Similarity solutions for a boundary layer problem in porous media

We consider heat transfer from a surface embedded in an unbounded porous me dium, saturated with a fluid at rest. A thermal boundary-layer approximatio n, based on the assumption that convection takes place in a thin layer arou nd the heating surface, is done. The use of boundary laver technics show th at we can find similarity solutions by solving a one-dimensional boundary v alue problem, involving a third-order nonlinear differential equation depen ding on a parameter. We prove existence and uniqueness results for some val ues of the parameter, non-existence for the other ones, and when it is poss ible, we construct explicit solutions. (C) 2000 Academie des sciences/Editi ons scientifiques et medicales Elsevier SAS.