Conduction heat and entropy transfer in a semi-infinite medium and wall with a combined periodic heat flux and convective boundary condition

Abstract

The influence of combined periodic heat flux and convective boundary condition on heat conduction and entropy transfer through semi-infinite and finite media is analytically studied in this work. The Cauchy's residue theorem is utilized to obtain the analytical solutions. It is found that fluctuations in the temperature inside each medium decreases as the Biot number ( Bi) increases or as the heat transfer parameter and the thermal oscillation parameter decrease. Also, the amplitude of the steady periodic noise in heat and entropy transfer is found to decrease as Bi increases or as the heat transfer parameter decreases. Moreover, it is found that the rate of entropy transfer to both media reaches maximum values at critical times lower than the time needed for both the applied heat flux and the rate of heat transferred to reach their maximum values. Finally, it is found that the decrease in the frequency of the applied heat flux and the increases in thermal diffusivity of the medium diminish the noise in temperature and both heat and entropy transfer without affecting their mean or steady state values. As such, this work paves a way on controlling the noise in thermal characteristics of solid media.