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The present study is concerned with the scattering of an incoming water wave over a single step below the upper surface where the height of the step may be finite or very large(infinite) in presence of a surface discontinuity. Using linear theory, the problem is formulated mathematically as a boundary value problem in two separate regions of the ocean corresponding to two different depths. By utilising the eigenfunction expansion of the velocity potentials in conjunction with the impendence conditions along the common vertical boundary of the two regions, the mathematical problem is reduced to a system of linear equations which are solved numerically to obtain the hydrodynamic coefficients. If the surface discontinuity is due to a semi-infinite floating dock over an infinite step at the bottom, use of Havelock expansion of the velocity potentials and impendence conditions, the boundary value problem leads to another system of linear equation involving integral equations. The explicit form of the reflection coefficient is computed numerically in terms of wave number of the incoming wave and a number of graphical representations is given.

Analytical expressions correlating the volumetric flow rate to the inlet and outlet pressures are derived for the time-independent flow of Newtonian fluids in cylindrically-shaped elastic tubes using a one-dimensional Navier-Stokes flow model with two pressure-area constitutive relations. These expressions for elastic tubes are the equivalent of Poiseuille and Poiseuille-type expressions for rigid tubes which were previously derived for the flow of Newtonian and non-Newtonian fluids under various flow conditions. Formulae and procedures for identifying the pressure field and tube geometric profile are also presented. The results are validated by a finite element method implementation. Sensible trends in the analytical and numerical results are observed and documented.

The magnetic field effect on laminar natural convection flow is investigated in a filled enclosure with internal heat generation using two-dimensional numerical simulation. The enclosure is heated by a uniform volumetric heat density and walls have constant temperature. A fixed magnetic field is applied to the enclosure. The dimensionless governing equations are solved numerically for the stream function, vorticity and temperature using finite difference method for various Rayleigh (Ra) and Hartmann (Ha) numbers in MATLAB software. The stream function equation is solved using fast Poisson's equation solver on a rectangular grid (POICALC function in MATLAB), voricity and temperature equations are solved using red-black Gauss-Seidel and bi-conjugate gradient stabilized (BiCGSTAB) methods respectively. The results show that the strength of the magnetic field has significant effects on the flow and temperature fields. For the square cavity, the maximum temperature reduces with increasing Ra number. It is also observed that at low Ra number, location of the maximum temperature is at the centre of the cavity and it shifts upwards with increase in Ra number. Circulation inside the enclosure and therefore the convection becomes stronger as the Ra number increases while the magnetic field suppresses the convective flow and the heat transfer rate. The ratio of the Lorentz force to the buoyancy force (Ha2/Ra) is as an index to compare the contribution of natural convection and magnetic field strength on heat transfer.

Air flow and heat transfer inside a yogurt cooling room were analysed using Computational Fluid Dynamics. Air flow and heat transfer models were based on 3D, unsteady state, incompressible, Reynolds-averaged Navier-Stokes equations and energy equations. Yogurt cooling room was modelled with the measured geometry using 3D design tool AutoCAD. Yogurt cooling room model was exported into the flow simulation software by specifying properties of inlet air, yogurt, pallet and walls of the room. Packing material was not considered in this study because of less thickness (cup-0.5mm, carton box-1.5mm) and negligible resistance created in the conduction of heat. 3D Computational domain was meshed with hexahedral cells and governing equations were solved using explicit finite volume method. Air flow pattern inside the room and the temperature distribution in the bulk of palletized yogurt were predicted. Through validation, the variation in the temperature distribution and velocity vector from the measured value was found to be 2.0oC (maximum) and 30% respectively. From the simulation and the measured value of the temperature distribution, it was observed that the temperature was non-uniform over the bulk of yogurt. This might be due to refrigeration capacity, air flow pattern, stacking of yogurt or geometry of the room. Required results were achieved by changing the location of the cooling fan.

A study has been carried out to analyze the effects of viscous-Ohmic dissipation and variable thermal conductivity on steady two-dimensional hydromagnetic flow, heat and mass transfer of a micropolar fluid over a stretching sheet embedded in a non-Darcian porous medium with non-uniform heat source/sink and thermal radiation. The governing differential equations are transformed into a set of non-linear coupled ordinary differential equations which are then solved numerically. A comparison with previously published work has been carried out and the results are found to be in good agreement. The effects of various physical parameters on velocity, temperature, and concentration distributions are shown graphically.

An analysis is presented to investigate the influences of viscous and pressure stress work on MHD natural convection flow along a uniformly heated vertical wavy surface. The governing equations are first modified and then transformed into dimensionless non-similar equations by using set of suitable transformations. The transformed boundary layer equations are solved numerically using the implicit finite difference method, known as Keller-box scheme. Numerical results for the velocity profiles, temperature profiles, skin friction coefficient, the rate of heat transfers, streamlines and isotherms are shown graphically. Some results of skin friction, rate of heat transfer are presented in tabular form for selected values of physical parameters.

Viscoelastic boundary layer flow and heat transfer over an exponential stretching continuous sheet have been investigated in this paper. Numerical solution of the highly non-linear momentum equation and heat transfer equation are obtained. Two cases are studied in heat transfer, namely (i) the sheet with prescribed exponential order surface temperature (PEST case) and (ii) the sheet with prescribed exponential order heat flux (PEHF case). The governing coupled, non-linear, partial differential equations are converted into coupled, non-linear, ordinary differential equations by a similarity transformation and are solved numerically using shooting method. The classical explicit Runge-Kutta-Fehlberg 45 method is used to solve the initial value problem by the shooting technique. The effects of various parameters such as viscoelastic parameter, slip parameter, Eckert number and Prandtl number on velocity and temperature profiles are presented and discussed. The results have possible technological applications in the liquid-based systems involving stretchable materials.

The numerical analysis of turbulent fluid flow and heat transfer through a rectangular elbow has been done by   model with standard wall function. Different inlet uniform velocities of 5m/s, 10m/s, 15 m/s, 20 m/s and 25 m/s corresponding to Reynolds numbers of Re1= 4.09× 104, Re2= 8.17 × 104, Re3= 12.25× 104, Re4= 16.34× 104 and Re5 =20.43 × 104 have been considered for the numerical experimentations. The fluid considered was incompressible, Newtonian non-reacting and the flow was fully turbulent. The heat transfer analysis has been carried out by considering the fluid having at a higher temperature while the wall kept at lower temperature. A detailed study of the turbulent fluid flow shows that presence of recirculation is inevitable at every corner position or at every bend indicating presence of secondary flow incurring energy losses. The velocity distributions at different stations along the downstream path of the elbow have been plotted. The presence of this adverse pressure gradient is confirmed by the reverse velocity or the negative velocity in the vicinity of the vertical wall. In the upper corner there is a vortex extending from the upper wall of the upper limb almost touching the end point of the left wall of the vertical portion of the elbow. The heat transfer also shows the similar tendency as the fluid flow field influences the convective heat transfer process. The detail temperature distributions across any cross section basically explain the dependence of the convective heat transfer on the fluid flow field.

This paper presents a study for the MHD flow of an incompressible generalized Burgers' fluid through a rectangular duct in porous medium. The flow is generated due to the velocity sawtooth pulses applied on the duct. Exact solutions of the governing equations are obtained by using the Laplace transform and double finite Fourier sine transform in this order. The obtained solutions satisfy all the initial and boundary conditions and are written as a sum of steady and transient solutions. Graphs are plotted for both developing and retarding flows. The effects of magnetic parameter, porosity parameter, and various parameters of interest on the flow characteristics are discussed. The problem reduces to the flow between two plates in the absence of side walls.

This study is interested in the effect of an axial magnetic field imposed on incompressible flow of electrically conductive fluid between two horizontal coaxial cylinders. The imposed magnetic field is assumed uniform and constant. The effect of heat generation due to viscous dissipation is also taken into account. The inner and outer cylinders are maintained at different uniform temperatures. The movement of the fluid is due to rotation of the cylinder with a constant speed. An exact solution of the equations governing the flow was obtained in the form of Bessel functions. A finite difference implicit scheme was used in the numerical solution. The velocity and temperature distributions were obtained with and without the magnetic field. The results show that for different values of the Hartmann number, the velocity between the two cylinders decreases as the Hartmann number increases. Also, it is found that by increasing the Hartmann number, the average Nusselt number decreases. On the other hand, the Hartmann number does not affect the temperature.

Thermal instability in a low Prandtl number nanofluid in a porous medium is investigated by using Galerkin weighted residuals method for free-free boundaries. For porous medium, Brinkman-Darcy modelis applied. The model used for the nanofluid describes the effects of Brownian motion and thermophoresis. Linear stability theory based upon normal mode analysis is employed to find the expression for stationary and oscillatory convection. The effects of Prandtl- number, Darcy number, Lewis number and modified diffusivity ratio on the stationary convection are investigated both analytically and graphically. The results indicated that the Prandtl and Darcy numbers have a destabilizing effect while the Lewis number and modified diffusivity ratio have a stabilizing effect for the stationary convection.

The present investigation addresses the effect of Newtonian heating in the laminar flow of power law nanofluid. The flow is induced by a stretching surface. The nonlinear analysis comprising flow and energy equations is computed. The problems are solved for the series solutions of velocity and temperature. Skin friction coefficient and Nusselt number are computed. A parametric study is performed for the influential parameters on the velocity and temperature. Physical interpretation of the derived solutions is presented.

The transition from laminar to turbulent flow in porous media is studied with a pore doublet model consisting of pipes with different diameter. The pressure drop over all pipes is recorded by pressure transducers for different flow rates. Results show that the flow in the parallel pipes is redistributed when turbulent slugs pass through one of them and six different flow zones were identified by studying the difference between the Re in the parallel pipes. Each flow zone starts when the flow regime of one of the pipe changes. Transitional flow of each pipe increases the correlation between different pipes pressure drop fluctuations. Frequency analysis of the pressure drops show that the larger pipe makes the system to oscillate by the presence of turbulent patches in its flow. However, when the flow in the smaller pipe enters into the transitional zone the larger pipe starts to follow the fluctuations of the smaller pipe.

In this paper different configurations of plasma actuator for controlling the flow around a circular cylinder made of Quartz were experimentally investigated. Three thin plasma actuator electrodes were flush-mounted on the surface of the cylinder and were connected to a DC high voltage power supply for generation of electrical discharge. Different configurations of plasma actuator were used for this study and pressure distribution experiments showed that the existence of the plasma decreases the pressure coefficient of the cylinder and the variation of the pressure coefficient can change the behavior of the lift and drag coefficient of the cylinder for all configurations. According to the pressure distribution data, two configurations of the plasma actuators made the best influence on the aerodynamic performance and also on the drag reduction.

In order to solve the velocity profile and pressure gradient of the unsteady unidirectional slip flow of Voigt fluid, Laplace transform method is adopted in this research. Between the parallel microgap plates, the flow motion is induced by a prescribed arbitrary inlet volume flow rate which varies with time. The velocity slip condition on the wall and the flow conditions are known. In this paper, two basic flow situations are solved, which are a suddenly started and a constant acceleration flow respectively. Based on the above solutions, linear acceleration and oscillatory flow are also considered.

In this study, a version of thermal immersed boundary-Lattice Boltzmann method (TIB-LBM) is used to simulate thermal flow problems within complex geometries. The present approach is a combination of the immersed boundary method (IBM) and the thermal lattice Boltzmann method (TLBM) under the double population approach. The method combines two different grid systems, an Eulerian grid for the flow domain and a Lagrangian grid for the boundary points immersed in the flow. In the present method, an unknown velocity correction is considered on the boundary points to impose the no-slip boundary condition. As a similar approach, an unknown internal energy correction on the boundary points is applied to satisfy the constant temperature boundary condition. The advantages of this approach are its second-order accuracy and straightforward calculation of the Nusselt number. The natural convection in an annulus with various outer cylinder shapes for different Rayleigh numbers have been simulated to demonstrate the capability and the accuracy of present approach. In terms of accuracy, the predicted results show an excellent agreement with those predicted by other experimental and numerical approaches.

The time periodic electroosmotic flow of Newtonian fluids through a semicircular microchannel is studied under the Debye–Hückel approximation. Analytical series of solutions are found, and they consist of a time-dependent oscillating part and a time-dependent generating or transient part. Some new physical phenomena are found. The electroosmotic flow driven by an alternating electric field is not periodic in time, but quasi-periodic. There is a phase shift between voltage and flow, which is only dependent on the frequency of external electric field.

A combined experimental and numerical investigation was conducted into impact of rigid wedges on water in two-dimensional fluid conditions. Drop test experiments were conducted involving symmetric rigid wedges of varying angle and mass impacted onto water. The kinematic behaviour of the wedge and water was characterised using high-speed video. Numerical models were analysed in LS-DYNA® that combined regions of Smoothed Particle Hydrodynamics particles and a Lagrangian element mesh. The analysis captured the majority of experimental results and trends, within the bounds of experimental variance. Further, the combined modelling technique presented a highly attractive combination of computational efficiency and accuracy, making it a suitable candidate for aircraft ditching investigations.