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Based on the combined finite-discrete element method (FDEM), a two-dimensional coupled hydro-thermal model is proposed. This model can simulate fluid flow and heat transfer in rock masses with arbitrary complex fracture networks. The model consists of three parts: a heat conduction model of the rock matrix, a heat-transfer model of the fluid in the fracture (including the heat conduction and convection of fluid), and a heat exchange model between the fluid and rock at the fracture surface. Three examples with analytical solutions are given to verify the correctness of the coupled model. Finally, the coupled model is applied to hydro-thermal coupling simulations of a rock mass with a fracture network. The temperature field evolution, the effect of thermal conductivity of the rock matrix thermal conductivity and the fracture aperture on the outlet temperature are studied. The coupled model presented in this paper will enable the application of FDEM to study rock rupture driven by the effect of hydro-thermo-mechanical coupling in geomaterials such as in geothermal systems, petroleum engineering, environmental engineering and nuclear waste geological storage.

Purpose This study aims to examine the impacts of higher memory dependencies on a novel semiconductor material that exhibits generalized photo-piezo-thermo-elastic properties. Specifically, the research focuses on analyzing the behavior of the semiconductor under three distinct temperature models. Design/methodology/approach The study assumes a homogeneous and orthotropic piezo-semiconductor medium during photo-thermal excitation. The field equations have been devised to encompass higher order parameters, temporal delays and a specifically tailored kernel function to address the problem. The eigenmode technique is used to solve these equations and derive analytical expressions. Findings The research presents graphical representations of the physical field distribution across different temperatures, higher order plasma heat conduction models and time. The results reveal that the amplitude of the distribution profile is markedly affected by factors such as the memory effect, time, conductive temperature and spatial coordinates. These factors cannot be overlooked in the analysis and design of the semiconductor. Research limitations/implications Specific cases are also discussed in detail, offering the potential to advance the creation of precise models and facilitate future simulations. Practical implications The research offers valuable information on the physical field distribution across various temperatures, allowing engineers and designers to optimize the design of semiconductor devices. Understanding the impact of memory effect, time, conductive temperature and spatial coordinates enables device performance and efficiency improvement. Originality/value This manuscript is the result of the joint efforts of the authors, who independently initiated and contributed equally to this study.

Purpose The purpose of this study is to compare interpolation algorithms and deep neural networks for inverse transfer problems with linear and nonlinear behaviour. Design/methodology/approach A series of runs were conducted for a canonical test problem. These were used as databases or “learning sets” for both interpolation algorithms and deep neural networks. A second set of runs was conducted to test the prediction accuracy of both approaches. Findings The results indicate that interpolation algorithms outperform deep neural networks in accuracy for linear heat conduction, while the reverse is true for nonlinear heat conduction problems. For heat convection problems, both methods offer similar levels of accuracy. Originality/value This is the first time such a comparison has been made.

Quantum physics predicts that there is a fundamental maximum heat conductance across a single transport channel and that this thermal conductance quantum, G Q , is universal, independent of the type of particles carrying the heat. Such universality, combined with the relationship between heat and information, signals a general limit on information transfer. We report on the quantitative measurement of the quantum-limited heat flow for Fermi particles across a single electronic channel, using noise thermometry. The demonstrated agreement with the predicted G Q establishes experimentally this basic building block of quantum thermal transport. The achieved accuracy of below 10% opens access to many experiments involving the quantum manipulation of heat.

Purpose The purpose of this paper is to address unsteady heat conduction in two subsets of ordinary bodies. One subset consists of a large plane wall, a long cylinder and a sphere in one dimension. The other subset consists of a short cylinder and a large rectangular bar in two dimensions. The prevalent assumptions in the two subsets are: constant initial temperature, uniform surface heat flux and thermo-physical properties invariant with temperature. The engineering applications of the unsteady heat conduction deal with the determination of temperature–time histories in the two subsets using electric resistance heating, radiative heating and fire pool heating. Design/methodology/approach To this end, a novel numerical procedure named the enhanced method of discretization in time (EMDT) transforms the linear one-dimensional unsteady, heat conduction equations with non-homogeneous boundary conditions into equivalent nonlinear “quasi–steady” heat conduction equations having the time variable embedded as a time parameter. The equivalent nonlinear “quasi–steady” heat conduction equations are solved with a finite difference method. Findings Based on the numerical computations, it is demonstrated that the approximate temperature–time histories in the simple subset of ordinary bodies (large plane wall, long cylinder and sphere) exhibit a perfect matching over the entire time domain 0 < t < ∞ when compared against the rigorous exact temperature–time histories expressed by classical infinite series. Furthermore, using the method of superposition of solutions in the convoluted subset (short cylinder and large rectangular crossbar), the same level of agreement in the approximate temperature–time histories in the simple subset of ordinary bodies is evident. Originality/value The performance of the proposed EMDT coupled with a finite difference method is exhaustively assessed in the solution of the unsteady, one-dimensional heat conduction equations with prescribed surface heat flux for: a subset of one-dimensional bodies (plane wall, long cylinder and spheres) and a subset of two-dimensional bodies (short cylinder and large rectangular bar).

The three-dimensional numerical manifold method (3D-NMM), which is based on the derivation of Galerkin’s variation, is a powerful calculation tool that uses two cover systems. The 3D-NMM can be used to handle continue-discontinue problems and extend to THM coupling. In this study, we extended the 3D-NMM to simulate both steady-state and transient heat conduction problems. The modelling was carried out using the raster methods (RSM). For the system equation, a variational method was employed to drive the discrete equations, and the crucial boundary conditions were solved using the penalty method. To solve the boundary integral problem, the face integral of scalar fields and two-dimensional simplex integration were used to accurately describe the integral on polygonal boundaries. Several numerical examples were used to verify the results of 3D steady-state and transient heat-conduction problems. The numerical results indicated that the 3D-NMM is effective for handling 3D both steady-state and transient heat conduction problems with high solution accuracy.

In this article, the local fractional Homotopy perturbation method is utilized to solve the non-homogeneous heat conduction equations. The operator is considered in the sense of the local fractional differential operator. Comparative results between non-homogeneous and homogeneous heat conduction equations are presented. The obtained result shows the non-differentiable behavior of heat conduction of the fractal temperature field in homogeneous media.

The non-Fourier effects, such as wave-like temperature propagation and boundary temperature jumps, arise in nanosized systems due to the multiple time and space scales nature of out-of-equilibrium heat transport. The relaxation to equilibrium occurs in successive time and space scales due to couplings between different excitations, whose relaxation times have different physical meanings and may differ significantly in magnitude. The out-of-equilibrium temperature evolution is described by a hierarchy of partial differential equations of a higher order, which includes both the diffusive and wave modes of heat transport. The critical conditions of transition from wave to diffusive modes are identified. We demonstrate that the answer to the question concerning which of these modes would be detected by experimental measurements may also depend on the accuracy of the experimental setup. Comparisons between the proposed approach and other non-Fourier models, such as the Guyer–Krumhansl and Jeffreys type, are carried out. The results presented here are expected to be useful for the theoretical and experimental treatment of non-Fourier effects and particularly heat wave phenomena in complex nanosized systems and metamaterials.

A new kernel function, termed the closed-box kernel function, has been developed to address numerical simulation of transient heat conduction in the same medium. Firstly, this method is versatile and not limited to specific industrial scenarios or designated materials. Secondly, the method solves the spatial temperature at each time point only once, eliminating the need for multiple iterations. Thirdly, the method allows for controlled and adjustable simulation speed of heat conduction while maintaining high accuracy. After 24,700 iterations in the transient process, the relative error in temperature values is merely 0.000072. Fourthly, this numerical technique can break data dependency between spatial nodes, making it suitable for parallel computing with Graphics Processing Units (GPUs). The average speedup achieved is 94.0712 times faster compared to Central Processing Unit (CPU) computations. Finally, we provide mathematical examples to verify the correctness and accuracy of this numerical approach and present a computational framework for parallel computing in the Visual Studio (VS) programming environment to demonstrate its practicality in engineering applications.

In this article, the nonlinear hygrothermally induced vibrational behavior of bidirectional functionally graded porous beams is studied through a numerical approach. Two-dimensional material and temperature distributions, even and uneven porosity distributions, temperature-dependent nature of material properties, and hygroscopic effects are all taken into account in studying beam’s lateral deflection. All material properties are assumed to vary along both thickness and axial directions of beam following a modified power-law distribution in terms of volume fractions of the material constituents, which are considered temperature dependent using Touloukian experiments. Beam's upper surface is subjected to a sudden temperature rise, while its lower surface is kept at reference temperature or is thermally adiabatic; meanwhile, left and right boundaries are thermally insulated. Two-dimensional transient heat conduction equation is solved using generalized differential quadrature (GDQ) method for discretizing spatial derivatives, while time derivatives are approximated using Newmark-beta integration method. Nonlinear sinusoidal moisture concentration is assumed through the thickness direction. Governing equations of motion are derived based on Timoshenko beam theory (TBT) and with the assumption of Von-Kármán geometrical nonlinearity, which is solved afterward using an iterative scheme in conjunction with GDQ and Newmark's method. Finally, the effects of porosity volume fractions, porosity cases, thermal boundary conditions, moisture concentration, FG indexes, slenderness ratio, and temperature rise on maximum non-dimensional lateral deflection are investigated considering various boundary conditions.