The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water at 4 degrees C (maximum density) when the surface heat flux varies as x(m) and the velocity outside the boundary layer varies as x((1+2m)/2), where x measures the distance from the leading edge, is discussed. Assisting and opposing flows are considered with numerical solutions of the governing equations being obtained for general values of the flow parameters. For opposing flows, there are dual solutions when the mixed convection parameter; is greater than some critical value lambda(c) (dependent on the power-law index m). For assisting flows, solutions are possible for all values of lambda. A lower bound on m is found, m > -1 being required for solutions. The nature of the critical point lambda(c) is considered as well as various limiting forms; the forced convection limit (lambda = 0), the free convection limit (lambda -> infinity) and the limits as m -> infinity and as m -> -1.