The effect of conjugation on the enhancement of heat transfer in a liquid metal flow past a thermally conducting and sinusoidally oscillating infinite flat plate, when a constant temperature gradient is superimposed on the fluid, is investigated. The plate is made up of the materials compatible with the liquid metals used and is considered to be of finite thickness. Analytical solutions for the velocity and the temperature of the fluid and the solid are obtained. The effects of thermal conductivity and the thickness of the plate on the total time averaged heat flux transported and the thermal boundary layer thickness are investigated in detail. It is found that the effects of wall thickness and wall thermal conductivity on the heat flux transported depend on their effects on the transverse temperature gradient at any frequency. The optimum value of wall thickness at which the net heat flux transported attains the maximum value, for each fluid and for each wall material under consideration, is reported. A maximum increase of 46.14 % in the heat flux transported can be achieved by optimizing the wall thickness. A maximum convective heat flux of 1.87 × 10 8 W /m 2 is achieved using Na with AISI 316 wall. All the results obtained have been compared with the experimental and analytical results reported in the literature and are found to be in good agreement. It is believed that the new insights gained will be of significant use while designing liquid metal heat transfer systems.