Penetrative convection in couple-stress fluid via internal heat source/sink with the boundary effects

Abstract

The effect of internal heat source/sink, heat extracted/input through the boundary and stresses present in a fluid with rigid boundaries is studied by both linear and nonlinear analysis. Linear instability analyzed by normal mode technique and energy method used for nonlinear stability. The value of critical Rayleigh number is obtained in presence of couple-stress parameter when (1) heat is extracted from the lower boundary with internal heat source and (2) heat input through boundary with the internal heat sink, by using the Chebyshev-pseudospectral method. Variation of critical Rayleigh number with internal heat parameter at a different value of the couple-stress parameter is presented graphically.