On an equation arising in natural convection boundary layer flow in a porous medium

A generalization of a boundary value problem treated previously by Magyari et al. (ZAMP 53:782-793, 2002a; Transp Porous Medium 46:91-102, 2002b), Zhang (Math Anal Appl 417:361-375, 2014) and Paullet (Appl Math E Notes 14:123-126, 2014) for a prescribed wall temperature and by Zhang (Appl Math Comput 339:367-373, 2018) for a prescribed wall heat flux is considered. The problem involves a parameter lambda and an exponent p. Numerical solutions are obtained for representative values of lambda and p, a feature of which is the existence of critical values lambda(c) of lambda with two solution branches in lambda > lambda(c), with lambda(c) dependent on p. Asymptotic solutions for large lambda and large p are derived for both types of boundary condition. For large lambda, the nature of the solution is essentially different on upper and on the lower branches with similar feature being seen in the behaviour for p large.