The phenomenon of forced convective heat transfer with internal heat generation in a micro-channel filled with a porous material saturated with a rarefied gas is studied using finite element method by varying wall heat flux and wall temperature ratio under local thermal non-equilibrium (LTNE) conditions. The Darcy–Brinkman model is used to describe the flow inside the porous material. Numerical solutions are obtained for both the fluid and solid temperature distributions by considering the case A for variable wall heat fluxes, case B for variable wall temperature ratio and case C for temperature jump coefficient. The Nusselt number for the fluid at the channel walls is calculated. The effect of significant parameters such as Biot number, wall temperature ratio, fluid and solid internal heat generation, fluid to solid effective thermal conductivity ratio are discussed. Comparative study on Nusselt number is carried out in case A with constant wall heat flux as well as variable wall heat flux. The Nusselt numbers obtained for case B indicate a strong dependency on the variation of internal heat generation for Bi = 0.5. The velocity slip coefficient is found to have negligible effect on the Nusselt numbers for all the three cases.