Investigation of Nonlinear Fluid Flow Equation in a Porous Media and Evaluation of Convection Heat Transfer Coefficient, by Taking the Forchheimer Term into Account

The steady-state fully developed fluid flow in a channel filled with porous media is known as one of the classical issues in the field of fluid mechanics. Darcy's, Brinkman's and Brinkman-Forchheimer's laws are well-known models for describing this kind of fluid. Darcy equation, as the most useful equations, is based on the description of fluid friction and porous matrix. In Brinkman equation, the term of viscosity similar to that of Laplacian in the Navier Stokes equation is added to the Darcy equation, and finally, Forchheimer term is able to account for second-order drag term due to the impact of solid in the fluid. Adding the Forchheimer term to the Darcy-Brinkman equation causes the nonlinearity of the equation. In this research, an analytical solution for several flow models in a porous medium channel is provided. The simplicity of use of the velocity profile, particularly for the study of the heat transfer problem and the exergy analysis of flow, is the most essential feature of the suggested approach. In addition to the analytical response of this equation, the convective heat transfer coefficient is estimated. The impacts of all parameters on the the Nusselt number are evaluated. The findings reveal that when the Forchheimer coefficient rises, the Nusselt number falls; this downward trend is sharp Delivered by Ingenta in smaller Darcy numbers; hence Nusselt number tends to its asymptotic values. While, as Darcy number increase, the downtrend is getting close to a linear one.

Automated summary

The study focuses on the steady-state fully developed fluid flow in a channel filled with porous media, utilizing well-known models such as Darcy's, Brinkman's, and Brinkman-Forchheimer's laws. The analytical solution for flow models and estimation of convective heat transfer coefficient are provided, along with evaluation of the impacts of parameters on the Nusselt number. Results show a downward trend in Nusselt number as Forchheimer coefficient increases, reaching asymptotic values at smaller Darcy numbers.