The present study focuses on the development of exact analytical solution for the investigations of the impacts of inclination angle and variable internal heat generation on the thermal behaviour of a porous fin heat sink. Through the developed analytical solution for the nonlinear thermal model, the study establishes that heat sink of inclined porous fin shows higher thermal performance compared to a heat sink of equal dimension with vertical porous fin. In addition, the study also shows that performance of inclined or tilted fin increases with the decrease in length–thickness aspect ratio. The study further reveals that increase in the internal heat generation parameter decreases the fin temperature gradient, which invariably decreases the heat transfer of the fin. The present study gives a good physical insight into the thermal problem and it could be used as a benchmark study for the numerical and approximation analytical investigation on the heat transfer problem.