Heat and Mass Transfer from a Convectively Heated Vertical Surface with Chemical Reaction and Internal Heat Generation
Abstract
A numerical approach has been adopted to investigate the steady chemically mixed convection boundary layer flow from the right face of a vertical plate of finite thickness. Cold fluid flowing over the right face of the plate contains a heat generation that decays exponentially with a dimensionless distance from the surface. The left face of the plate is in contact with a hot flowing fluid. The heating process on that side is characterized by a convective boundary condition that takes into account the conduction resistance of the plate as well as a possible contact resistance between the hot fluid and the left face of the plate. Using a pseudo similarity approach, the governing equations for the mixed convective flow over the right face of the plate are transformed into a set of coupled ordinary differential equations which give local similarity solutions. The effects of local Grashof numbers (defined to represent a mixed convection parameter), Prandtl number, and the internal heat generation parameter on the velocity, temperature and concentration profiles are illustrated and interpreted in physical terms.Keywords:
chemical reaction, natural convection, convective boundary condition, internal heat generation, buoyancy effectsReferences
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[6] Makinde O.D., On MHD boundary-layer flow and mass transfer past a vertical plate in a porous medium with constant heat flux, International Journal of Numerical Methods for Heat and Fluid Flow, 19(4): 546–554, 2009.
[7] Aziz A., Similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition, Communications in Nonlinear Science and Numerical Simulation, 14: 1064–1068, 2009.
[8] Bataller R.C., Radiation effects for the Blassius and Sakiadis flows with a convective surface boundary condition, Applied Mathematics and Computation, 206: 832–840, 2008.
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[10] Makinde O.D., Olanrewaju P.O., Buoyancy effects on thermal boundary layer over a vertical plate with a convective surface boundary condition, ASME Journal of Fluids Engineering, 132(4): 044502, 4 pages, 2010.
[11] Kasmani R.M., Sivasankaran S., Bhuvaniswari M., Siri Z., Effect of chemical reaction on convective heat transfer of boundary flow of nanofluid over a wedge with heat generation/absorption and suction, Journal of Applied Fluid Mechanics, 9(1): 379–388, 2016.
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[13] Ibrahim S.Y., Makinde O.D., Chemically reacting MHD boundary layer flow of heat and mass transfer over a moving vertical plate with suction, Scientific Research and Essays, 5(19): 2875–2882, 2010.
[14] Seini Y.I., Makinde O.D., MHD boundary layer flow due to exponential stretching surface with radiation and chemical reaction, Mathematical Problems in Engineering, Article ID: 163614, 7 pages, 2013.
[15] Arthur E.M., Seini Y.I., MHD thermal stagnation point flow towards a stretching porous surface, Chemical and Process Engineering Research, 33: 14–21, 2015.
[16] Etwire C.J., Seini Y.I., Azure D.A., MHD thermal boundary layer flow over a flat plate with internal heat generation, viscous dissipation and convective surface boundary conditions, International Journal of Emerging Technology and Advanced Engineering. 5(5): 335–342, 2015.
[17] Seini Y.I., Makinde O.D., Boundary layer flow near stagnation-points on a vertical surface with slip in the presence of transverse magnetic field, International Journal of Numerical Methods and Fluid Flow, 24(3): 643–653, 2014.
[18] Rajput U.S., Shareef M., Unsteady MHD flow past impulsively started vertical plate in porous medium with heat source and chemical reaction, International Journal of Chemical Science, 15(3):154, 2017.
[19] Veera Krishna M., Gangadhar Reddy M., MHD free convective boundary layer flow through porous medium past a moving vertical plate with heat source and chemical reaction, Materials Today: Proceedings, 5: 91–98, 2018.
[20] Ridwan Zahed N.M., Yeakub Ali Md., Jashim Uddin Md., Nasir Uddin M., Possible similarity cases for internal heat generation, thermal radiation and free convection of unsteady boundary layer flow over a vertical plate, Applied and Computational Mathematics, 6(1): 60–67, 2017.
[21] Heck A., Introduction to Maple, 3rd ed., Springer-Verlag, New York, 2003.
[22] Aziz A., Heat Conduction with Maple, R.T. Edwards, Inc., Philadelphia, 2006.
