Homotopy analysis method for predicting multiple solutions in the channel flow with stability analysis

The present theoretical investigation covers a study of finding the multiple solutions of a Jeffery-Hamel flow and heat transfer under the influence of magnetic field. An analytical technique (Homotopy Analysis Method) is applied to solve the cylindrical form of governing equations after getting non-dimensional system using suitable transformation. It is noticed that dual solutions exist only for convergent channel case. Critical values of channel angle (αc) are obtained which reveals the existence domain (αc < α < 0) for multiple solutions in convergent channel flow. Stability analysis is also performed by constructing eigenvalue problem to predict the physically stable solution. The minimum positive eigenvalue justifies the fact that the growth of disturbances given to the solution decays with time. The effect of various pertinent physical parameters is shown graphically on velocity, temperature, skin friction coefficient and Nusselt number.