Temperature Dependence Of Thermal Conductivity Research Articles

Impacts of Temperature Dependent Thermal Conductivity and Viscosity on Slipped Flow of Maxwell Nanofluid

The mathematical model to inspect the effects of changeable thermo-physical properties such as thermal conduction, slip effects and viscosity on Maxwellian nanofluid is proposed. The thermal conductivity increases rapidly due to presence of nanoparticles such as metals, carbides, oxides etc. in base fluid. The flow occurs from the stagnated point pass a stretched sheet with slipped conditions. The characteristics of the Brownian motion as well as the thermophoresis processes are also taken into consideration. By means of similarity transformations, the ODEs are reduced from the equations influencing the fluid flow. A built-in solver of MATLAB namely bvp4c which is a collocation formula implementing the Lobatto IIIa finite differences numerical method is applied to solve these transformed equations numerically. The graphs of the numerical outcomes representing impacts of variations in different parameters on the fluid movement, transfer of heat along with mass are analyzed. This investigation leads to an important aspect that as the thermal conductivity in the flow is intensified, the temperature of the fluid reduces with high aggregation of the nanoparticles near the sheet’s surface. Also, the rates of heat and mass transferral depletes due to the relaxation of Maxwellian fluid. Furthermore, the effectiveness of the present numerical computations is determined by carrying out comparisons of heat and mass transferred rates against the previous analytical results for several values of thermophoresis and Prandtl parameters. The effectiveness of its outcomes can be applied in nanoscience technology and polymeric industries for their developments.

To study the hyperbolic annular fin with temperature dependent thermal conductivity via optimized Chebyshev polynomials with interior point algorithm

To study the hyperbolic annular fin with temperature dependent thermal conductivity via optimized Chebyshev polynomials with interior point algorithm

Numerical analysis of thermoelectric power generation coupled with temperature-dependent material properties

Thermoelectric generator (TEG) with improved performance is a promising technology in power supply and energy harvesting. Existing studies primarily adopt constant material properties to investigate TEG performance. However, thermoelectric (TE) material properties are subjected to considerable variations with temperature. Thus, reasonable doubts have risen concerning the influence level of temperature-dependent material properties on TEG performance. To solve this problem, an efficient and a comprehensive one-dimensional numerical model is developed to fully consider the third-order polynomial temperature-dependent thermal conductivity, Seebeck coefficient, and electrical resistivity. Control volume and finite difference algorithms are compared, and experiments are conducted to verify the developed numerical model. The temperature distribution along the TE leg obviously differs from the parabolic shape, which is a classic temperature distribution under the assumption of constant material properties. Insights find that the local change rate of thermal conductivity and Thomson effect are the essential reasons for the abovementioned phenomenon. It has been found that Thomson heat is released in the part of the leg near the cold-end, whereas it is absorbed in the remaining parts of the leg near the hot-end. The electric power on the basis of constant material properties is confirmed to be accurate enough by the developed numerical model, but the parabolic shape of the TE efficiency can be only obtained when temperature-dependent material properties are considered. Furthermore, it is wise to improve the TE efficiency by structural optimization. The present work provides an efficient and a comprehensive one-dimensional numerical model to include temperature-dependent material properties. New insights into the temperature and heat flux distribution, Thomson influence, and structural optimization potential are also presented for the in-depth understanding of the TE conversion process.

Competing mechanisms govern the thermal rectification behavior in semi-stochastic polycrystalline graphene with graded grain-size distribution

Thermal rectifiers are devices that have different thermal conductivities in opposing directions of heat flow. The realization of practical thermal rectifiers relies significantly on a sound understanding of the underlying mechanisms of asymmetric heat transport, and two-dimensional materials offer a promising opportunity in this regard owing to their simplistic structures together with a vast possibility of tunable imperfections. However, the in-plane thermal rectification mechanisms in 2D materials like graphene having directional gradients of grain sizes have remained elusive. In fact, understanding the heat transport mechanisms in polycrystalline graphene, which are more practical to synthesize than large-scale single-crystal graphene, could potentially allow a unique opportunity, in principle, to combine with other defects and designs for effective optimization of thermal rectification. In this work, we investigate the thermal rectification behavior in periodic atomistic models of polycrystalline graphene whose grain arrangements were generated semi-stochastically to have different gradient grain-density distributions along the in-plane heat flow direction. We employ the centroidal Voronoi tessellation technique to generate realistic grain boundary structures for graphene, and the non-equilibrium molecular dynamics simulations method is used to calculate the thermal conductivities and rectification values. Additionally, detailed phonon characteristics and propagating phonon spatial energy densities are analyzed based on the fluctuation-dissipation theory to elucidate the competitive interplay between two underlying mechanisms, namely, (1) propagating phonon coupling and (2) temperature-dependence of thermal conductivity that determine the degree of asymmetric heat flow in graded polycrystalline graphene.

An improved micromechanical model for the thermal conductivity of multi-scale fiber reinforced ultra-high performance concrete under high temperatures

An improved micromechanical model to estimate the thermal conductivity of multi-scale fiber reinforced ultra-high performance concrete (MSFUHPC) subjected to elevated temperatures is formulated in this study. This model considers the contributions of microstructure, multiscale fibers, water/cement ratio, thermal dehydration of hydrates, thermal cracking, interfacial thermal resistance, heating rate and temperature dependent thermal conductivity of each phase. To verify the proposed model, comparisons with experimental data on MSFUHPC specimens are carried out. Accordingly, factors affecting the thermal conductivity of MSFUHPC are discussed through the proposed model. Results suggest that blending multi-scale fibers and increasing the sand content can significantly enhance the thermal conductivity of MSFUHPC. While adding cenosphere particles can reduce the thermal conductivity. Overall, the thermal conductivity of MSFUHPC exhibits a decreasing trend with temperature. Meanwhile, thermal cracking occurs beyond 400 °C can remarkably decrease the thermal conductivity of MSFUHPC. A higher interfacial thermal resistance between sands and the matrix can result in a lower thermal conductivity. It is also found that thermal conductivity mainly depends on the maximum temperature experienced rather than the heating rate.

Computational analysis of entropy generation in three-dimensional mixed convection flow with thermal dissipation and variable thermal conductivity

Entropy generation in steady three-dimensional thermal flow is investigated under the coupled influence of viscous dissipation and mixed convection. The stretching sheet with an exponential velocity profile induces the flow. In this examination, we presume that the fluid is incompressible and possesses a Newtonian behavior and temperature-dependent thermal conductivity. Using the appropriate classical similarity variables reduces the dimensional nonlinear dynamical system of governing equations to a dimensionless nonlinear dynamical set of ordinary differential equations. It’s important to note that the selection of an exponentially varying surface temperature is deliberate, as it enables precise similarity transformations to be established in situations involving both viscous dissipation and buoyancy forces. The simplified finite difference approach (SFDM) is used to solve the acquired nonlinear dynamical set of ordinary differential equations. The tridiagonal matrix approach is used to solve the resulting system of algebraic equations. In a particular situation, the present numerical simulation is numerically checked with the previously available results and observed a good agreement. The effects of physical parameters on velocity, temperature, surface stresses and heat tranfer rate, entropy generation, and the irreversibility parameter are investigated. The entropy generation rate exhibits a decreasing trend with respect to the mixed convection parameter in the vicinity of the stretching surface. Entropy reduction can be achieved by employing a working fluid with a low Prandtl number and by minimizing the fluid friction.

Computing of temperature-dependent thermal conductivity and viscosity correlation for solar energy and turbulence appliances via artificial neuro network algorithm

The growing popularity of artificial intelligence approaches has led to their application in a wide range of engineering fields. The most widely used artificial intelligence tool, artificial neural networks, can be used to predict data with high accuracy. An artificial neural network approach is being used to predict effective and accurate thermal conductivity and viscosity models for hybrid nanofluid systems. Here, new types of correlations relating to the thermophysical properties of Fly Ash–Cu nanoparticles with diameter sized 15.2[Formula: see text]nm and which are temperature-dependent are developed. The highest thermal conductivity and viscosity values were obtained for hybrid nanofluids with a mixture ratio of 20:80, with maximum amplification exceeding 83.2% and 65%, respectively, over the base fluid. The Fly Ash–Cu/water hybrid nanofluid’s viscosity and thermal conductivity are evaluated for a concentration range of 0–4%. The evaluation of the Fly Ash–Cu/water hybrid nanofluids system at concentrations ranging from 0 to 4% most likely entails a scientific or engineering study aimed at understanding the behavior and properties of this nanofluid mixture. Nanoparticles can agglomerate or settle in the base fluid over time, compromising the stability of the nanofluids. Researchers may be interested in determining how varied quantities of Fly Ash and Cu nanoparticles affect the nanofluid’s stability and sedimentation behavior. The heat transfer potential is examined within the optimistic range of temperatures of 30–80∘C. Many fruitful results for turbulence and solar energy have been drawn. The Mouromtseff number achieved an optimal value for all concentration levels. The heat transfers of turbulent flow and thermal conductivity of hybrid nanofluids increase with the augmented values of concentrations and temperature. Researchers found an increase in thermal conductivity of hybrid nanofluids at 0–4% concentrations, potentially impacting heat transfer applications. The conclusion explores the potential integration of the developed correlations and neural network model into practical engineering or industrial applications involving solar energy and turbulence appliances. In this work, we extend the work of Kanti et al. [Sol. Energy Mater. Sol. Cells 234 (2022) 111423] which is on the properties of water-based fly ash-copper hybrid nanofluid for solar energy applications.

Exponential approximation of the coherence contribution to the thermal conductivity of complex clathrate-type crystals

The low-temperature properties of guest-host crystals, such as clathrates and skutterudites, offer a rich playground for discovering novel physical phenomena and developing new materials with unique properties. The temperature dependence of thermal conductivity in these materials can exhibit both crystal-like and glass-like behavior, which reflects the properties of the phonon excitations and various scattering mechanisms. The ultra-low thermal conductivity of clathrate crystals is closely related to the concept of minimal thermal conductivity, which is determined by the intrinsic phonon scattering in the material. In this work, the temperature dependence of thermal conductivity for both crystal-like and glass-like behavior of different structural types of clathrates and skutterudites was analyzed using the ”Unified theory of thermal transport in crystals and glasses” of M. Simoncelli, N. Marzari & F. Mauri. A method was proposed and tested for the coherence contribution related to wave-like tunneling and loss of coherence between different vibrational eigenstates. The temperature dependence of the coherence contribution to thermal conductivity was approximated by the exponential function of an Arrhenius type with characteristic energy E and characteristic minimal thermal conductivity parameter κ0. The coherence contribution is intertwined with other phonon scattering mechanisms, and over a wide temperature range, its temperature dependence is universal with parameters depending on the crystal structure, positional disorder, and impurity doping. This work provides insights into the temperature dependence of thermal conductivity in guest-host materials and its importance for designing and optimizing their properties for various applications, such as thermoelectric generators.

Magnetohydrodynamic hybrid nanofluid flow through moving thin needle considering variable viscosity and thermal conductivity

In modern science and technology, industrial applications that deal with the problem of continuously moving thin needle, surrounded with fluid in sectors like hot rolling, crystal growing, heat extrusion, glass fiber drawing, etc., are rapidly increasing. Such processes involve high temperatures which may affect the fluid properties that is, viscosity and thermal conductivity. So, it’s crucial to understand temperature-dependent fluid properties. Focused on these assumptions, the main objective of the current research work is to investigate how temperature-dependent fluid properties might improve the heat transfer efficiency and performance evolution of hybrid nanofluid in the presence of transverse magnetic field over a moving thin needle. Variable Prandtl number is also introduced to observe flow fluctuation, the effect of adding nanoparticles, and enhancement in heat transmission. The results are obtained for different needle thicknesses, temperature-dependent viscosity, temperature-dependent thermal conductivity, and heat generation. Moreover, Fe3O4/Graphene nanoparticles are considered to be dispersed in water. The governing partial differential equations of flow and heat transfer are transformed into a system of coupled nonlinear ordinary differential equations using analysis of similarity conversion. Subsequently, the numerical solution of the problem is attained by employing the MAPLE software. The fourth-fifth-order Runge-Kutta-Fehlberg (RFK45) approach is used by default in this MAPLE program to address the numerical problem of boundary value. The velocity and temperature field are pictured for different values of the parameters as well as physical quantities of interest such as skin friction coefficient and rate of heat transfer are visually depicted in graphs and tables. It is found that fluid motion and energy transport are highly regulated by the variation of magnetic field strength. As the volume fraction of Fe3O4 is increased, the heat generation, and thermal conductivity parameter vehemently enhance the temperature profile which leads to a rise in thermal boundary layer. A strong augmentation in the heat transfer rate has been found with the increment in the variable Prandtl number.

Stability of magnetohydrodynamics free convective micropolar thermal liquid movement over an exponentially extended curved surface

Micro polar fluids have a wide variety of applications in biomedical, manufacturing, and technical activities, such as nuclear structures, biosensors, electronic heating and cooling, etc. The aim of this study is to investigate the properties of heat transfer on a magnetohydrodynamic free convection movement of micro polar fluid over an exponentially stretchable curved surface. The flow is non-turbulent and steady. The effects of Joule heating, varying thermal conductivity, irregular heat reservoir, and non-linear radiation are anticipated. The modelled PDEs are converted to ODEs via transformation, and the integration problems are then addressed using ND-Solve method along with bvp4c package. It is observed that velocity is reduced and the micro rotation field is increased as the micro rotation parameter is increased. It is witnessed that the temperature of the fluid enhances as the Eckert number is augmented. The velocity is increasing function of the curvature parameter while the decreases with increasing magnetic factor. The distribution of temperature is improved by a rise in temperature-dependent thermal conductivity characteristic. It is investigated that as the values of temperature ratio, Prandtl number, and the Biot number are increased the temperature distribution is enhanced. For the stability of the numerical results, the mean square residue error (MSRE) and total mean square residue error (TMSRE) are computed. For the confirmation of the present analysis, a comparison is done with the published study and excellent settlement is found.

Aspect ratio's critical role in enhancing natural convective heat transfer with temperature-dependent nanofluids within rectangular enclosures

Significant research has been performed on natural convection involving nanofluids inside rectangular enclosures since they are extensively used in thermal engineering. However, a significant gap remains in comprehending the conflicting results in nanofluid behavior observed between experimental and numerical studies. This study seeks to bridge this divide by examining natural convective heat transfer within vertical and horizontal enclosures filled with Al2O3/Water nanofluid. Using temperature-dependent viscosity and thermal conductivity, we aim to elucidate the key parameters influencing nanofluid enhancement. The results obtained through numerical simulations, using the finite difference method, showed the impact of different parameters namely nanoparticle volume fraction, 0 ≤ φ ≤ 0.05, nanoparticle size, dnp = 13, 29, and 45 nm, and aspect ratio, 0.25 ≤ A ≤ 4, on various factors, including heat transfer rates, maximal stream function, and temperature and stream function contours. The outcomes revealed that the use of nanofluids leads to improvements in heat transfer, but only when the aspect ratio is below certain critical values, Acr = 0.56, 0.48, and 0.53 for φ = 0.01, 0.03, and 0.05 respectively. Beyond these values, pure water performs better than the nanofluids in terms of heat transfer where the enhancement drops to -8%, -23%, and -22% when φ = 0.01, 0.03, and 0.05 respectively. Additionally, this critical value relies on the nanoparticle volume fraction and it rises as the nanoparticle diameter augments. This effect is believed to be caused by the high enhancement in viscosity compared to thermal conductivity when the convective mode dominates the conductive one. Furthermore, a larger aspect ratio leads to better heat transfer and the smaller nanoparticles are favorable for better heat transfer for a particular nanoparticle volume fraction. These findings carry significant implications for the field of nanofluid engineering, emphasizing the indispensable consideration of aspect ratios in optimizing thermal performance.

Entropy generation analysis of non-miscible couple stress and Newtonian fluid in an inclined porous channel with variable flow properties: HAM Analysis

The aim of this study is to investigate the entropy production characteristics of two non-miscible fluids in an inclined porous channel with temperature-dependent thermal conductivity and viscosity. The porous region of the channel is divided in two regions. In region-1 and region-2, the Couple stress and Newtonian fluid take place due to constant pressure gradient, respectively, under the influence of a uniform magnetic field. Here, the Darcy–Brinkman model is used for the flow of immiscible fluid through the porous media. In this work, we used a semi-analytical method named as homotopy analysis method (HAM) to solve the coupled nonlinear ordinary differential equations. The goal of the considered problem is to examine the consequences of a variety of thermophysical parameters, including Hartmann number, varying viscosity parameter, varying thermal conductivity parameters, and Grashof number on the characteristics of entropy generation, Bejan number distribution, thermal behavior and flow characteristics of non-miscible couple stress and Newtonian fluid passing through a porous channel. The novel aspect of this study is the formation of entropy and Bejan number as a result of non-miscible Newtonian and couple stress fluids with varying thermal conductivity and viscosity in porous media. In terms of rheological investigation, a semi-analytical simulation for changeable thermal and flow properties in an immiscible Newtonian and couple stress fluid via an inclined porous channel is a brand-new concept, and the behaviors of such flows have not been examined yet. From this study, it is concluded that on raising the variable thermal conductivity, Hartmann number and the permeability of the porous medium, the flow velocity, thermal characteristics and entropy generation number decrease. The authors also come to the significant conclusion that non-miscible Newtonian and couple stress fluids have larger entropy production numbers, flow velocities, and temperature profiles for higher values of Grashof number, variable viscosity parameter, and couple stress parameter. The findings of this work have also been graphically validated through the previously established work. The results of the present analysis can be used in petroleum industry, lubrication theory, etc.

Effect of variable thermal conductivity of ternary hybrid nanofluids over a stretching sheet with convective boundary conditions and magnetic field

In this study, a partial velocity slip of the boundary layer flow and an analysis of the MHD two-dimensional ternary hybrid nanofluid with fluid based on polymers with variable thermal conductivity are conducted. On a stretching sheet with a convective boundary condition, the investigation was conducted. Model equations with boundary conditions were transformed into a set of ODEs in order to study the flow. The resulting system of equations was solved by using the Runge-Kutta fourth-order method in conjunction with the shooting method. A numerical analysis was done to determine the impact of several key factors on the system's heat transfer characteristics and flow field velocity. Computed the flow field's velocity and heat transfer properties by varying these physical parameters, then graphically displayed the results. Additionally, tables covered the local shear stress and rate of heat transfer respectively, describe the flow's resistance to motion and the rate of local heat transfer of ternary hybrid nanofluid. For a thorough comparison, the results were compiled in tables. Additionally, the results were compared to data already available for regular fluids, and it was discovered that there was a very high degree of agreement between the two sets of results. This raises confidence in the precision of their numerical computations. New findingsThe explicit formulas that have been derived make it simple to understand how changes in temperature-dependent thermal conductivity and nanoparticle volume fraction affect significant parameters, such as sk.fsdain friction and heat transfer rate, in the study of ternary hybrid nanofluids.

Analysis of temperature-dependent thermal conductivity and fin efficiency: Direct Akbari-Ganji method

The vast majority of engineering issues, particularly heat transport equations, have a non-linear form. The analytical solution of temperature distribution, fin effectiveness, and fin efficiency of straight convective fins that transport heat with temperature-dependent thermal conductivity convection is derived in this work using the Direct Akbari-Ganji method (DAGM). DAGM is an effective methodology that is very simple and takes less time to solve non-linear temperature distribution fin problems. In the present investigation, Direct Akbari-Ganji technique offers desirable solutions to heat transfer problems. The round-off error is smaller compared to other methods. For the purpose of calibrating the error accuracy of the suggested direct technique, this result is compared with the numerical and earlier solution. The outcomes show that the DAGM for heat transfer equations in engineering situations has excellent validity and considerable promise. Finally, it is clear that when the thermo-geometric fin parameter increases, so does the fin efficiency. The homogeneity of the fin is due to the variable thermal conductivity. Four convection conditions with constant coefficients, growing and decaying convection coefficient with fin temperature are discussed.

Precise channel temperature prediction in AlGaN/GaN HEMTs via closed-form empirical expression

In this study, we introduced a closed-form empirical expression for estimating the channel temperature in AlGaN/GaN HEMTs. This model incorporates parameters such as substrate thickness, gate length, gate width, and temperature-dependent thermal conductivity. The model's validity was rigorously established through comprehensive comparisons involving the channel temperature measurement procedure (DC) and TCAD device simulations. The outcomes exhibited a noteworthy alignment with the observed model data, reinforcing its credibility. The model yields a notably improved accuracy in channel temperature estimation compared to assumptions based on constant thermal conductivity. This observation holds particular significance for GaN/Sapphire HEMTs. The utilization of the closed-form expression enables the simultaneous optimization of both electrical and thermal properties, utilizing conventional computer-aided design tools.

An inverse methodology to estimate the thermal properties and heat generation of a Li-ion battery

Accurate estimation of temperature-dependent orthotropic thermal properties and volumetric heat generation of a Li-ion battery is crucial for thermal modeling, thermal safety, and the design of thermal management systems for electric vehicles. Though various studies are available on estimating thermophysical properties and heat generation, simple and easily applicable methods are rare. Moreover, these studies failed to report temperature sensitivity and standard deviation of the estimates. In this study, the temperature-dependent orthotropic thermal conductivities (kr,kθ,kz), specific heat (cp), and volumetric heat generation (qv) of Panasonic NCR18650BD cylindrical battery are estimated using an inverse approach (Metropolis Hastings-Markov Chain Monte Carlo algorithm based Bayesian method) with the help of experimentally obtained surface temperatures measured at convenient locations on the battery. From the estimation, the average values of kr,kθ,kz and cv are observed to be 3.18 ± 0.19, 20.34 ± 1.26, 19.89 ± 1.29 (W/mK), and 3180 ± 202 (J/kgK), respectively. The average heat generation rates from the same battery obtained using the same methodology are 0.1 ± 0.005, 0.34 ± 0.012, and 1.51 ± 0.026 W for 0.5, 1, and 2C discharge rates, respectively. The estimated thermophysical properties and heat generation rates are in good agreement with the results obtained from both in-house experiments and literature. In addition to the estimation of thermophysical properties and heat generation, the proposed methodology opens vistas to predict the strength and location of hotspots in the battery domain, which helps in designing appropriate and effective thermal management systems for battery packs.

Influence of inclined magnetic field and cross diffusion on transient forced convective heat and mass transfer flow along a porous wedge with variable Prandtl number

The unsteady 2-D forced convective mass and heat transfer flow of an incompressible, viscous and electrically conducting fluid along a porous wedge is examined in this article using numerical analysis to survey the effects of a magnetic field and thermophoresis. This is done in the existence of temperature-dependent thermal conductivity, a variable Prandtl number, and the effect of cross diffusion. The governing nonlinear PDEs have been converted into nonlinear ODEs by using a similarity transformation. The modified ODEs are solved for similar solutions using the shooting technique and the Runge–Kutta fourth-order method. The temperature, velocity, concentration, thermophoretic velocity, and thermophoretic particle deposition velocity results for various parameters are provided. The Dufour number’s effect enhances the temperature profile and rate of heat transfer. Moreover, it is noted that the rate of mass transfer is meaningfully influenced by the variation of the thermophoresis parameter and Soret number. Thus, in any physical model where the thermal conductivity of the fluid is temperature dependent, the Prandtl number within the BL have to be treated as variable rather than constant.

Thermophysical Properties of Neodymium and Gadolinium Zirconate Hafnates

Pyrochlore-type neodymium and gadolinium zirconate hafnates have been prepared and identified. The heat capacities of the prepared samples have been measured by differential scanning calorimetry in the range 310–1800 K. Temperature-dependent cubic unit cell parameters have been determined and thermal expansion coefficients assessed in the range 298–1273 K using high-temperature X-ray diffraction. The thermal diffusivity of the samples was measured by the laser flash method, and the temperature-dependent thermal conductivity was calculated taking into account the porosity of the samples.

Flow and heat transfer analysis of Couette and Poiseuille flow of a hybrid nanofluid with temperature-dependent viscosity and thermal conductivity

The purpose of this research is to quantify the influence of a number of independent parameters (−0.5≤α1,β1,β2≤0.5) on the heat transmission rate and the temperature of a nanofluid hybrid flowing between parallel plates. The linked nonlinear momentum and energy equations are solved using the regular perturbation method for two different cases resembling the plane Couette flow and Poiseuille flow. By combining engine oil with multiwalled carbon nanotubes (MWCNT) and aluminum oxide nanoparticles, a hybrid nanofluid is produced with wide-ranging lubricating and industrial applications. It has been found that the hybrid nanofluid can function as a coolant provided the relevant parameters are adjusted appropriately. It is demonstrated that these additives have a tendency to stabilise the thermal and the volume flow rate, hence decreasing randomization that is necessary for a good lubricant to function. The findings of the study indicate that β1 has a greater influence on temperature, while β2 has a stronger effect on velocity. In addition to the variable model, the results for the constant model have also been deduced, and the novel study demonstrates that the considered variable viscosity model tends to produce a more uniform temperature distribution.

A hybrid numerical method for non-linear transient heat conduction problems with temperature-dependent thermal conductivity

This paper introduces a hybrid numerical technique aimed at effectively addressing two-dimensional (2D) non-linear transient heat conduction problems, featuring temperature-dependent thermal conductivity. This scheme involves integrating the Krylov deferred correction (KDC) method in the temporal discretization and the generalized finite difference method (GFDM) in the spatial discretization. The core of the KDC method introduces a new unknown variable in the form of the first-order time derivative of temperature, leading to a non-linear equation after temporal discretization. Subsequently, the corresponding non-linear equation is solved in the spatial domain using the GFDM, supported by the Jacobian-free Newton–Krylov (JFNK) solver and fourth-order Taylor series expansion. The accuracy and stability of the hybrid approach are verified through two numerical experiments, demonstrating the strong performance of the present algorithm known as the KDC-GFDM for the simulations of the interested problems in long-time intervals.