Journal
TRANSPORT IN POROUS MEDIA
Volume 95, Issue 1, Pages 111-131Publisher
SPRINGER
DOI: 10.1007/s11242-012-0035-8
Keywords
Mixed convection; Non-Darcy model; Perturbation method; Runge-kutta shooting method; Biot numbers
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Funding
- University Grants Commission, New Delhi, India
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Combined free and forced convection flow in a parallel plate vertical channel filled with porous matrix is analyzed in the fully developed region with boundary conditions of third kind. The flow is modeled using the Brinkman-Forchheimer-extended Darcy equations. The plates exchange heat with an external fluid. Both conditions of equal and different reference temperatures of the external fluid are considered. Governing equations are solved numerically by shooting technique that uses classical explicit Runge-Kutta scheme and Newton-Raphson method as a correction scheme and analytically using perturbation series method for Darcy model. The velocity field, the temperature field and Nusselt numbers are obtained for governing parameters such as porous parameter, inertia term and perturbation parameter for equal and unequal Biot numbers and are displayed graphically. The dimensionless mean velocity and bulk temperature are also determined. It is found that the numerical solutions agree for small values of the perturbation parameter in the absence of the inertial forces.
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