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多孔介质期刊
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ISSN 打印: 1091-028X
ISSN 在线: 1934-0508

多孔介质期刊

DOI: 10.1615/JPorMedia.v20.i11.80
pages 1043-1058

EFFECT OF CHEMICAL REACTION ON MIXED CONVECTIVE FLOW IN A VERTICAL CHANNEL CONTAINING POROUS AND FLUID LAYERS

J. Prathap Kumar
Department of Mathematics, Gulbarga University, Gulbarga, Karnataka, India
Jawali C. Umavathi
Department of Mathematics, Gulbarga University, Kalaburgi-585106, Karnataka, India
Shreeedevi Kalyan
Department of Mathematics, Gulbarga University, Gulbarga, Karnataka, India

ABSTRACT

We analyze the free convection flow through a vertical channel filled with a composite porous medium in the presence of a first-order chemical reaction. The flow is modeled using a Darcy–Lapwood–Brinkman equation model. The viscous and Darcy dissipation terms are also included in the energy equation. Analytical and numerical solutions for the governing coupled nonlinear ordinary differential equations are obtained by perturbation series method and by finite difference method, respectively. Separate solutions are matched at the interface by using suitable matching conditions. The approximate solutions have been obtained for velocity, temperature, and concentration distributions in the two regions of the composite channel. The effects of various parameters, such as thermal Grashof number, mass Grashof number, porous parameter, viscosity ratio, width ratio, conductivity ratio, and chemical reaction parameter, on the flow field are presented graphically and discussed. The volumetric flow rate, total species rate, total heat rate added to the flow, and Nusselt number are also evaluated. It is found that the thermal Grashof number and mass Grashof number enhance the flow in both regions in the presence or in the absence of a first-order chemical reaction. It is also found that the Nusselt number at the left wall is enhanced and at the right wall is reduced for large values of mass Grashof number. The values obtained by finite difference method are justified by comparing with the values obtained by perturbation method, and these values agree to the order of 10-4 in the absence of Brinkman number.


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