• D. M. Auwal Department of Mathematics and Statistics, Umaru Musa Yar’adua University, Katsina-Nigeria.
  • M. M. Gafai Department of Mathematics and Statistics, Umaru Musa Yar’adua University, Katsina-Nigeria.
  • A. A. Garba Department of Electrical and Electronics, Katsina State Institute of Technology and Management, PMB2101, Katsina State, Nigeria.
  • Mustapha Shehu Department of Physics, Federal University Dutse, Jigawa state, Nigeria
Keywords: Heat Transfer, Similarity variable, Prandtl number, Dimensionless velocity, Stream function, Kinematics viscosity


In this study, we investigate the laminar boundary layer flow in two dimensions, steadiness, and incompressibility around a moving vertical flat plate in a uniform free stream of fluid with a convective surface boundary condition. The similarity transformation technique has been applied to convert the governing nonlinear partial differential equation into two nonlinear ordinary differential equations. By combining the finite difference method with the shooting technique, the problem is solved numerically. We present a tabular and graphical representation of the variation in dimensionless temperature and fluid-solid interface characteristics for various values of the Prandtl number. As a special case of the problem, a comparison between the current result and the previously published result demonstrates a good agreement.


Ahmad R., and Ahmed W. K. (2014). Numerical Study of Heat and Mass Transfer MHD Viscous Flow Over a Moving Wedge in the Presence of Viscous Dissipation and Heat Source/Sink with Convective Boundary Condition. Heat Trans Asian Res, 43(1): 17–38. DOI 10.1002/htj.21063 DOI: https://doi.org/10.1002/htj.21063

Aziz, A. (2009). A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition. Commum. Nonlinear Science Numerical Simulation, 14: 1064-1068. DOI: https://doi.org/10.1016/j.cnsns.2008.05.003

Blasius, H. (1908). “Grenzschichten in Flussigkeiten mitkleiner reibung”, Z. Mathematical physics, 56:1-37.

Basant K. J., Isah B.Y., and Uwanta I.J., (2016). Combined effect of suction/injection on MHD free-convection flow in a vertical channel with thermal radiation. Ain Shams Engineering Journal. Volume 9, Issue 4, PP 1069-1088. DOI: https://doi.org/10.1016/j.asej.2016.06.001

Desale S. and Pradhan V. H. (2015). Numerical Solution of Boundary Layer Flow Equation with Viscous Dissipation Effect Along a Flat Plate with Variable Temperature. Procedia Engineering Volume 127 PP 846-85 DOI: https://doi.org/10.1016/j.proeng.2015.11.421

Fox-Kemper, B., & Ferrari, R. (2009). An eddifying Parsons model. Journal of physical oceanography, 39(12), 3216-3227. DOI: https://doi.org/10.1175/2009JPO4104.1

Ghorbani, S., Amanifard, N.H., Deylami, H.M. (2015). An integral solution for the Blasius Equation. Computational Research Progress in Applied Science and Engineering. Vol 01(03), PP 93-102.

Hussein E. and Hani B. (2018). Boundary-Layer Theory of Fluid Flow past a Flat-Plate: Numerical Solution using MATLAB. International Journal of Computer Applications, 180(18): 0975 – 8887. DOI: https://doi.org/10.5120/ijca2018916374

Makinde, O. D. (2011). Similarity solution for natural convection from a moving vertical plate with internal heat generation and a convective boundary condition,” Thermal Science, 15(1): 137-143. DOI: https://doi.org/10.2298/TSCI11S1137M

Makinde, O. D. (2005). Free-convection flow with thermal radiation and mass transfer past a moving vertical porous plate. International communications in heat and mass transfer, 32: 1411-1419. DOI: https://doi.org/10.1016/j.icheatmasstransfer.2005.07.005

Makinde, O. D. and Ogulu, A. (2008). The effect of thermal radiation on the heat and mass transfer flow of a variable viscosity fluid past a vertical porous plate permeated by a transverse magnetic field, Chemical Engineering Communications, 12: 1575 – 1584. DOI: https://doi.org/10.1080/00986440802115549

Omokhuale E. and Dange M. S. (2003). Heat absorption effect on magnetohydrodynamic (mhd) flow of jeffery fluid in an infinite vertical plate. FUDMA Journal of Science (FJS), Vol 7(2) pp 45-51 DOI: https://doi.org/10.33003/fjs-2023-0702-1200

Olanrewaju, P. O., Arulogun, O. T. and Adebimpe, K. (2012). Internal heat generation effect on thermal boundary layer with a convective surface boundary condition, American journal of fluid Dynamics, 2(1): 1-4. DOI: https://doi.org/10.5923/j.ajfd.20120201.01

Olanrewaju, P.O. (2012). Study the similarity solution for natural convection from a moving vertical plate with internal heat generation and convective boundary condition in the presence of thermal radiation and viscous dissipation. Rep Opinion, 4(8): 68-76.

Pantokratos A. (2005). Effect of viscous dissipation in natural convection along a heated vertical plate. Applied Mathematical Modelling 29(6):553-564 DOI: 10.1016/j.apm.2004.10.007 DOI: https://doi.org/10.1016/j.apm.2004.10.007

Prandtl, L. (1904). Verhandlung des III Internationalen MathematikerKongresses (Heidelberg, 1904), pp. 484-491.

Parand, K., Denghan, M., and Pirkhedri A., (2009). Sinc collection method for solving the Blasius equation. Physics latters A, 373: 4060-4065. DOI: https://doi.org/10.1016/j.physleta.2009.09.005

Rafeal, C.B., (2010). Numerical comparison of Blasius and Sakiadis flow, Matematika, 26(2): 187-197.

Sakiadis, B. C. (1961). Boundary-layer Behaviour on Continuous Solid Surfaces; Boundary layer Equations for 2-dimensional and Axisymmetric Flow. Advance International Chemical Engineering Journal, 7: 26–28. DOI: https://doi.org/10.1002/aic.690070108

How to Cite
Auwal D. M., Gafai M. M., Garba A. A., & Shehu M. (2023). A NUMERICAL APPROACH FOR THE STUDY OF HEAT GENERATION IN THE PRESENCE OF THERMAL BOUNDARY LAYER FOR A FLAT PLATE. FUDMA JOURNAL OF SCIENCES, 7(6), 261- 266. https://doi.org/10.33003/fjs-2023-0706-2086