On the multiple solutions of boiling fins with heat generation

• Published in: International journal of heat and mass transfer Vol. 80; pp. 236 - 242
• Main Author: Krikkis, Rizos N.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2015
• Subjects: Bifurcation analysis; Boiling; Fins; Heat generation; Heat transfer; Heat transfer coefficients; Heat transmission; Internal heat generation; Mass transfer; Mathematical models; Multiplicity; Pin fins; Internal heat generation; Boiling; Multiplicity; Bifurcation analysis; Pin fins
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2014.09.020

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.