusselt numbers are tabulated. It is observed that Ethylenebased nano fluids have higher local heat flux than waterbased nano fluids. Computed numerical results of skin friction coefficient are in good agreement with the existing available literature for the limited case.





Study of Heat Transfer over a Square Cylinder in Cross Flow using Variable Resolution Modeling


Pages :
13671379


Authors :
P. Ranjan,
A. Dewan,
In the present study, a method of PartialAveraged NavierStokes (PANS) equations, purported to perform variable resolution modeling, is used to predict the heat transfer over a square cylinder in a crossflow. The PANS closure is based on the RANS SST kω model paradigm. The simulations were carried out using an open source software, namely, Open FOAM, at Reynolds number = 22000. The open source code and the PANS model are validated against the experimental work reported in the literature and it was observed that both the mean flow properties and turbulent statistics were in good agreement with the experimental results. Further the capability of the PANS approach in predicting heat transfer in turbulent flow is also studied. An algebraic wall function is used for the near wall treatment of the energy equation. The computed, average and local Nusselt numbers are compared with the experimental and LES results reported in the literature. The phaseaveraged analysis of the shedding phenomenon is studied to understand the heat transfer phenomenon at different faces of the cylinder and turbulent heat fluxes are also considered to understand the effect of turbulence on convection.





Effects of Slip Condition, Variable Viscosity and Inclined Magnetic Field on the Peristaltic Motion of a NonNewtonian Fluid in an Inclined Asymmetric Channel


Pages :
13811393


Authors :
A. Afsar Khan,
A. Sohail,
S. Rashid,
M. Mehdi Rashidi,
N. Alam Khan,
The peristaltic motion of a third order fluid due to asymmetric waves propagating on the sidewalls
of a inclined asymmetric channel is discussed. The key features of the problem includes longwavelength and lowReynolds number assumptions. A mathematical analysis has been carried out
to investigate the effect of slip condition, variable viscosity and magnetohydrodynamics (MHD).
Followed by the nondimensionalization of the nonlinear governing equations along with the nonlinear boundary conditions, a perturbation analysis is made. For the validity of the approximate
solution, a numerical solution is obtained using the iterative collocation technique.





Enhancement of Heat Transfer in a Liquid Metal Flow past a Thermally Conducting and Oscillating Infinite Flat Plate


Pages :
13951407


Authors :
P. Puvaneswari,
K. Shailendhra,
The effect of conjugation on the enhancement of heat transfer in a liquid metal flow past a thermally
conducting and sinusoidally oscillating infinite flat plate, when a constant temperature gradient is
superimposed on the fluid, is investigated. The plate is made up of the materials compatible with the
liquid metals used and is considered to be of finite thickness. Analytical solutions for the velocity
and the temperature of the fluid and the solid are obtained. The effects of thermal conductivity and
the thickness of the plate on the total time averaged heat flux transported and the thermal boundary
layer thickness are investigated in detail. It is found that the effects of wall thickness and wall thermal conductivity on the heat flux transported depend on their effects on the transverse temperature
gradient at any frequency. The optimum value of wall thickness at which the net heat flux transported attains the maximum value, for each fluid and for each wall material under consideration, is
reported. A maximum increase of 46.14 % in the heat flux transported can be achieved by optimizing
the wall thickness. A maximum convective heat flux of 1.87 × 108W/m2 is achieved using Na with
AISI 316 wall. All the results obtained have been compared with the experimental and analytical
results reported in the literature and are found to be in good agreement. It is believed that the new
insights gained will be of significant use while designing liquid metal heat transfer systems.





Hydromagnetic Mixed Convective Nanofluid Slip Flow past an Inclined Stretching Plate in the Presence of Internal Heat Absorption and Suction


Pages :
14091419


Authors :
S. P. Anjali Devi,
P. Suriyakumar,
The steady twodimensional mixed convective boundary layer flow of nanofluid over an inclined stretching plate with the effects of magnetic field, slip boundary conditions, suction and internal heat absorption have been investigated numerically. Two different types of nanoparticles, namely copper and alumina with water as the base fluid are considered. Similarity transformations are employed to transform the governing nonlinear partial differential equations into coupled nonlinear ordinary differential equations. The influence of pertinent parameters such as magnetic interaction parameter, angle of inclination, volume fraction, suction parameter, velocity slip parameter, thermal jump parameter, heat absorption parameter, mixed convection parameter and Prandtl number on the flow and heat transfer characteristics are discussed. A representative set of results are displayed graphically to illustrate the issue of governing parameters on the dimensionless velocity and temperature. Numerical values of skin friction coefficient and the Nusselt number are shown in tabular form. A comparative study between the previously published work and the present results in a limiting sense reveals excellent agreement between them.





LES of Flow past Circular Cylinder at Re = 3900


Pages :
14211435


Authors :
B. N. Rajani,
A. Kandasamy,
Sekhar Majumdar,
Transitional flow past a circular cylinder in the lower subcritical regime (Re = 3900) has been analysed using Large Eddy Simulation (LES) coupled to Smagorinsky and dynamic sub grid scale models. These simulations have been carried out using a parallel multiblock structured finite volume
code which is based on SIMPLE algorithm. The predictions are validated against detailed measurement data for mean as well as turbulence quantities. The present LES prediction in general agree
reasonably well with the measurement data in the near wake region but deviates from the measurement data in the far wake region which may be due to the coarse resolution of the grid in this region.
The influence of the SGS model on mean flow quantities as well as on the flow structures are also
discussed.





Flow and Heat Transfer over an Unsteady Stretching Sheet in a Micropolar Fluid with Convective Boundary Condition


Pages :
14371445


Authors :
S. A. Shehzad,
M. Waqas,
A. Alsaedi,
T. Hayat,
This article is concerned with the flow of micropolar fluid over an unsteady stretching surface with convective boundary condition. The governing partial differential equations are first converted into ordinary differential equations using appropriate transformations and then solved for the series solutions. Influence of micropolar parameter, unsteadiness parameter, boundary parameter, Prandtl number and Biot number on the flow and heat transfer characteristics is examined. Numerical values of local Nusselt number and skin friction coefficient are presented and analyzed. It is observed that temperature is an increasing function of Biot number.





Soret and Dufour Effects on MHD Mixed Convection Heat and Mass Transfer of a Stagnation Point Flow towards a Vertical Plate in a Porous Medium with Chemical Reaction, Radiation and Heat Generation


Pages :
14471455


Authors :
S. Karthikeyan,
M. Bhuvaneswari,
S. Sivasankaran,
S. Rajan,
The objective of this paper is to analyze the effects of heat and mass transfer in the presence of thermal radiation, internal heat generation and Dufour effect on an unsteady magnetohydrodynamic mixed convection stagnation point flow towards a vertical plate embedded in a porous medium. The nonlinear partial differential equations governing the flow are transformed into a set of ordinary differential equations using suitable similarity variables and then solved numerically using shooting method together with RungeKutta algorithm. The effects of the various parameters on the velocity, temperature and concentration profiles are depicted graphically and values of skin friction coefficient, Nusselt number and Sherwood number for various values of physical parameters are tabulated and discussed. It is observed that the temperature increases for increasing values of the internal heat generation, thermal radiation and the Dufour number and hence thermal boundary layer thickness increases.





Sensitivity Analysis of Pulsatile Hydromagnetic Biofluid Flow and Heat Transfer with Non Linear DarcyForchheimer Drag


Pages :
14571465


Authors :
S. Rawat,
R. Bhargava,
S. Kapoor,
S. Sharma,
In the present paper we examine the pulsatile hydromagnetic flow and heat transfer of a nonNewtonian biofluid through a saturated nonDarcian porous medium channel. The upper plate of the channel is heated and the lower plate is cooled. The NakamuraSawada rheological model is employed which provides a higher yield stress than the Casson model. A DarcyForchheimer porous medium drag force model is incorporated to simulate blood vessel blockage with deposits in the cardiovascular system. Viscous heating is also included in the energy equation. The governing conservation equations for mass, momentum and energy equation are transformed into a system of nonlinear, coupled ordinary differential equations and these are solved numerically using finite element method. The effect of other important parameters such as magnetohydrodynamic parameter (Nm), Reynolds number (Re), Eckert number (Ec), Darcian parameter (), Forchheimer parameter (NF) and Prandtl number on velocity and temperature profiles are studied graphically. Spatialtemporal velocity and temperature profile visualizations are also presented. Numerical results shows that normalized fluid velocity (U) increases throughout the channel (1 < Y < 1) with an increase in Reynolds number, Darcian parameter, steady pressure gradient parameter and rheological parameter; conversely velocity is decreased with the increase in magnetic parameter and Forchheimer quadratic drag parameter. Higher Eckert number (Ec = 3) is also found to have a considerable effect on temperature () profile. Finite difference numerical computations are also compared with the finite element solutions to verify efficiency and accuracy.





Unsteady Free Convection Fluid Flow over an Inclined Plate in the Presence of a Magnetic Field with Thermally Stratified High Porosity Medium


Pages :
14671475


Authors :
A. A. Foisal,
Md. M. Alam,
MHD free convection over an inclined plate in a thermally stratified high porous medium in the presence of a magnetic field has been studied. The dimensionless momentum and temperature equations have been solved numerically by explicit finite difference technique with the help of a computer programming language Compaq Visual Fortran 6.6a. The obtained results of these studies have been discussed for the different values of well known parameters with different time steps. Also, the stability conditions and convergence criteria of the explicit finite difference scheme has been analyzed for finding the restriction of the values of various parameters to get more accuracy. The effects of various governing parameters on the fluid velocity, temperature, local and average shear stress and Nusselt number has been investigated and presented graphically.





Eulerian ISPH Method for Simulating Internal Flows


Pages :
14771490


Authors :
M. Ordoubadi,
A. Farhadi,
F. Yeganehdoust,
H. Emdad,
M. Yaghoubi,
E. Goshtasebi Rad,
In this article the possibility to use Eulerian approach in the conventional ISPH method in simulation of internal fluid flows is studied. The use of Eulerian approach makes it possible to use nonuniform particle distributions to increase the resolution in the sensitive parts of the domain, different boundary conditions can be employed more freely and particle penetration in the solid walls and tensile instability no longer require elaborate procedures. The governing equations are solved in an Eulerian framework containing both the temporal and local derivatives which make the momentum equations nonlinear. Some special treatment and smaller time steps are required to remedy this nonlinearity of the problem. In this study, projection method is used to enforce incompressibility with the evaluation of an intermediate velocity and then this velocity is projected on the divergencefree space. This method is applied to the internal fluid flows in a sheardriven cavity, Couette flow, a flow inside a duct with variable area and flow around a circular cylinder within a constant area duct. The results are compared with the results of Lagrangian ISPH and WCSPH methods as well as finite volume and Lattice Boltzmann grid based schemes. The results of the studied scheme have the same accuracy for velocity field and have better accuracy in pressure distribution than ISPH and WCSPH methods. Nonuniform particle distributions are also studied to check the applicability of this method and Good agreement is also observed between uniform and nonuniform particle distributions.





Numerical Simulation of Flow and Heat Transfer of Nanofluid around a Heated Square Cylinder


Pages :
14911501


Authors :
L. Bouazizi,
S. Turki,
A numerical investigation was conducted to study the forced and mixed convection of nanofluid in a horizontal channel with a builtinheated square cylinder. The nanofluid considered in this study is composed of metal nanoparticles(Cu) suspended in water (base fluid). The governing equations are solved using the finite volume method based SIMPLER algorithm. Different Reynolds numbers and volume fractions of nanoparticles ranging respectively from Re= 85 to 200 and from φ= 0%to12%, have been considered. The effect of the nanoparticles volume fraction on the critical Reynolds number value defining the transition between two flow regimes (stationary and periodic)as well as on the overall flow coefficients is firstly studied. In the thermal study, we have established correlations to evaluate the heat flux transferred from the obstacle to the flow for different nanoparticles volume fractions. Results show a marked improvement in heat transfer compared to the base fluid. This improvement is more pronounced for higher Richardson numbers and higher nanoparticles volume fractions.





MHD Stagnation Flow of a Newtonian Fluid towards a Uniformly Heated and Moving Vertical Plate


Pages :
15031513


Authors :
M. S. Demir,
S. Barış,
Stagnation flow of an electrically conducting incompressible viscous fluid towards a moving vertical plate in the presence of a constant magnetic field is investigated. By using the appropriate transformations for the velocity components and temperature, the partial differential equations governing flow and heat transfer are reduced to a set of nonlinear ordinary differential equations. These equations are solved approximately using a numerical technique for the following two problems: (i) twodimensional stagnationpoint flow on a moving vertical plate, (ii) axisymmetric stagnationpoint flow on a moving vertical plate. The effects of nondimensional parameters on the velocity components, wall shear stresses, temperature and heat transfer are examined carefully.





Group Theoretical Analysis of nonNewtonian Fluid Flow, Heat and Mass Transfer over a Stretching Surface in the Presence of Thermal Radiation


Pages :
15151524


Authors :
M. Nazim Tufail,
A. Saeed Butt,
A. Ali,
The present article examines the flow, heat and mass transfer of a nonNewtonian fluid known as
Casson fluid over a stretching surface in the presence of thermal radiations effects. Lie Group analysis is used to reduce the governing partial differential equations into nonlinear ordinary differential
equations. These equations are then solved by an analytical technique known as Homotopy Analysis Method (HAM). A comprehensive study of the problem is being made for various parameters
involving in the equations through tables and graphs.





Peristaltic Transport with Convective Conditions of Heat and Mass Transfer


Pages :
15251532


Authors :
F. M. Abbasi,
T. Hayat,
A. Alsaedi,
The objective of present communication is to discuss the effect of mass convective condition on the peristaltic transport of viscous fluid in an asymmetric channel. Analysis has been carried out in the presence of Soret and Dufour effects. Comparative study of temperature and concentration fields in the presence and absence of convective conditions through heat and mass transfer is carefully examined. Numerical values of heat and mass transfer rates are computed and analyzed.





Lagrangian Particle Tracking in VelocityVorticity Resolved Viscous Flows by Subdomain BEM


Pages :
15331549


Authors :
J. Ravnik,
M. Hriberšek,
J. Lupše,
A numerical study of particle motion in a cubic lid driven cavity is presented. As a computational
tool, a boundary element based flow solver with a Lagrangian particle tracking algorithm is derived.
Flow simulations were performed using an inhouse boundary element based 3D viscous flow solver.
The Lagrangian particle tracking algorithm is capable of simulation of dilute suspensions of particles
in viscous flows taking into account gravity, buoyancy, drag, pressure gradient and added mass. The
derived algorithm is used to simulate particle behaviour in a cellular flow field and in a lid driven
cavity flow. Simulations of particle movement in a cellular flow field were used to validate the
algorithm. The main goal of the paper was to numerically simulate the flow behaviour of spheres of
different densities and different diameters, as experimentally observed in work of Tsorng et al.The
study of slightly buoyant and nonbuoyant particles in a lid driven cavity was aimed at discovering
cases when particles leave the primary vortex and enter into secondary vortices, a phenomenon
described in the work of Tsorng et al. A parametric study of this phenomenon was preformed.
The presented computational results show excellent agreement with experiments, confirming the
accuracy of the developed computational method.





Onset of Benard–Marangoni Convection in a Composite Layer with Anisotropic Porous Material


Pages :
15511558


Authors :
Y. H. Gangadharaiah,
The effects of thermal anisotropy and mechanical anisotropy on the onset of BernardMarangoni convection in composite layers with anisotropic porous material is studied. The upper fluid surface, free to atmosphere is considered to be deformable. The eigen value problem is solved using a regular perturbation technique with wave number as perturbation parameter. It is observed that both stabilizing and destabilizing factors can be enhanced thermal anisotropic parameter and mechanical anisotropic parameter so that a more precise control (suppress or augment) of thermal convective instability in a layer of fluid or porous medium is possible.



