This paper reports an investigation of the hydrodynamic and thermal behaviour in a steady-periodic regime of a fully developed laminar mixed convection flow in an inclined channel filled with porous material. One of the channel walls is kept at a constant temperature, while the other is heated sinusoidally. The flow formation inside the porous media is modelled using Darcy-Brinkman model. The resulting governing dimensionless momentum and energy equations are separated into steady and periodic parts and solved analytically by the method of undetermined coefficients. In order to see the effect of the governing parameters on the thermal and hydrodynamic behaviour of the fluid flow, the results are depicted pictorially. These are seen to depend strongly on the dimensionless frequency of the periodic heating, Darcy number and the Prandtl number of the working fluid. The result is also seen to be in strong agreement with the existing analytical work, when the Darcy number is large. For sufficiently high Prandtl number, it is observed that the amplitude of the friction factor oscillation is maximised at a resonance frequency at the wall where there is periodic heating; also increasing Darcy number (Da) increases the amplitude of the friction factor oscillation, while it reduces the resonance frequency.