Nonlinear Thermal Conductivity Research Articles

Overlapping Grid-Based Spectral Collocation Technique for Bioconvective Flow of MHD Williamson Nanofluid over a Radiative Circular Cylindrical Body with Activation Energy

The amalgamation of motile microbes in nanofluid (NF) is important in upsurging the thermal conductivity of various systems, including micro-fluid devices, chip-shaped micro-devices, and enzyme biosensors. The current scrutiny focuses on the bioconvective flow of magneto-Williamson NFs containing motile microbes through a horizontal circular cylinder placed in a porous medium with nonlinear mixed convection and thermal radiation, heat sink/source, variable fluid properties, activation energy with chemical and microbial reactions, and Brownian motion for both nanoparticles and microbes. The flow analysis has also been considered subject to velocity slips, suction/injection, and heat convective and zero mass flux constraints at the boundary. The governing equations have been converted to a non-dimensional form using similarity variables, and the overlapping grid-based spectral collocation technique has been executed to procure solutions numerically. The graphical interpretation of various pertinent variables in the flow profiles and physical quantities of engineering attentiveness is provided and discussed. The results reveal that NF flow is accelerated by nonlinear thermal convection, velocity slip, magnetic fields, and variable viscosity parameters but decelerated by the Williamson fluid and suction parameters. The inclusion of nonlinear thermal radiation and variable thermal conductivity helps to enhance the fluid temperature and heat transfer rate. The concentration of both nanoparticles and motile microbes is promoted by the incorporation of activation energy in the flow system. The contribution of microbial Brownian motion along with microbial reactions on flow quantities justifies the importance of these features in the dynamics of motile microbes.

A coupled thermomechanical peridynamic correspondence model for damage prediction in a freezing rock

This study presents a coupled thermomechanical (TM) bond-associated non-ordinary state-based peridynamic (BA-NOSB PD) (correspondence) model for simulating the thermal behavior and crack propagation in a saturated rock due to freeze. Considering the change in thermal property and the latent water–ice phase transition at low-temperature conditions, the PD form of the nonlinear thermal conduction equation is derived by using the PD differential operator (PDDO). The deformation response is obtained in the framework of BA-NOSB PD model considering the pore ice pressure and thermal expansion. The accuracy of the TM BA-NOSB PD model is verified by simulating the thermal behavior of tuff and sandstone and crack propagation in specimens with pre-existing cracks at low-temperature conditions. The PD predictions of temperature and frost heaving strain are in close agreement with the experimental and previous numerical results. The present model also accurately predicts crack propagation and coalescence in saturated rocks due to the freezing frost.

Thermal-field analytical modeling of machined surface layer in high-speed-dry milling UD-CF/PEEK considering thermal anisotropy and nonlinear thermal conductivity

The high-speed-dry (HSD) machining is now recognized as a strong potential dry-cutting technique to tackle the rapidly growing productivity demand of carbon-fiber-reinforced-polyetheretherketone (CF/PEEK). The thermal-field is an essential breakthrough for eliminating the severe thermal effect of cutting temperature beyond CF/PEEK glass transition temperature Tg. However, the anisotropy and temperature-sensitive thermal conductivity of CF/PEEK lead to great challenges in thermal analytical modeling. Addressing this issue, a novel thermal-field analytical model that incorporates fiber orientation-dominated thermal anisotropy is developed to investigate the thermal field of machined surface layer for unidirectional (UD) CF/PEEK HSD milling, where the nonlinear thermal conductivity of CF/PEEK are imported into this model. With experiment verification, the thermal-field model can forecast the spatio-temporal distribution of workpiece temperature. Then, the thermal mechanisms of fiber orientations and milling parameters are clarified to restrict workpiece temperature within the Tg for limited thermal damage and reveal the feasibility essence of CF/PEEK HSD milling.

Self-optimization wavelet-learning method for predicting nonlinear thermal conductivity of highly heterogeneous materials with randomly hierarchical configurations

In the present work, we propose a self-optimization wavelet-learning method (SO-W-LM) with high accuracy and efficiency to compute the equivalent nonlinear thermal conductivity of highly heterogeneous materials with randomly hierarchical configurations. The randomly structural heterogeneity, temperature-dependent nonlinearity and material property uncertainty of heterogeneous materials are considered within the proposed self-optimization wavelet-learning framework. Firstly, meso- and micro-structural modeling of random heterogeneous materials are achieved by the proposed computer representation method, whose simulated hierarchical configurations have relatively high volume ratio of material inclusions. Moreover, temperature-dependent nonlinearity and material property uncertainties of random heterogeneous materials are modeled by a polynomial nonlinear model and Weibull probabilistic model, which can closely resemble actual material properties of heterogeneous materials. Secondly, an innovative stochastic three-scale homogenized method (STSHM) is developed to compute the macroscopic nonlinear thermal conductivity of random heterogeneous materials. Background meshing and filling techniques are devised to extract geometry and material features of random heterogeneous materials for establishing material databases. Thirdly, high-dimensional and highly nonlinear material features of material databases are preprocessed and reduced by wavelet decomposition technique. The neural networks are further employed to excavate the predictive models from dimension-reduced low-dimensional data. At the same time, advanced intelligent optimization algorithms are utilized to self-search the optimal network structure and learning rate for obtaining the optimal predictive models. Finally, the computational accuracy and efficiency of the presented approach are validated via various numerical experiments on realistic random composites.

Phase Stability of Hexagonal/Cubic Boron Nitride Nanocomposites.

Boron nitride (BN) is an exceptional material, and among its polymorphs, two-dimensional (2D) hexagonal and three-dimensional (3D) cubic BN (h-BN and c-BN) phases are most common. The phase stability regimes of these BN phases are still under debate, and phase transformations of h-BN/c-BN remain a topic of interest. Here, we investigate the phase stability of 2D/3D h-BN/c-BN nanocomposites and show that the coexistence of two phases can lead to strong nonlinear optical properties and low thermal conductivity at room temperature. Furthermore, spark-plasma sintering of the nanocomposite shows complete phase transformation to 2D h-BN with improved crystalline quality, where 3D c-BN possibly governs the nucleation and growth kinetics. Our demonstration might be insightful in phase engineering of BN polymorph-based nanocomposites with desirable properties for optoelectronics and thermal energy management applications.

A distributed thermal model of GaN HEMT considering nonlinear thermal conductivity and PCB effect

A distributed thermal model for analyzing the heat distribution of GaN high electron mobility transistor (HEMT) is presented in this paper. The thermal resistance calculation of multi-gate GaN HEMT with nonlinear thermal conductivity is derived. Considering the heat conduction of PCB and the nonlinear thermal conductivity, the model developed in COMSOL realizes the consistency between the simulation results and the measurement results. Based on the model, the surface and internal temperatures can be extracted for the thermal resistance calculation. The proposed method combined model simulation with numerical calculation will be helpful for designers to analyze the thermal distribution of transistors and the circuits.

Enhanced nonlinear conductivity of silicone rubber composites with hybrid graphene and alumina for cable accessory

The electric field distortion and charge accumulation in cable accessories are still challenges for high voltage direct current transmission (HVDC). Using silicone rubber (SR) based materials with nonlinear conductivity properties can ameliorate these problems in cable accessories. Herein, SR composites with hybrid filler network were prepared by adding graphene (G; 0.25 phr) and alumina particles (Al2O3; 5–40 phr) to SR to obtain good nonlinear conductivity and relative high breakdown strength, along with thermal conductivity. The SEM results showed that graphene was well dispersed between Al2O3 particles and a hybrid filler network was constructed in the SR matrix. The G/Al2O3/SR composites exhibited favorable nonlinear electrical conductivity properties and thermal conductivity properties while sustaining high breakdown strength under different electrical and temperature field. The non-linear conductivity α of the 0.25G/40Al2O3/SR composite reached 6.68 at 23 °C, whereas the breakdown field strength E0 of 49.1 kV/mm could comparable to that of pure SR. Moreover, the thermal conductivity of 0.25G/30Al2O3/SR was 0.28 Wm−1K−1 at 23 °C, which increased by 114.98% compared to pure SR. This work suggests the promising application of G/Al2O3/SR composites as cable accessory.

The approximate solution of nonlinear heat equation

AbstractNowadays there are many approximate methods for thermal conductivity calculation, that lead to satisfactory outcomes in engineering practice. With the new approach, the solution of the nonlinear thermal conductivity equation was investigated. In addition to this, we reviewed the approximate solution of the nonlinear equation of thermal conductivity with cubic nonlinearity. To solve the problems of mathematical analysis, differential and integral equations, and boundary value problems of mathematical physics, difference, and interpolation are applied. Thus, for thinking of the effectiveness and reasonableness of these approaches, it is crucial for their theoretical investigation. The solution to these questions was found for each class of equation and each of its methods in their way and was often represented as significant difficulty, and in many cases was an obstacle for the current time. A natural approach to solving this issue is the use of the ideas of functional analysis. The variational principle initially was considered as a variational approach for solving linear functional equations and finding eigenvalues of linear operators. As in any variational approach, the problem of solving an equation will be brought to finding the extremum of the certain function of a special type, given over the entire space. It was found that the approach is useful in a way of minimizing functions of the more general type.

Heat transfer and thermal analysis in a semi-spherical fin with temperature-variant thermal properties: an application of Probabilists’ Hermite collocation method

Finned surfaces are utilized in several industrial and technological applications including radiators in cars, air conditioning systems, and computer CPU heat sink to dissipate heat through convection or radiation. In this regard, the heat transfer enhancement utilizing the fins has received more attention in the scientific field. Motivated by this, the present research explicates temperature variation through a convective-radiative semi-spherical fin (SSF) with internal heating by taking into consideration of linear and nonlinear temperature-dependent heat transfer coefficient and thermal conductivities. Furthermore, the efficiency and heat transfer aspects of the fin are elaborated. The Rosseland approximation is used in this study to analyze radiation heat exchange. The developed energy equation is converted to a nonlinear ordinary differential equation (ODE) using dimensionless terms, and the probabilists’ Hermite collocation method (PHCM) is used to solve this problem. The governing parameters have been varied in their appropriate ranges to illustrate their impact on the thermal profile, and the results have been portrayed graphically. Some notable key findings of the current analysis are that as the scale of the convection–conduction and the radiation number upsurges, the thermal distribution through SSF drops. On the other hand, thermal distribution escalates for heat generation and thermal conductivity parameters.

Computational Investigations of an Internally Heated Convective-Radiative Porous Fin subjected to Magnetic Field: Comparative Methods and Parametric Studies

The concern of this paper is to compare the computational efficiencies and accuracies of three approximate analytical methods; namely, homotopy analysis method (HAM), optimal homotopy asymptotic method (OHAM) and differential transform method (DTM) for the nonlinear thermal performance analysis of a convective-radiative porous fin with temperature-dependent internal heat generation under the influence of magnetic field. To establish the computational accuracies of the three methods, the results of the three series solutions are compared with the results of the developed exact analytical and numerical methods. Also, the symbolic solutions developed in this work are used to explore the impacts of the controlling parameters on the performance of the passive device. It is established that as the coductive-convective, conductive-radiative and magnetic field parameters increase, the fin temperature distribution decreases and hence, the fin thermal efficiency is improved. An increase in temperature distribution in the fin is noticed as the nonlinear thermal conductivity parameter increases. It is envisaged that the present study will give a good insight into the nonlinear analysis of extended surfaces which will aid proper design in thermal systems.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

The new sea ice thermodynamics code for the INM RAS Earth System model: The design and comparison of one- and zero-dimensional approaches with the observational data

Abstract This work is devoted to the comparison of one- (1-D) and zero-dimensional (0-D) models of sea ice thermodynamics. 1-D thermodynamics solvers imply the solution of the diffusion equation with penetrating radiation in the moving domain (moving boundary problem), while 0-D implementations neglect the heat capacity of ice and penetrating radiation, that leads to a linear temperature profile by the construction. So far, some climate models use 0-D implementation of thermodynamics in a block of sea ice, while other models use 1-D implementation with a small number of nodes. In this work we present our fully implicit 0-D and 1-D version of snow–ice thermodynamics, which relieves the model of Courant-type time step constraints. Implicitness is achieved by the relaxation method for nonlinear heat capacity and thermal conductivity coefficients with simultaneous search for the temperature that satisfies the boundary conditions. We introduce the experiment with analytical forcing to compare evolution of temperature profiles. This model experiment shows that 0-D model underestimates ice thickness and overestimates the amplitude of temperature profile variation compared to 1-D solution. Despite the large differences in thickness and internal temperatures, the surface temperatures are very close. The models were also validated on the data of the SHEBA field experiment. According to comparison with observation data, the 0-D model predicts ice thickness and spatiotemporal temperature distribution much worse compared to 1-D model, but the amplitude of error in surface temperature is slightly greater for 0-D code. It can be concluded that 0-D model of sea ice thermodynamics is a good tool for predicting surface temperature, but it gives a large error in thickness and temperature distribution.

On Stationary Flow of Dense Plasma under Localized Energy Deposition

The paper presents a one-dimensional gas-dynamic model that gives an opportunity to establish the necessary conditions for the emergence and determine characteristics of a stationary flow of a compressible continuous medium with nonlinear thermal conductivity, an example of which is a fully or partially ionized plasma, in the presence of a localized heat source with a given power.

Analysis of Error and Stability of Nanofluid over Horizontal Channel with Heat/Mass Transfer and Nonlinear Thermal Conductivity

The current investigation aims to analyze the nanofluid flow between two infinite rotating horizontal channels. The lower plate is porous and stretchable. The impact of physical parameters such as Hall current, thermal characteristics, heat source/sink, chemical reaction on velocity, temperature, and concentration profiles are discussed through graphs. The governing equations are transformed to ordinary differential equations using suitable transformations and then solved numerically using the RK4 approach along with the shooting technique. For varying values of the Schmidt number (SN) and the chemical reaction factor (CRF), the concentration profile declines, but decreases for the activation energy. It is observed that the velocity profile declines with the increasing values of the suction factor. The velocity profile increases when the values of the rotation factors are increased. The temperature field exhibits a rising behavior with increasing values of the thermophoresis factor, Brownian motion, and the thermal radiation factor. It is also observed that the heat transfer rate is significant at the lower wall with the increasing values of the Prandtl number (PN). For the numerical solution, the error estimation and the residue error are calculated for the stability and confirmation of the mathematical model. The novelty of the present work is to investigate the irregular heat source and chemical reaction over the porous rotating channel. A growing performance is revealed by the temperature field, with the increase in the Brownian motion (BM), thermophoresis factor (TF), thermal conductivity factor (TCF), and the radiation factor (RF).

VARIABLE THERMAL CONDUCTIVITY AND VISCOSITY EFFECTS ON THIN FILM FLOW OVER AN UNSTEADY POROUS STRETCHING SHEET

The aim of our current investigation is to examine, heat and mass transfer rates of thin liquid film, considering a permeable stretching sheet. In this study, we assume that the medium is porous, the sheet is unstable, and the flow is two-dimensional with nonlinear radiation, variable viscosity, and variable thermal conductivity. Similarity variables are used to convert partial differential equations (PDEs) into dimensionless ordinary differential equations (ODEs), which are solved numerically by Runge-Kutta-Fehlberg (RKF45) method along with shooting technique. MATLAB R2017a is used to illustrate the effects of unsteady, magnetic field, permeability, radiation, suction, temperature ratio, and chemical reaction parameter on velocity, temperature, and concentration profiles. Numerical values of physical quantities are provided in tabular form. The velocity profile tends to diminish as the permeability parameter increases. Our current results show great agreement with the previously reported investigations.

Explicit Thermal Resistance Model of Self-Heating Effects of AlGaN/GaN HEMTs with Linear and Non-Linear Thermal Conductivity

We presented an explicit empirical model of the thermal resistance of AlGaN/GaN high-electron-mobility transistors on three distinct substrates, including sapphire, SiC, and Si. This model considered both a linear and non-linear thermal resistance model of AlGaN/GaN HEMT, the thickness of the host substrate layers, and the gate length and width. The non-linear nature of channel temperature-visible at the high-power dissipation stage-along with linear dependency, was constructed within a single equation. Comparisons with the channel temperature measurement procedure (DC) and charge-control-based device modeling were performed to verify the model's validity, and the results were in favorable agreement with the observed model data, with only a 1.5% error rate compared to the measurement data. An agile expression for the channel temperature is also important for designing power devices and monolithic microwave integrated circuits. The suggested approach provides several techniques for investigation that could otherwise be impractical or unattainable when utilizing time-consuming numerical simulations.

Nonlinear Thermal Response Analysis of an Internally Heated Radiative-Convective Porous Fin subjected to Magnetic Fields using Method of Lines

This paper demonstrated the computational efficiency and accuracy of method of lines for the nonlinear transient thermal response analysis of a radiative-radiative porous fin with temperature-dependent internal heat generation under the influence of magnetic fields. To establish the computational accuracy of the method, the results of the solution are compared with the results of the developed exact analytical method. Also, the numerical solutions through the method of lines are adopted to explore the impacts of the model parameters on the performance of the passive device. It is found that as the conductive-convective, conductive-radiative, and magnetic field parameters increase, the fin temperature distribution in the fin decreases. The temperature distribution in the fin increases through the ?n as the nonlinear thermal conductivity parameter increases. It is hoped that the present study gives a good insight into the nonlinear analysis of the extended surface which will aid the proper design of the extended surfaces in thermal systems.

Determination of thermophysical characteristics in a nonlinear inverse heat transfer problem

This paper presents a detailed and developed method for finding soil nonlinear thermophysical characteristics. Two-layer container complexes are constructed. The side faces of which are thermally insulated, so that one can use the one dimensional heat equation. In order not to solve the boundary value problem with a contact discontinuity and not to lose the accuracy of the solution method, a temperature sensor was placed at the junction of the two media, and a mixed boundary value problem is solved in each region of the container. In order to provide the initial data for the inverse coefficient problem, two temperature sensors are used: one sensor was placed on the open border of the container and recorded the temperature of the soil at this border, and the second sensor was placed at a short distance from the border, which recorded the air temperature. The measurements were carried out in the time interval (0,4tmax). At first, the initial-boundary value problem of nonlinear thermal conductivity equation with temperature dependent coefficients of thermal conductivity, heat capacity, heat transfer and material density is investigated numerically. The nonlinear initial-boundary value problem is solved by the finite difference method. Two types of difference schemes are constructed: linearized and nonlinear. The linearized difference scheme is implemented numerically by the scalar Thomas’ method, and the nonlinear difference problem is solved by the Newton’s method. Assuming the constancy of all thermophysical parameters, except for the thermal conductivity of the material, on the segment (0,tmax), the quadratic convergence of Newton’s method is proved and the thermal conductivity is calculated, while the solution of the linearized difference problem was taken as the initial approximation for the Newton’s method. By freezing all other thermophysical parameters, and using the measured temperatures in the segment (tmax,2tmax), the coefficient of specific heat of the material is found. Proceeding in a similar way, using the initial data on the segment (2tmax,3tmax), the density of the soil is determined. Also, based on the measured initial data on the segment (3tmax,4tmax), the heat transfer coefficient is determined.Based on the experimentally measured data, at each time interval, the corresponding functional is minimized using the gradient descent method. The differentiation of a nonlinear difference problem with respect to the desired parameter method is used to find the gradient of the functional. This method allows you to find the functional gradient and the damping coefficient of the gradient descent in an explicit form. In this case, the compilation and solution of the conjugate problem, which is a frequently used method for solving the inverse problems, is not needed.The performed numerical calculations show that for small time intervals the solutions of the linearized difference problem differ little from the solution of the nonlinear difference problem (1 - 3%). And for long periods of time, tens of days or months, the solutions of the two methods differ significantly, sometimes exceeding 20%. In addition, all thermophysical characteristics (8 coefficients) were found for a two-layer container with sand and black soil. Also the dependence of the temperature difference at the boundary between the environment and the soil for the heat transfer coefficient was shown.

A Stefan problem with nonlinear thermal conductivity

The solution is obtained and validated by an existence and uniqueness theorem for the following nonlinear boundary value problem which was proposed in 1974 by Cho and Sunderland to represent a Stefan problem with a nonlinear temperature‐dependent thermal conductivity on the semi‐infinite line . The modified error function of two parameters is introduced to represent the solution of the problem above, and some properties of the function are established. This generalizes the results obtained in earlier studies.

Spectral relaxation computation of Maxwell fluid flow from a stretching surface with quadratic convection and non-Fourier heat flux using Lie symmetry transformations

A mathematical model for nonlinear quadratic convection with non-Fourier heat flux in coating boundary layer flow of a Maxwell viscoelastic fluid is presented. Nonlinear quadratic thermal radiation and heat source/ sink effects are also considered. The transformations of Lie symmetry are employed. The resultant nonlinear differential equations with defined boundary conditions are numerically solved using the spectral relaxation technique (SRM), a robust computational methodology. Graphical visualization of the velocity and temperature profiles is included for a range of different emerging parameters. For skin friction and the Nusselt number, numerical data are also provided. There is a very strong correlation between the outcomes of this study and those published in the literature. Higher values of the nonlinear thermal radiation, mixed convection, thermal conductivity, nonlinear convection and heat source/ generation parameters increase temperature as well as the thickness of the thermal boundary layer. However, a higher Prandtl number, thermal relaxation parameter and heat sink/ absorption parameter all reduce temperature. Deborah number causes velocity to be raised (and momentum boundary layer thickness to be lowered), whereas raising nonlinear mixed convection parameter causes velocity to be decreased (and momentum boundary layer thickness to be increased), and a velocity overshoot is calculated. The models are applicable to simulations of high-temperature polymeric coatings in material processing.

An Application of the Finite Element Method for Heat and Mass Transfer of Boundary Layer Flow Using Variable Thermal Conductivity and Mass Diffusivity

Since mass diffusivity and thermal conductivity cannot be considered constants in practical analysis, an existing heat and mass transfer model of unsteady mixed convection flow over a stretching sheet is modified by incorporating the effects of nonlinear mixed convection variable thermal conductivity and mass diffusivity and solved its dimensionless form by applying the finite element method which is the main novelty of this work. Nonlinear governing equations are created because of changing thermal conductivity and mass diffusivity. Nonlinear solutions can be achieved by employing the Galerkin finite element approach. Temperature and concentration-based thermal conductivity and mass diffusivity are considered. The model is expressed as a set of partial differential equations, and furthermore, it is reduced to a system of dimensionless ordinary differential equations. These obtained equations are solved with the finite element method with linear interpolating polynomials and numerical integration. In addition, a Matlab solver bvp4c is also considered for comparison purposes or validation of the computed results. The graphs depict the effect of various parameters on the velocity, temperature, and concentration curves. The results show that thermal and diffusive wave propagation is significantly affected by thermal conductivity and mass diffusivity changes. Results show that flow velocity escalates by rising values of thermal and solutal Grashof numbers.