The present paper outlines analytical investigation of the validity of total resistance model suggested by Kahwaji  for the heat dissipation when applied to longitudinal fins, the model will be as given in equation (22). Three distributions of heat transfer coefficient were used and represented as power, linear and exponential distributions to proved the validity of total resistance model at any variable heat transfer coefficient. Further more, a finite difference solution is devised to serve too the two purposes of verifying the two dimensional heat transfer and to cover wide range of variable and compare with the analytical solution. The results were agreement and proved the validity of the suggestion equation model above using the variable heat transfer coefficient and this model can be used in the constant or variable heat transfer coefficient in the heat transfer calculation for longitudinal fin.
Key words: longitudinal fin , variable heat transfer coefficient , total resistance