Steady-state conjugate heat transfer study of a slab and a fluid is carried out for a two-dimensional laminar incompressible wall jet over a backward-facing step. Unsteady stream function-vorticity formulation is used to solve the governing equation in the fluid region. An explicit expression has been derived for the conjugate interface boundary. The energy equation in the fluid, interface boundary and the conduction equation in the solid are solved simultaneously. The conjugate heat transfer characteristics, Nusselt number are studied with flow property (Re), fluid property (Pr), and solid to fluid conductivity ratio $(k)$. Average Nusselt number is compared with that of the nonconjugate case. As $k$ is increased, average Nusselt number is increased, asymptotically approaching the non-conjugate value.