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Computational Thermal Sciences: An International Journal
ESCI SJR: 0.249 SNIP: 0.434 CiteScore™: 1.4

ISSN Imprimer: 1940-2503
ISSN En ligne: 1940-2554

Computational Thermal Sciences: An International Journal

DOI: 10.1615/ComputThermalScien.2017019221
pages 447-465

MIXED CONVECTIVE HEAT TRANSFER OF IMMISCIBLE FLUIDS IN A VERTICAL CHANNEL WITH BOUNDARY CONDITIONS OF THE THIRD KIND

J. Prathap Kumar
Department of Mathematics, Gulbarga University, Gulbarga, Karnataka, India
Jawali C. Umavathi
Department of Mathematics, Gulbarga University, Kalaburgi-585106, Karnataka, India
Ali J. Chamkha
Mechanical Engineering Department, Prince Sultan Endowment for Energy and Environment, Prince Mohammad Bin Fahd University, Al-Khobar 31952, Saudi Arabia; RAK Research and Innovation Center, American University of Ras Al Khaimah, P.O. Box 10021, Ras Al Khaimah, United Arab Emirates
Y. Ramarao
Department of Mathematics, Gulbarga University, Gulbarga-585 106, Karnataka, India

RÉSUMÉ

The effect of viscous dissipation and boundary conditions of the third kind on fully developed mixed convection for the laminar flow in a parallel plate vertical channel filled with two immiscible viscous fluids is studied analytically. The plate exchanges heat with an external fluid. Both conditions of equal and different reference temperatures of external fluid are considered. Separate solutions are matched at the interface using suitable matching conditions. First, the simple cases of the negligible Brinkman or negligible Grashof numbers are solved. Then, the combined effects of buoyancy forces and viscous dissipation are analyzed by the perturbation series method (PM), valid for small values of the perturbation parameter, and by the differential transform method (DTM), valid for all values of perturbation parameter. Numerical results are presented graphically for the distribution of velocity and temperature fields for varying physical parameters, such as the mixed convection parameter, perturbation parameter, viscosity ratio, width ratio, conductivity ratio, and Biot numbers. The effect of these parameters on the Nusselt number at the walls is also presented graphically. It is found that the mixed convection parameter and perturbation parameter enhance the flow field; whereas, the viscosity ratio, width ratio, and conductivity ratio suppress the flow field. It is also found that both PM and DTM solutions agree very well for small values of the perturbation parameter.


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