Analytical Analysis of Effects of Buoyancy, Internal Heat Generation, Magnetic Field, and Thermal Radiation on a Boundary Layer over a Vertical Plate with a Convective Surface Boundary Condition

Solomon Bati Kejela,Mitiku Daba Firdi,Ram N Quintanilla

doi:10.1155/2020/8890510

Solomon Bati Kejela, Mitiku Daba Firdi + Show 1 more

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https://doi.org/10.1155/2020/8890510

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Abstract

In this paper, the effects of magnetic field, thermal radiation, buoyancy force, and internal heat generation on the laminar boundary layer flow about a vertical plate in the presence of a convective surface boundary condition have been investigated. In the analysis, it is assumed that the left surface of the plate is in contact with a hot fluid, whereas a stream of cold fluid flows steadily over the right surface, and the heat source decays exponentially outwards from the surface of the plate. The governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations with the help of similarity transformation which were solved analytically by applying the optimal homotopy asymptotic method. The variations of fluid velocity and surface temperature for different values of the Grashof number, magnetic parameter, Prandtl number, internal heat generation parameter, Biot number, and radiation absorption parameter are tabulated, graphed, and interpreted in physical terms. A comparison with previously published results on similar special cases of the problem shows an excellent agreement.

Highlights

In physics and fluid mechanics, a Blasius boundary layer defines the steady two-dimensional laminar boundary layer that forms on a semi-infinite plate which is apprehended parallel to a constant unidirectional flow
Blasius obtained a laminar boundary layer equation (Blasius equation) which is a third-order nonlinear ODE. e notion of the similarity solution formulated by Blasius for the boundary layer flow of a Newtonian fluid over a flat surface forms the foundation for numerous consequent studies
Analytical computations have been carried out for different embedded parameters in the flow model controlling the fluid dynamics in the flow regime. e influence of different parameters in the flow model on the velocity and temperature profiles has been analyzed for different values of Prandtl number (Pr), internal heat generation (λ), magnetic parameter (M), Biot number (Bi), radiation parameter (Ra), and Grashof number (Gr), and the results have been displayed in figures and tables for the selected parameters

Summary

Introduction

In physics and fluid mechanics, a Blasius boundary layer defines the steady two-dimensional laminar boundary layer that forms on a semi-infinite plate which is apprehended parallel to a constant unidirectional flow. Blasius used the similarity transformation method in the governing equation to diminish the Navier–Stoke equation for the viscous incompressible steady laminar flow over a solid boundary from the PDE to the ODE. E notion of the similarity solution formulated by Blasius for the boundary layer flow of a Newtonian fluid over a flat surface forms the foundation for numerous consequent studies. Later, it has been extended by various researchers [3,4,5,6] to explore the similar solutions for thermal boundary layer flows over a flat plate under altered flow configurations and boundary conditions. For similarity boundary-layer flows, velocity profiles are alike, but this kind of similarity is missing for nonsimilarity flows [8,9,10,11]

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