A global approach for the time-dependent solution of natural convection in a tilted porous cavity

Abstract

Natural convection in an inclined cavity filled with saturated porous media has been investigated. A time-dependent solution using a spectral weighted residual method is determined. Preparing the governing equations by the substitution of the stream functions, we obtained a system of nonlinear ordinary differential equations. Integrating in time using the Runge-Kutta method of variable order the final system is determined. The study consisted of the investigation of the problem in the transient and unsteady modes. For each configuration, the solution is developed for different values of Rayleigh numbers and different inclination levels of the cavity. The high accuracy of the results with the reduced computational cost is well proved by the comparison with results determined using a finite element method that has shown an excellent agreement with our developed solution. This work is very efficient to understand from a physical insight the effect of the inclination parameters on the unsteady and transient mode of changes in the mechanisms of natural convection. The results provide a set of high-accurate data that can be used as a benchmark case for the time-dependent natural convection problems. As a result, the inclination effect of the cavity has clearly influenced the heat transfer process and the fluid flow. Therefore, the inclination can be considered as a control parameter for heat and fluid flow effectively.