Heat transfer near the stagnation point of an unsteady three-dimensional flow

In this paper, the unsteady laminar three-dimensional flow of an incompressible viscous fluid in the neighbourhood of a stagnation point is studied. The magnetic field is applied normal to the surface and the effects of viscous dissipation and Ohmic heating are taken into account. The unsteadiness in the flow is caused by the external free stream varying arbitrarily with time. The governing equations are solved both analytically and numerically. An approximate analytical solution has been obtained for flow and heat transfer in the form of series solution using Homotopy Analysis Method while the numerical solutions are computed using the Runge–Kutta–Fehlberg Method with a shooting technique. The influence of various parameters such as the viscous dissipation, unsteadiness, ratio of the velocity gradient and magnetic field effects on flow and heat transfer parameters are studied. A detailed error analysis is done to compute the averaged square residual errors for velocity and temperature. The optimal values of the convergence control parameter are computed for the flow which is used for obtaining all the other results presented.