Asish Mitra,



Convective Boundary Condition,Laminar Convection,Matlab,Numerical Simulation,Vertical Plate,


In the present numerical study, laminar convection over a vertical plate with convective boundary condition is presented.  It is found that the similarity solution is possible if the convective heat transfer associated with the hot fluid on the left side of the plate is proportional to x1/2, and the thermal expansion coefficient β is proportional to x-1. The numerical solutions thus obtained are analyzed for a range of values of the embedded parameters and for representative Prandtl numbers of 0.72, 1, 3 and 7.1. The results of the present simulation are then compared with the reports published in literature and find a good agreement.


1) Blasius, H., “Grenzschichten in Flussigkeiten mit kleiner reibung,” Z. Math Phys.,
vol. 56, pp. 1–37, 1908.
2) Weyl, H., “On the Differential Equations of the Simplest Boundary Layer Problem,” Ann. Math., vol. 43, pp. 381–407, 1942.

3) Magyari, E., “The Moving Plate Thermometer,” Int. J. Therm. Sci., 47, pp. 14361441, 2008.

4) Cortell, R., “Numerical Solutions of the Classical Blasius Flat-Plate Problem,” Appl. Math. Comput., vol. 170, pp. 706–710, 2005.

5) He, J. H., “A Simple Perturbation Approach to Blasius Equation,” Appl. Math. Comput., vol. 140, pp. 217–222, 2003.

6) Bataller, R. C., “Radiation Effects for the Blasius and Sakiadis Flows With a Convective Surface Boundary Condition,” Appl. Math. Comput., vol. 206, pp. 832–840, 2008.

7) Aziz, A., “A Similarity Solution for Laminar Thermal Boundary Layer Over a Flat Plate With a Convective Surface Boundary Condition,” Commun. Nonlinear Sci. Numer. Simul., vol. 14, pp. 1064–1068, 2009.

8) Makinde, O. D., and Sibanda, P., “Magnetohydrodynamic Mixed Convective Flow and Heat and Mass Transfer Past a Vertical Plate in a Porous Medium With Constant Wall Suction,” ASME J. Heat Transfer, vol. 130, pp. 112602, 2008.

9) Makinde, O. D., “Analysis of Non-Newtonian Reactive Flow in a Cylindrical Pipe,” ASME J. Appl. Mech., vol. 76, pp. 034502, 2009.

10) Cortell, R., “Similarity Solutions for Flow and Heat Transfer of a Quiescent Fluid Over a Nonlinearly Stretching Surface,” J. Mater. Process. Technol., pp. 176–183, 2008.

Autho(s): Asish Mitra View Download