The objective of the paper is to study the Rayleigh-Bѐnard convection in second order fluid by replacing the classical Fourier heat law by non-classical Maxwell-Cattaneo law using Galerkin technique. The eigen value of the problem is obtained using the general boundary conditions on velocity and third type of boundary conditions on temperature. A linear stability analysis is performed. The influence of various parameters on the onset of convection has been analyzed. The classical Fourier flux law over predicts the critical Rayleigh number compared to that predicted by the non-classical law. The present non-classical Maxwell-Cattaneo heat flux law involves a wave type heat transport (SECOND SOUND) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. It is found that the results are noteworthy at short times and the critical eigen values are less than the classical ones. Over stability is the preferred mode of convection.
The Bulletin of Society for Mathematical Services and Standards (Volume 2)
S. S. Nagouda and S. Pranesh, "Rayleigh-Bѐnard Convection in a Second-Order Fluid with Maxwell-Cattaneo Law", The Bulletin of Society for Mathematical Services and Standards, Vol. 2, pp. 24-32, 2012