Solution of transient heat transfer in graded‐material fins of varying thickness under step changes in boundary conditions using the Lattice Boltzmann Method.

Graded materials (GM) possess superior thermo‐mechanical properties, which are not feasible to obtain with homogeneous materials (HM), and hence in this paper, the transient response of a longitudinal fin of varying geometry made up of GM is reported. The temperature‐dependent convection coefficient and heat generation parameters are considered to account for real‐world high‐temperature applications of fins. Fin material properties such as density and specific heat remain constant while thermal conductivity is assumed to vary axially based on four different physically possible variations namely, linear, quadratic, power, and exponential variations. The typical nonlinear differential equation obtained for fins was solved by using a mesoscopic scale‐based particle tracking method called the Lattice Boltzmann method. The Lattice Boltzmann solver has been implemented in form of an in‐house MATLAB code and validated with existing results, thereafter it is developed for solving the foregoing problems. The results obtained are reported for rectangular, triangular, convex, and concave profiles under step change in base temperature and base heat flux. The performance of graded fins is investigated in terms of time required to attain steady‐state and fin tip temperature which are inherent design parameters in the case of the transient fin. Inhomogeneity index and profile function have a significant effect on the performance of fin in terms of resistance to heat flow. Hereby, in comparison with HM fins, GM fins have lower resistance to heat flow irrespective of fin profiles. Concurrently, comparative analysis for fins of different profiles made of HM and GM is also done to facilitate the designer in selecting the most appropriate fins. [ABSTRACT FROM AUTHOR]