A DG-FEM based numerical investigation has been performed to explore the influence of the various geometric configurations on the thermal performance of the conjugate heat transfer analysis in the triangular finned double pipe heat exchanger. The computed results dictate that Nusselt number in general rises with values of the conductivity ratio of solid and fluid, for the specific configuration parameters considered here. However, the performance of these parameters shows strong influence on the conductivity ratio. Consequently, these parameters must be selected in consideration of the thermal resistance, for better design of heat exchanger.