Taylor–Galerkin–Legendre-wavelet approach to the analysis of a moving fin with size-dependent thermal conductivity and temperature-dependent internal heat generation.

In heat transfer, fins are commonly used to enhance the heat transfer rate from surfaces and are widely applicable in heat exchangers and thermal energy storage systems. The material used for fins typically has a high heat conductivity. While the study of temperature-dependent heat conductivity for fins is already available, an insufficient mathematical description is observed in the case of size-dependent heat conductivity and convective heat transfer. In the current work, a heat transfer study is presented to estimate the temperature field in a moving fin that accounts for size-dependent heat conductivity and internal heat generation that depends on temperature under periodic boundary conditions. To observe the temperature field, we have developed a hybrid numerical method based on Taylor–Galerkin and Legendre wavelets. The stability analysis of the developed method is discussed in detail. Our numerical method shows excellent agreement with the analytical solution obtained in a special case. The impact of problem parameters is extensively discussed. This study shows that fin temperature decreases periodically with a space-dependent heat conductivity. In addition, for a problem which accounts for constant heat conductivity and movable fin, have greater temperature response, and standard problem which accounts for constant heat conductivity have weaker temperature response while it is between them for a problem that includes size-dependent heat conductivity and moving fin. It is shown that fin efficiency can be improved by lowering the value of the Knudsen number. Moreover, fin problem with fixed thermal conductivity offer greater efficiency in comparison with size-dependent thermal conductivity. [ABSTRACT FROM AUTHOR]