Analytical Study of The Nonlinear Fluid Flow Equation In The Porous Media With The Considering of The Forchheimer Term and The Convection Heat Transfer Coefficient Evaluation

Document Type : full paper

Authors

• Mohammadreza Shahnazari ¹
• Mir Hedayet Musavi ²

¹ Mechanical Faculty , K.N.T University of technology

² M.S. Student, Mechanical Faculty of K.N.Toosi University of Technology,Tehran, Iran

Abstract

Fluid developed flow in a channel filled with porous medium is known as one of the classical problems in the field of fluid mechanics. The Darcy model, Brinkman and Brinkman Forchheimer are well-known models for describing this flow. Darcy's equation is the most widely used equation based on the description of frictional force between fluid and porous solid network. In the Brinkman equation, the term of viscosity similar to that of Laplacian in the Navier Stokes equation is added to the Darcy equation. Finally, the Forchheimer term expresses a quadrature drag term due to the solid effect on the fluid. Adding the Forchheimer term to the Brinkman equation leads to the nonlinearity of the equation. In this paper, in addition to providing an analytical solution for this equation, the convection heat transfer coefficient is valuated. The effect of all parameters on the Nusselt number is estimated.
The results show that with the increase of the Forchheimer coefficient, the Nusselt number decreases; this decreases in smaller Darcy numbers is suddenly, and the Nusselt number converges to its asymptotic values. While increasing the Darcy number, the trend is closer to a linear trend.

Keywords

• Porous Media
• Brinkman- Forchheimer
• Developed Fluid Flow
• Fluid Flow Instability

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