The present analysis is presented to predict the heat transfer rate between two natural convection systems at different temperatures separated by a vertical plate, where the effects of ope-dimensional heat conduction along the plate and transverse heat conduction will be discussed. Thus, the countercurrent boundary layer flow is formed on the two sides. Governing boundary layer equations with their corresponding boundary conditions for these two natural convection systems are cast into dimensionless forms by using the non-similarity transformation. The resulting system of equations is solved by using the finite difference approximation for the heat conduction equation and the local non-similarity method in conjunction with the Nachtsheim-Swigert iteration scheme for boundary layer equations. Excellent agreement between the present results predicted by using the approximation of heat conduction along the plate and reliable experimental data is obtained. This implies that the present analysis provides accurate prediction for such problems.