A coupled conduction–convection heat transfer analysis is carried out for a two‐dimensional rectangular, vertical parallel plate channel producing volumetric energy (uniform and nonuniform), subjected to laminar forced‐convection incompressible fluid flow under steady‐state conditions. The equations governing the thermal and flow field are solved by using finite difference method, and the resulting algebraic equations are solved by using the tridiagonal matrix algorithm method. Four coolants with their Prandtl numbers (Pr), namely, liquid sodium (Pr = 0.005), sodium‐potassium (Pr = 0.00753), lead (Pr = 0.02252), and helium (Pr = 0.666) are used for the present conjugate analysis. Effects of different thermal and fluid flow parameters such as Reynolds number (ReH) ranging from 500 to 1500, conduction–convection parameter (Ncc), and total heat generation (Qt) on average exit temperature (θae) of coolants are studied. From the obtained results, it is found that the θae of coolant strongly depends on Pr, ReH, Ncc, and Qt when the aspect ratio (Ar) is kept constant. It is also found that with a nonuniform rate of heat generation, the coolant θae is high compared to uniform heat generation rate, whereas with increasing Ncc, the θae decreases, and with increasing Qt, the θae increases irrespective of coolants.