An Analytic Approach for Some Equations Arising in Heat Transfer in a Quiescent Medium with Exponential Nonlinearities

In this article, the homotopy analysis method (HAM) has been applied to obtain the analytical approach for obtaining approximate series solutions to some initial value problems arising in heat transfer in a quiescent medium. This method does not need linearization, weak nonlinearity assumptions or perturbation theory. The validity of this method has successfully been accomplished by applying it to some examples. The results show that the method is very effective and convenient for solving such equations.