lattice boltzmann solution of concave longitudinal fins under step-changing base boundary conditions associated with accumulated nonlinearity

This article reports the transient numerical solution of concave profile longitudinal fins under two cases of step-changing base boundary conditions involving heat flux and temperature, respectively. although the analysis of concave fin has been carried out under step-changing base temperature, the transient solution of concave fin under step-changing base heat flux has seldom been reported in the literature. additionally, earlier reported studies of a fin merely address the linear and power law temperature-dependent variation of thermal parameters. herein, the thermal parameters of fin namely volumetric heat generation and thermal conductivity are treated to be a second-order polynomial function of temperature to address the nonlinear material properties. furthermore, the convection coefficient is treated to be a power law function of temperature to mimic the different fluid regimes. the accumulated non-linearity arising in governing differential equations due to temperature-dependent thermal properties physically characterizes the realistic application of fins. the results of aforementioned governing equation with accumulated non-linearity are computed by employing lattice boltzmann method (lbm) accompanied by in-house matlab code. the reported results comprise time-temperature history at different fin locations until the attainment of an equilibrium state and instantaneous temperature variation at a specified time. in order to facilitate the designing of fins, a broad range of thermal parameters and their significance on temperature distribution is reported, it reveals that the exact curve fitting analysis pertinent to each material is inherently necessary for accurately predicting the temperature distributions in fins.