This paper reports a theoretical investigation of the boundary layer flow over a vertical flat plate embedded in a porous medium filled with water near the vicinity of its density maximum associated with the temperature of 3.98 degrees C at atmospheric pressure. The study aims at determining similarity solutions of the governing boundary layer equations for a class of problems where the variable wall temperature (VWT), variable heat flux (VHF), or variable heat transfer coefficient (VHTC), vary as power functions of the distance from the leading edge of the plate. The existence and uniqueness of the solutions are considered and studied. The analytical and numerical solutions of the similarity form of the boundary layer equations yield velocity and temperature profiles as well as values of the stream function at the edge of the boundary layer, the heat transfer coefficient and the temperature on the plate. (c) 2006 Elsevier Ltd. All rights reserved.