This paper presents a numerical analysis of the conjugate heat exchange inside a square enclosure full of a copper-water nanofluid. The enclosure also contains a heat-generating solid triangular block (a source of heat) at the center. While the horizontal walls of the enclosure are viewed as adiabatic, its perpendicular walls are operated at a consistently low temperature. The second order upwind scheme is used for the convective term and SIMPLE algorithm, to lead the numerical analysis and solve the discrete equations using the commercial software FLUENT 15.0. The consequences of the numerical investigations are then used to clear up the effect of length-ratio and transfer of heat. As per observations, the expansion in the length-ratio influences the rate of heat transfer.