keywords: Chemical reaction, heat, irregular channel, mass transfer, radiation
An analysis of the effects of thermal-radiation and chemical reaction on free convective heat and mass transfer flow through an irregular (wavy) vertical channel (made up of a finitely long wavy wall at one end and a parallel flat wall at the other) with constant volumetric heat absorption/generation is carried out. The Rosseland approximation is used to describe radiative heat transfer in the limit of optically thick fluids. The non-dimensional governing equations which comprises of continuity, momentum, energy and species equations were simplified using perturbation method and hence written in terms of zeroth and first order set of coupled differential equations. The solutions of these sets of coupled differential equations were obtained for velocity, temperature, concentration and pressure drop of the fluid, using Adomian decomposition method. The expressions for the fluid variables and those of some characteristics of heat and mass transfer namely Skin friction, Nusselt number and Sherwood number obtained from fluid variables are evaluated numerically and presented graphically for various parameters involved in the problem. By carrying out comparisons with the available data in the literature, our numerical results were validated and excellent agreements were obtained. It is noticed among others, that an increase in the radiation and chemical reaction parameters leads to a decrease in the fluid velocity across the entire width of the channel. The temperature decreases with an increase in the radiation parameter, while an increase in the temperature is observed with an increase in the chemical reaction parameter.
Abubakar JU 2014. Natural convective flow and heat transfer in a viscous incompressible fluid with slip confined within spirally enhanced channel, Ph.D. thesis, University of Ilorin, Nigeria. Adesanya SO 2013. Thermal stability analysis of reactive hydromagnetic third-grade fluid through a channel with convective cooling. J. Nig. Math. Soc., 32: 61-72. Chen W & Lu Z 2004. An algorithm for adomian decomposition method. Appl. Maths. & Computa., 15:221-235. Dada MS & Disu AB 2015. Heat transfer with radiation and temperature dependent heat source in MHD free convection flow in a porous medium between two vertical wavy walls.J. Nig. Math. Soc., http://dx.doi.org/10.1016/j.jnnms 2014.12.001. Das UN & Ahmed N 1992. Free convective MHD flow and heat transfer in a viscous incompressible fluidconfined between a long vertical wavy wall and a parallel at wall. Indian J. Pure Math., 23(4): 295-304. Davika B, SatyaNarayana PV & Venkataramana S 2013. Chemical reaction effects on MHD free convection flow in an irregular channel with porous medium.Int. J. Math. Archive, 4(4): 282-295. Fasogbon PF 2006. Bouyancy driven flow in a rough channel. J. Applic. Functional Differential Equation (JAFDE), 1(1): 45-58. Fasogbon PF & Omolehin JO 2008. Radiation effect on natural convection in spirally enhanced channel. leJEMTA 3(1): 1-28. Fasogbon PF 2010. Analytical studies of heat and mass transfer by free convection in a two dimensional irregular channel. Int. J. Appl. Math. & Mech., 6(4): 17-37. Gbadeyan JA, Olanrewaju MA & Olanrewaju PO 2011. Boundary layer flow of a Nano-fluid past a stretching sheet with a convective boundary conditionin the presence of magnetic field and thermal radiation.Australian J.Basic & Appl. Sci., 5(9): 1322-1334. Gbadeyan JA and Dada MS 2013. On the influence of radiation and heat transfer on anunsteady MHD non-Newtonian fluid flow with slip in a porous medium. J.Maths. Res., 5(3): 40-50. Hayat T, Abass Z, Pop I & Asghar S 2010. Effects of radiation and magnetic field on the mixed convection stagnation-point flow over a vertical stretching sheet in a porous medium. Int. J. Heat & Mass Transfer, 53: 466-474. Kumar H 2011. Heat transfer with radiation and temperature dependent heat source in MHD free convection flow confined between two vertical wavy walls.Int. J. Appl. Math. & Mech., 7(2): 77-103. Loganathan P, Iranian D & Ganesan P 2011. Effect of chemical reaction on unsteady free convective and mass transfer flow past a vertical plate with variable viscosity and thermal conductivity.Eur. J. Scientific Res., 59(31): 403-416. Olanrewaju PO & Gbadeyan JA 2011. Effect of Soret, Dufour, chemical reaction, thermal radiation and volumetric heat generation/absorption on mixed convection stagnation-point flow on an iso-thermal vertical plate in porous media.Pacific J. Sci. & Techn., 12(20): 234-245. Olanrewaju PO, Adeniyan A & Sanmi FA 2013. Soret and Dufour effects on hydromagnetic free convection flow with heat and mass transfer past a porous plate in the presence of chemical reaction and thermal radiation. Far East J. Appl. Maths., 80(1): 41-66. Oyekunle TL 2015. Thermal-diffusion, Diffusion-thermo and Radiation effects on chemically reacting magneto-hydrodynamics flow of heat and mass transfer within an irregular channel, Ph.D. thesis, University of Ilorin, Nigeria. Rajasekhar NS, Prasad PMV & PrasadaRao DRV 2013. Effect of chemical reaction and radiation absorption on unsteady convective heat and mass transfer flow of a viscouselectrically conducting fluid in a vertical wavy channel with traveling thermal waves and Hall effects.Int. J. Engr. Res. & Applic., 3(1): 1733-1747. Sudershan Reddy G, Ramana Reddy GV & Jayarami Reddy K 2012. Radiation andchemical reaction effects on free convection MHD flow through a porous medium bounded by vertical surface.Advances in Appl. Sci. Res., 3(3): 1603-1610. Srihari K & Avinsh K 2014. Effect of radiation on unsteady MHD flow of a chemically reacting fluid past a hot vertical porous plate.A Finite Difference Approach, 5(1): 50-69. Shateyi S, Motsa SS & Sibanda P 2010. The effect of thermal radiation, Hall currents, Soret and Dufour on MHD flow by mixed convection over a vertical surface in a porous media.Mathematical Problems in Engineering, Article ID 62747:20 pages. Vajravelu K & Sastri KS 1978. Free convective heat transfer in a viscous incompressible fluid confined between a long vertical wavy wall and a parallel at wall. J. Fluid Mech., 86(2): 365-383.