[en] One dimensional heat conduction equation has been investigated for periodic heat transfer in an inhomogeneous bounded medium. Exact analytical solutions for some typical thermal conductivity profiles have been obtained. Also an approximate solution has been attempted for the first time for heat conduction problems which is applicable for any arbitrary variation of thermal conductivity. Numerical appreciation for a parabolic thermal conductivity profile shows that results from approximate approach are in excellent agreement with those obtained by the exact analytical approach. (author)