On singular solutions of a magnetohydrodynamic nonlinear boundary layer equation

Abstract

This paper concerns the singular solutions of the equation ƒ‴ + ꃃ″ - βƒ′2 = 0 where β < 0 and κ = 0 or 1. This equation arises when modelling heat transfer past a vertical flat plate embedded in a saturated porous medium with an applied magnetic field. After suitable normalization, ƒ′ represents the velocity parallel to the surface or the non-dimensional fluid temperature. Our interest is in solutions which develop a singularity at some point (the blow-up point). In particular, we shall examine in detail the behavior of ƒ near the blow-up point.