Abstract
The aim of the present study is to investigate the two-dimensional heat transfer analysis in arrayed fins with thermal dissipation substrate. The governing equations for the fins and the substrate are expressed with Laplace equations, and the boundary conditions around the fins and substrate are Robin conditions. The present investigation first aims to provide a solution with regard to the geometry models by a series truncation method. Then the research will compare the results of the series truncation method with the point-matching method. Furthermore, the present study will also discuss the effects of dimension and Biot number of the fins on local dimensionless temperature, mean temperature, and heat transfer rate.
Highlights
Fins are used mainly to increase the extent of the heat transfer surface area in order to enhance the overall heat transfer or heat flux
Since the definition of the Bi1 is h∞1P/k1, the larger value of Bi1 will lead to an increased heat transfer rate and elevated mean temperature
The following conclusions can be drawn from the results of the present theoretical study
Summary
Fins are used mainly to increase the extent of the heat transfer surface area in order to enhance the overall heat transfer or heat flux. Some important researches in the early stages have been based on one-dimensional or two-dimensional, steady state analysis. Levitsky [1] investigated the criteria for validity of the one-dimensional fin approximation. The analysis of temperature distribution and heat flux in fins customarily makes use of a one-dimensional fin approximation. Irey [2] compared the errors between the one-dimensional and two-dimensional fin solutions, and the ratios of the interior to exterior resistance and the Biot number. The results showed that only for a small Biot number is the one-dimensional solution a satisfactory approximation. Lau and Tan [3] investigated the errors in one-dimensional heat transfer analysis in straight and annular fins. Sparrow and Lee [4] researched the effects of fin base-temperature depression in a multifin array
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