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It has been recognized that an increase in the rate of heat transfer to or from a solid body can be accomplished by extending surfaced called fins. There are a variety of fins such as rectilinear or parabolic fins protruding from a flat wall, or thin circular or rectangular fins on a tube. In all cases the heat transfer designers are interested in the optimum heat loss or gain. Considerable experimental work has been done in order to establish the empirical values of convective heat transfer coefficient to predict the amount of heat transfer from a particular fin configuration. The limitation of the experimental approach is that the results for each particular fin cannot be applied widely to others. An alternative way to meet the problem is by means of analytical theory. This constitutes treating the problem as a boundary value problem for which a governing differential equation is derived and appropriate boundary conditions are specified. The advantage of this approach is that the results can often be widely applied just by specification of certain geometric and physical parameters. The purpose of this thesis is to find analytically the temperature distribution and heat loss of a square fin on constant thickness on a tube. (