Research Letters

Effects of internal heat generation, thermal radiation and buoyancy force on a boundary layer over a vertical plate with a convective surface boundary condition

Philip O. Olanrewaju, Jacob A. Gbadeyan, Tasawar Hayat, Awatif A. Hendi
South African Journal of Science | Vol 107, No 9/10 | a476 | DOI: https://doi.org/10.4102/sajs.v107i9/10.476 | © 2011 Philip O. Olanrewaju, Jacob A. Gbadeyan, Tasawar Hayat, Awatif A. Hendi | This work is licensed under CC Attribution 4.0
Submitted: 14 October 2010 | Published: 07 September 2011

About the author(s)

Philip O. Olanrewaju, Department of Mathematics, Covenant University, Nigeria
Jacob A. Gbadeyan, Department of Mathematics, Covenant University, Nigeria
Tasawar Hayat, Department of Mathematics, Quaid-I-Azam University, Pakistan
Awatif A. Hendi, Department of Physics, Faculty of Science, King Saud University, Saudi Arabia


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Abstract

In this paper we analyse the effects of internal heat generation, thermal radiation and buoyancy force on the laminar boundary layer about a vertical plate in a uniform stream of fluid under a convective surface boundary condition. In the analysis, we assumed that the left surface of the plate is in contact with a hot fluid whilst a stream of cold fluid flows steadily over the right surface; the heat source decays exponentially outwards from the surface of the plate. The similarity variable method was applied to the steady state governing non-linear partial differential equations, which were transformed into a set of coupled non-linear ordinary differential equations and were solved numerically by applying a shooting iteration technique together with a sixth-order Runge–Kutta integration scheme for better accuracy. The effects of the Prandtl number, the local Biot number, the internal heat generation parameter, thermal radiation and the local Grashof number on the velocity and temperature profiles are illustrated and interpreted in physical terms. A comparison with previously published results on similar special cases showed excellent agreement.

Keywords

thermal radiation; buoyancy force; internal heat generation; vertical plate; Biot number; boundary layer

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