Effects of throughflow and internal heat generation on the onset of convection in a fluid layer

Abstract

The throughflow and internal heat generation effects on the onset of convection in an infinite horizontal fluid layer are investigated. The boundaries are considered to be rigid (however permeable) and perfectly conducting. The resulting eigenvalue problem is solved by using the Galerkin method, and the effects of various parameters in the stability results are analyzed. The results indicate that the stability of the system is significantly affected by both throughflow and internal heat generation in the fluid layer. The Prandtl number comes into play due to the presence of throughflow and it has a profound effect on the stability of the system. It is found that, in the presence of internal heating, throughflow in one direction supresses convection while throughflow in the other direction encourages it.