Journal of Applied Fluid MechanicsJAFMMechanical Engineeringhttp://jafmonline.net1admin173535721735364510.18869/acadpub.jafmenjalali1395411gregorian20167195online1fulltexten10.18869/acadpub.jafm.68.236.25597Unsteady Boundary Layer Flow over a Vertical Surface due to Impulsive and Buoyancy in the Presence of Thermal-Diffusion and Diffusion-Thermo using Bivariate Spectral Relaxation MethodgeneralResearchIn this article, unsteady boundary layer ﬂow formed over a vertical surface due to impulsive motion
and buoyancy is investigated. The mathematical model which properly accounts for space and
temperature-dependent internal heat source in a ﬂowing ﬂuid is incorporated into the energy equation.
This model is presented in this study as a term which accounts for two different forms of
internal heat generation during the short time period and long time period. Due to the ﬂuid ﬂow
under consideration, the inﬂuence of thermal-diffusion and diffusion-thermo are incorporated into
the governing equation since it may not be realistic to assume that both effects are of smaller order
of magnitude than the effects described by Fourier’s or Fick’s law. The corresponding effect of internal
heat source on viscosity is considered; the viscosity is assumed to vary as a linear function
of temperature. The ﬂow model is described in terms of a highly coupled and nonlinear system of
partial differential equations. The governing equations are non-dimensionalized by using suitable
similarity transformation which unraveled the behavior of the ﬂuid ﬂow at short time and long time
periods. The dimensionless system of non-linear coupled partial differential equations (PDEs) is
solved using Bivariate Spectral Relaxation Method (BSRM). A parametric study of selected parameters
is conducted and results of the surface shear stress, heat transfer and mass transfer at the wall
are illustrated graphically and physical aspects of the problem are discussed.Unsteady; Mixed convection; Impulsive motion; Variable viscosity; Bivariate Spectral Relaxation method; Space-heat source.26052619http://jafmonline.net/JournalArchive/download?file_ID=40913&issue_ID=236SandileMotsasandilemotsa@gmail.com`NoSchool of Mathematics,University of Kwa-Zulu Natal, Private Bag X01, Scottsville 3209, South Africa`

`Isaac LareAnimasaunanizakph2007@gmail.com``YesDepartment of Mathematical Sciences, Federal University of Technology, Akure, Ondo State, Nigeria`