STABILITY OF VISCOUS FLOW IN A CURVED CHANNEL WITH RADIAL TEMPERATURE GRADIENT
Keywords:Stability, Radial temperature gradient, Galerkinâ€™s method, Curved channel, Narrow gap.
In this paper, the stability of Deanâ€™s problem in the presence of a radial temperature gradient is studied for narrow gap case. The analytical solution of the eigen value problem is obtained by using the Galerkinâ€™s method. The critical values of parameters and Î› are computed, where Â is wave number and Î› is a parameter determining the onset of stability from the obtained analytical expressions for the first, second and third approximations. It is found that the difference between the numerical values of critical Î› corresponding to the second and third approximations is very small as compared to the difference between first and second approximations. The critical values of Î› obtained by the third approximation agree very well with the earlier results computed numerically by using the finite difference method. This clearly indicates that for the better result one should obtain the numerical values by taking more terms in approximation. Also, the amplitude of the radial velocity and the cell-patterns are shown on the graphs for different values of the parameter M, which depends on difference of temperatures of outer cylinder to the inner one i.e. on (), whereÂ is the temperature of inner cylinder and Â is the temperature of outer cylinder.