Mathematical Solution for Free Convection Flow of Brinkman Type Fluid in the Channel with the Effect of Accelerated Plate

Abstract

The main purpose of this research is to formulate the mathematical models and solution for the effect of accelerated plate on free convection flow in Brinkman type fluid through two vertical channels. Using the appropriate dimensionless variables, the dimensional governing energy and momentum equations are reduced to dimensionless equations subjected to the associated initial boundary conditions. The analytical solutions are obtained by using Laplace transform method. Dimensionless parameters are obtained through dimensionless processes such as Grashof number Gr, Acceleration plate parameter, R, Prandtl number Pr, Brinkman type fluid parameter and time, t. The mathematical findings for velocity and temperature are graphically plotted to investigate the influence of dimensionless variables on profiles. It is observed that fluid velocity increases with increasing of Gr and t whereas it decreases with increasing of , R and Pr. Besides that, it is found that temperature profiles decrease with a high value of Prandtl number, Pr while increase with high value of time, t. In order to validate the results, the obtained results in limiting cases are compared with the published results and also with numerical Gaver-Stehfest algorithm. Both comparisons show that the solution is to be in a mutual agreement.