Effect of constant heat flux at outer cylinder on stability of viscous flow in a narrow-gap annulus with radial temperature gradient

Abstract

In this paper, the stability of the Couette flow of a viscous incompressible fluid between two concentric rotating cylinders is studied in the presence of a radial temperature gradient, when the outer cylinder is maintained at a constant heat flux. The analytical solution of the eigen-value problem is obtained by using the trigonometric series method, when the gap between the cylinders is narrow. The numerical values of the critical wave number and critical Taylor number are computed from the obtained analytical expressions for the first, second and third approximations. It is found that the difference between the numerical values of the critical Taylor number corresponding to the second and third approximations are very small as compared to the difference between first and second approximations. The critical Taylor numbers obtained by the third approximation agree very well with the earlier results computed numerically by using the shooting method. This clearly indicates that for the better result one should obtain the numerical values by taking more approximations. Also, the amplitude of the radial velocity and the cell-pattern are shown on the graphs for different values of the ratio of the angular velocities.

Keywords: Radial temperature gradient, trigonometric series method, constant heat flux, Taylor number.