Analytical approximate solution of the cooling problem by Adomian decomposition method

The Adomian decomposition method (ADM) can provide analytical approximation or approximated solution to a rather wide class of nonlinear (and stochastic) equations without linearization, perturbation, closure approximation, or discretization methods. In the present work, ADM is employed to solve the momentum and energy equations for laminar boundary layer flow over flat plate at zero incidences with neglecting the frictional heating. A trial and error strategy has been used to obtain the constant coefficient in the approximated solution. ADM provides an analytical solution in the form of an infinite power series. The effect of Adomian polynomial terms is considered and shows that the accuracy of results is increased with the increasing of Adomian polynomial terms. The velocity and thermal profiles on the boundary layer are calculated. Also the effect of the Prandtl number on the thermal boundary layer is obtained. Results show ADM can solve the nonlinear differential equations with negligible error compared to the exact solution.