The combined effect of conjugation, external magnetic field and oscillation on the enhancement of heat transfer in the laminar flow of liquid metals between parallel plate channels is analyzed. In order to make our results useful to the design engineers, we have considered here only the wall materials that are widely employed in liquid metal heat exchangers. Indeed, all the results obtained through this mathematical investigation are in excellent agreement with the available experimental results. The effective thermal diffusivity κ_e is increased by 3×10^6 times due to oscillation and that the heat flux as high as 1.5×10^10 (W/m^2) can be achieved. Based on our investigation, we have recommended the best choice of liquid metal heat carrier, wall material and its optimum thickness along with the optimum value of the frequency to maximize the heat transfer rate. At the optimum frequency, by choosing a wall of high thermal conductivity and optimum thickness, an increase of 19.98% in κ_e can be achieved. Our results are directly relevant to the design of a heat transfer device known as electromagnetic dream pipe which is a very recent development.