Automobile radiators are heat exchangers that are used to transfer thermal energy from automobile engine to the surrounding atmosphere for the purpose of cooling the engine. Over 33% of heat energy generated by the engine through combustion is loss as heat dissipated in the atmosphere. The method of solution employed in this project work to solve the governing equations is the Galerkin-integral weighted-residual method, which is achieved following the steps of transforming the governing equations into Galerkin-integral weighted residual weak form, determination of interpolations functions, determination of element properties, assemblage of elements equations into domain equations and imposition of boundary conditions and solving of the assembled domain equations.The results showed that for temperature and velocity distributions in the radiator tubes and inlet hose to radiator as the number of elements is increased the more the finite element solution approximates the analytical solutions. Temperature values are observed to decrease, with increase in length, from 150 o C to 80 o C in the radiator tubes for finite element analysis, analytical, and ANSYS software used; and the finite element solutions exactly approximate analytical solutions at the nodes and agree with the ANSYS result. For velocity distribution in the radiator tube diameter, at the tube walls the no-slip boundary conditions are satisfied with velocity increasing from the wall at velocity of 0 to the midsection at velocity of 50.195m/s; while for the inlet hose diameter, velocity increases from wall at velocity 0 to the maximum at the midsection velocity 669.269m/s. Finally, the finite element analysis method can be used to determine how temperature will be distributed during radiator design stage in order to improve on its efficiency.