Instantaneous Heat Flow Characteristic of Two-Dimensional Graded Extended Surfaces Abhishek Sahu, Shubhankar Bhowmick Journal of Thermophysics and Heat Transfer, 2026 This paper comprehensively investigates the instantaneous heat flow characteristics of a two-dimensional (2-D) thermal structure with material grading associated with diabatic imparity arising owing to the asymmetrical convection coefficient. A 2-D thermal structure like an extended surface (fins) subjected to an asymmetrical convection coefficient owing to natural and/or essential boundary conditions signifies pragmatic industrial application. To investigate the same, the response of 2-D fin under the root surface boundary conditions of i) step-changing temperature and ii) step-changing heat flow is graphically recorded in terms of instantaneous isotherms, threshold isotemporal lines, and steady-state isotherms. In normalized coordinates, Biot number [Formula: see text] is taken in the range 0.01–10.0 and the thermophysical property [Formula: see text] is assumed to vary from 0.1 to 4.0 to account for all practical scenarios of heat transfer. Diabatic imparity commences a heat current in transverse and longitudinal directions, consequently altering the direction of heat propagation, resulting in shifting of the threshold isotemporal lines toward the fin surface having a larger magnitude of [Formula: see text]. Additionally, the contour plot shows that for the same average thermal conductivity graded material (GM) and homogeneous material (HM) fin, the GM fin has a higher magnitude of steady-state isotherms and faster attainment of steady state.
Continuous composite longitudinal fins under oscillating boundary conditions: a lattice Boltzmann solution Abhishek Sahu, Shubhankar Bhowmick Engineering Computations Swansea Wales, 2024 PurposeTransient response of continuous composite material (CCM) fin made of high thermally conductive composite material is presented. The continuously varying effective properties of composite material such as thermal conductivity, heat capacity and density have been modelled using the Mori-Tanaka homogenization theory and rule of mixture. Additionally, temperature dependency of thermal conductivity, heat generation (composite materials) and convection coefficient (fluid properties) have also been incorporated. Different base boundary conditions are addressed such as oscillating heat flow, oscillating temperature, step-changing heat flow and step-changing temperature. At the other boundary, the fin is assumed to have a convective tip.Design/methodology/approachLattice Boltzmann method is implemented using an in-house source code for obtaining the numerical solution of typical non-linear heat balance equation of the aforementioned problem under various transient base boundary conditions.FindingsThe effects of various thermal parameters such as material diffusivity ratio and conductivity ratio, area ratio and Biot number on transient response of fin and temperature distribution of fins are studied and interpreted. The heat transfer rate and time for attainment of steady state temperature of metal matrix composite (MMC) fin are found to be proportionally dependent on their diffusivity ratio. Additionally for higher values of area ratio and biot number, MMC fins are reported to dissipate the heat more efficiently in comparision to homogeneous fins in terms of time required to attain the steady state and surface temperature.Practical implicationsResponse of transient fin associated with advanced class of material can facilitates the practicing engineers for designing high-performance and/or miniaturized thermal management devices as used in electronic packaging industries.Originality/valueStudies of composite fin consisting of laminating second layer of material over the first layer have been reported previously, however transient response of CCM fin fabricated by continuously varying the volume fraction of two materials along the fin length has not been reported till date. Such material finds its application in thermal management and electronic packaging industries. Results are plotted in form of a graph for different application-wise material combinations that have not been reported earlier, and it can be treated as design data.
Graded Longitudinal Fins Having Spatially Varying Temperature-Dependent Thermophysical Properties Abhishek Sahu, Shubhankar Bhowmick Journal of Thermophysics and Heat Transfer, 2023 This paper reports transient responses of graded longitudinal fins subject to step change in base temperature and base heat flux wherein the graded fin materials are theorized to have spatial- and temperature-dependent thermal conductivity. Microstructure variations in graded materials (GMs) are addressed by axially varying the thermal conductivity; because GMs are potentially high-temperature application materials, consequently, thermal conductivity and heat generation are, respectively, assumed as polynomial and linear functions of temperature. Additionally, most of the applicable pragmatic fluid regimes are accounted for using the power law convection coefficient. The numerical solution of a typical nonlinear governing differential equation is obtained by using a particle tracking-based method called the lattice Boltzmann method (LBM). The LBM is a mesoscopic-based simulation method centered around the principles of kinetic theory and statistical mechanics. The LBM formulation accompanied with the in-house MATLAB code of the aforesaid problem with varying parameters is reported; also, it is validated with a previously available solution. The foregoing analysis is carried out to enhance the performance of a fin by using the superior thermomechanical property of graded materials. Furthermore, the inclusion of temperature-dependent thermophysical properties and heat generation will provide more accurate design data. The reported graph reveals that, even though a linear GM fin tip possesses thermal conductivity that is 25% less in magnitude in comparison to the Type-II homogeneous material (HM-2), the GM fin always yields a higher fin tip temperature because of grading. In addition, the tip temperature deficits between GMs and HM-2 proportionally increase from 0.4 to 2.1% for values of [Formula: see text] increasing from 0.1 to 2.0, respectively, for step changes in temperature; whereas in the case of the step change base flux, the deficits increase from 8.72 to 12.1% for values of [Formula: see text] decreasing from 3.0 to 1.0, respectively.
Solution of transient heat transfer in graded-material fins of varying thickness under step changes in boundary conditions using the Lattice Boltzmann Method Abhishek Sahu, Shubhankar Bhowmick Heat Transfer, 2022 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.
Transient Response of Longitudinal Fins under Step Changes in Base Temperature and Heat Flux using Lattice Boltzmann Method A. Sahu, Shubhankar Bhowmick Journal of Applied and Computational Mechanics, 2022 The present article reports the transient response of longitudinal fins having linear and non-linear temperature dependent thermal conductivity, convection coefficient and internal heat generation under two cases of base boundary condition, (i) step change in base temperature and (ii) step change in base heat flux. The fin tip is assumed to be adiabatic. Both, linear and non-linear, temperature dependency of thermo-physical properties is addressed in the mathematical formulation and the solution for the above cases is obtained using Lattice Boltzmann method (LBM) implemented in an in-house source code. LBM, being a dynamic method, simulates the macroscopic behavior by using a simple mesoscopic model and offers enormous advantages in terms of simple algorithm to handle even the most typical of boundary conditions that are easy and compact to program even in case of complicated geometries too. Although the transient response of longitudinal fins has been reported earlier, however power law variation of thermo physical properties for the above two base condition has not been reported till date. The present article first establishes the validity of LBM code with existing result and then extends the code for solving the transient response of the longitudinal fin under different sets of application-wise relevant conditions that have not been treated before. Results are reported for several combination of thermal parameter and are depicted in form of graphs.
Numerical investigation of transient responses of triangular fins having linear and power law property variation under step changes in base temperature and base heat flux using lattice Boltzmann method Abhishek Sahu, Shubhankar Bhowmick Numerical Heat Transfer Part A Applications, 2021 In this article, transient response of triangular longitudinal fin with internal heat generation under step change in (i) base temperature and (ii) base heat flux assuming is reported. The convection coefficient is assumed to be power law function of temperature, accounting for different practical application. Moreover, thermal conductivity and heat generation coefficient are assumed as linear and power law functions of temperature. The nonlinear differential equation of triangular fins is solved using Lattice Boltzmann method (LBM) with the aid of in-house MATLAB code. Till date, transient response of triangular fins with linear temperature dependence are only reported, under the step change in base temperature. Further, internal heat generation under the step change in base heat flux with power law temperature dependent properties for fins have been rarely reported. The results are first validated with available benchmarks and subsequently results for different thermal and geometry parameter are reported in graphical form.
