On the multiple solutions of boiling fins with heat generation

A numerical bifurcation analysis is carried out in order to determine the solution structure of pin fins subject to multi-boiling heat transfer with internal heat generation. The analysis reveals that a complex and interesting solution structure exists. In contrast to the case without heat generation where up to three solutions exist, a large number of solutions may emerge arranged in a nested series of cusp points and isolas as the internal heat generation rate increases. The increased number of multiplicities imposes a number of both monotonic and non-monotonic temperature distributions along the fin height and reversal of the heat flow is observed at certain operating conditions. The fin profile has a profound effect on the solution by either increasing or decreasing the number of the singular points depending on whether a cylindrical or a trapezoidal profile is utilized. A generalized and smooth boiling heat transfer coefficient has been adopted so the results are not restricted to a particular working fluid.