Investigation of diabatic imparity involving asymmetric convection in two-dimensional longitudinal fins using lattice Boltzmann solver

Abstract

This manuscript investigates the effect of diabatic imparity on two-dimensional (2-D) transient fins having naturally obtained non-linear variation of temperature-dependent conductivity. The diabatic imparity arises due to asymmetrical convection coefficient on the surfaces, implemented using different Biot numbers on each respective surface of the fin, which resembles pragmatic industrial applications. The transient solution of 2-D fin has been obtained using a Lattice Boltzmann (LB) solver, firstly, the suitability of 2-D LB formulation is established with the validity of the existing results, and subsequently extending the LB formulation for the present study. The numerical solution is determined under the two types of step-changing boundary conditions at the fin root having (i) heat flow and (ii) temperature. Results have been plotted graphically, and these include instantaneous isotherms, equilibrium isotherms, and threshold iso-temporal lines. Reported results facilitate the fin designer to examine the effect of diabatic imparity on the attainment of steady-state and occurrence of transverse temperature gradient on 2-D transient fin. The reported results provided are pertinent to the pragmatic application and are seldom reported in the literature. The outcomes of the present investigation are eminently informative to practising engineers and will serve as design monograms.