Investigation of Effect Thermal Conductivity on Straight Fin Performance with DTM

Abstract

In this study, considered new type of temperature dependent thermal conductivity and problem is solved analytically with differential transformation method (DTM). In this paper suppose thermal conductivity varies with temperature exponentially, and investigated effect of thermal conductivity on fin performance, and results compared with case that thermal conductivity varies with temperature linearly. The obtained differential transformation approximate analytic solution is in the form of an infinite power series, so that with obtained explicit form of temperature profile, the fin tip temperature, fin base heat transfer rate, and fin efficiency can be calculated directly from temperature profile easily. Temperature profile obtained for several assigned value of exponential parameter, that shown effect of exponential parameter on fin performance. In this paper for comparison of results, problem solved numerically with fourth-order Range-Kutta method that results of numerical have good agreement with results of DTM, as well as DTM results indicate that series converge rapidly with high accuracy

Keywords

• differential transformation method, exponentially, fin, numerical solution, heat transfer

References

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