Bénard–Taylor Convection in Temperature-Dependent Variable Viscosity Newtonian Liquids with Internal Heat Source

This study demonstrates a theoretical investigation of linear and weakly non-linear Rayleigh–Bénard convection problem with rotation, variable viscosity and internal heat source. The linear stability analysis shows that an increase in the strength of rotation is to stabilize the system but an increasing internal heat generation and the thermorheological parameter destabilizes the system. The generalized Lorenz model derived for the problem is essentially fifth-order autonomous system of first ordered coupled differential equation with its coefficients depending on internal Rayleigh number, thermorheological parameter and Taylor number. The result on the parameter influence on critical Rayleigh number explains their influence on the Nusselt number as well. Quantification of heat transfer is made possible due to the numerical solution of the autonomous system. It is found that the effect of increasing the strength of rotation is found to have diminished heat transport but in the case of increasing internal Rayleigh number and thermorheological parameter enhances the same. © 2020, Springer Nature India Private Limited.