Abstract
We consider a steady state problem for heat transfer in fins of various geometries, namely, rectangular, radial, and spherical. The nonlinear steady state problem is linearizable provided that the thermal conductivity is the differential consequence of the term involving the heat transfer coefficient. As such, one is able to construct exact solutions. On the other hand, we employ the Lie point symmetry methods when the problem is not linearizable. Some interesting results are obtained and analyzed. The effects of the parameters such as thermogeometric fin parameter and the exponent on temperature are studied. Furthermore, fin efficiency and heat flux along the fin length of a spherical geometry are also studied.
Highlights
Heat transfer rate from a hot body to the surrounding may be increased by surfaces which extended into that surrounding
Detailed theory and applications of Lie symmetry groups may be found in the texts such as those of [13,14,15,16,17]
Since in this study we deal with nonlinear second order ODEs we will restrict our discussion to the determination of symmetries for such equations
Summary
Heat transfer rate from a hot body to the surrounding may be increased by surfaces which extended into that surrounding. It was claimed that exact solutions of steady fin problems exist only when thermal conductivity and heat transfer coefficients are constants [6]. Ndlovu and Moitsheki [11] provided the approximate analytical solutions to steady state heat transfer in fins of different profiles which could not be solved exactly. In their studies an excellent comparison between exact and approximate solutions was established.
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