Heat Transport Law Research Articles

Nonanomalous heat transport in a one-dimensional composite chain.

Translation-invariant low-dimensional systems are known to exhibit anomalous heat transport. However, there are systems, such as the coupled-rotor chain, where translation invariance is satisfied, yet transport remains diffusive. It has been argued that the restoration of normal diffusion occurs due to the impossibility of defining a global stretch variable with a meaningful dynamics. In this Letter, an alternative mechanism is proposed, namely, that the transition to anomalous heat transport can occur at a scale that, under certain circumstances, may diverge to infinity. To illustrate the mechanism, I consider the case of a composite chain that conserves local energy and momentum as well as global stretch, and at the same time obeys, in the continuum limit, Fourier's law of heat transport. It is shown analytically that for vanishing elasticity the stationary temperature profile of the chain is linear; for finite elasticity, the same property holds in the continuum limit.

Influence of memory-dependent derivative on generalized thermoelastic rotating porous solid via three-phase-lag model

This paper is concerned with the influence of memory-dependent heat transport law on rotating thermoelastic medium with voids via three-phase-lag. The entire pervious medium is rotating with a invariant angular haste, where the bounding airplane is subordinated to a thermal shock and is free of tractions. By employing the normal mode analysis, the exact expressions for the displacement components, stresses, temperature distribution and change in volume fraction field have been depicted graphically in the presence and the absence of gyration and memory-dependent outgrowth. The effect of the voiding is also bandied in the literature review.

A Water and Heat Coupling Model for GW-SW Interaction Considering Nonuniform Heat Transfer Effects of Soil.

An accurate groundwater-surface water (GW-SW) and heat coupling model (WHCM) aids in exploration of water migration and heat transport laws in the sedimentary layers of riverbeds and riparian zones, which is critical for understanding the transport patterns of contaminants in sediments. In this paper, a novel WHCM for GW-SW interaction is proposed by incorporating an effective soil thermal conductive model (ESTCM) into the advection-dispersion equation to address the shortcomings of current simulations that fail to account for the nonuniform heat transfer of soil. The model is developed in COMSOL, and the numerical implementation method is illustrated in detail. Furthermore, six recommended ESTCMs are examined in the WHCM to validate and compare the model simulation effects based on field test observations in the Walker River, USA. The results demonstrate that the proposed model performs better than the model that does not account for the nonuniform heat transfer effects of the soil in simulating GW-SW water and heat exchange. Meanwhile, the proposed model's simulation effects based on the Y2019 model perform the best. The orthogonal test revealed that the hydraulic conductivity ks and porosity n are the two most sensitive parameters influencing the model output results of groundwater seepage velocity and temperature, respectively. The efforts of this work can offer technical assistance and a guide for enhancing the simulation effect of river GW-SW water and heat exchange.

Analysis on Cattaneo-Christov heat flux in three-phase oscillatory flow of non-Newtonian fluid through porous zone bounded by hybrid nanofluids

The primary aspect of this study is a theoretical analysis of heat transfer enhancement in the unsteady three-phase oscillatory flow of Casson fluid bounded by the layers of nanofluid and hybrid nanofluids flowing adjacent to the walls of a long-infinite horizontal composite channel. Stoke’s model is employed to define Casson fluid, and one phase model is implemented for nanofluid. Moreover, Cattaneo–Christov heat flux model is also considered. This model amends Fourier’s law of heat transport using thermal relaxation time due to which heat passes through the channel within a finite limit. Analytical solutions are attained through a regular perturbation technique by employing periodic and non-periodic functions and presented through graphical illustrations by implementing the MATHEMATICA program. The outcomes are exhibited with three types of nanomaterials such as copper Cu , copper oxide CuO and copper alumina Cu–Al 2 O 3 with base fluid as water. It is noted that the momentum and heat transport is significant in the case of Casson fluid with porous zone sandwiched between Cu water NFs as compared to Cu–CuO–H 2 O (phase I) and Cu–Al 2 O 3 –H 2 O (phase III) HNFs. Moreover, in the case of injection, it is observed that the effects of Cu nanomaterials are dominant on temperature. On the other side, in suction, the impacts of Cu–Al 2 O 3 nanomaterials are significant on temperature. The results are also compared with a well-known numerical method named as finite element method.

Influence of snow cover on temperature field of frozen ground

Research on the effect of snow on the temperature field of frozen ground is of great significance to the laying of underground oil pipelines, design of roads, and control of frost damage in cold regions. The heat transport laws of frozen ground with phase changes under periodic temperature boundary conditions were analyzed based on data monitoring in this paper. Based on the boundary conditions determined by the monitoring data, the numerical calculations of frozen ground and subgrade with/without snow cover were carried out, and the effects of snow cover on the temperature fields of frozen ground and subgrade in cold regions were explored. Monitoring results demonstrate that the temperature at different sections of frozen ground with phase change presents a sine-like function under the periodic temperature boundary condition. According to monitoring data, when the thickness of the natural surface snow cover is about 25 cm, the daily average minimum temperature of soil at 0.1 m from the surface will rise by about 10 °C compared to that without snow cover during a year (in a cycle); nevertheless, when combined with numerical calculation, the permafrost table increases by about 2.87 m, and the permafrost base decreases by more than 5.59 m. Under the boundary conditions set in this paper, the permafrost under the subgrade disappears in a greater area due to the construction of the subgrade in the snow-covered area. In addition, the elliptical thawing soil area produced by the lower part of the slope of a snow-covered subgrade will adversely affect its stability.

Nonlocal effects in a functionally graded thermoelastic layer due to volumetric absorption laser

The primary focus of the present contribution is to develop a new system of differential equations describing the nonlocal thermoelasticity theory. The problem deals with the thermoelastic interaction in a nonhomogeneous thermoelastic layer induced by absorbing penetrating laser radiation throughout its volume. The heat conduction equation has been formulated in the context of memory dependent three-phase lag model. The surfaces of the layer are thermally insulated and free of traction. Employing the integral Laplace transform technique, the solutions of the field quantities have been achieved in the transformed domain. The corresponding solutions in the space–time domain have been derived using the numerical inversion of the Laplace transform by Riemann-sum approximation technique. The numerical estimates of the field quantities have been depicted graphically to address the effects of nonlocality and memory effects on the temperature profile, displacement and stress components. The effect of the delay time, nonhomogeneity and various choices of linear and nonlinear kernel functions in the heat transport law have also been reported.

Effect of nonlocality in the vibration of a microscale ribbon due to laser pulse

ABSTRACT The vibration analysis of elastic medium is very important along with the miniaturization of the device and wide application of ultra-fast lasers, where size effect on heat conduction and elastic deformation increase and classical theory of thermoelastic coupling does not hold any more. Due to these, size-dependent thermoelastic model have been introduced for higher order simple material to adopt both the size effect of heat conduction and elasticity with the aids of extended irreversible thermodynamics and generalized free energy. Keeping this in mind, the present analysis reports the effect of ultra-short-pulsed laser heating in coupled thermoelastic vibration of a microscale ribbon resonator. The heat transport law of the current problem is defined by incorporating the three-phase-lag heat transport law in the context of Caputo–Fabrizio (CF) derivative. Finite sinusoidal Fourier and Laplace transform techniques have been employed to determine the lateral vibration of the ribbon and the temperature increment within the microscale ribbon. The result provides the direction how the nonlocality and size-dependence can control the vibration analysis and some excellent predictive capability have been demonstrated due to the presence of energy absorption depth and the order of CF derivative also.

Authors’ reply to Comment on “Magneto-thermoelastic interaction in a reinforced medium with cylindrical cavity in the context of Caputo–Fabrizio heat transport law, S. Mondal, A. Sur, M. Kanoria, Acta Mech 230, 4367–4384 (2019)” by A. Pantokratoras

Authors’ reply to Comment on “Magneto-thermoelastic interaction in a reinforced medium with cylindrical cavity in the context of Caputo–Fabrizio heat transport law, S. Mondal, A. Sur, M. Kanoria, Acta Mech 230, 4367–4384 (2019)” by A. Pantokratoras

The Caputo‐Fabrizio heat transport law in vibration analysis of a microscale beam induced by laser

AbstractIn the application of pulsed laser heating, such as laser hardening of metallic surfaces, conduction limited process is the dominant mechanism during the laser–workpiece interaction. As a consequence, time unsteady analysis of this problem becomes necessary. The present study examines the effect of ultra‐short‐pulsed laser heating in coupled thermoelastic vibration of a microscale beam resonator. The heat transport equation for the current problem is defined by incorporating the three‐phase‐lag heat transport law in the context of Caputo‐Fabrizio (CF) derivative. Finite sinusoidal Fourier and Laplace transform techniques have been employed to determine the lateral vibration of the beam and the temperature increment within the microscale beam. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed. Excellent predictive capability is demonstrated due to the presence of energy absorption depth and the order of CF derivative also.

Comment on the paper “Magneto-thermoelastic interaction in a reinforced medium with cylindrical cavity in the context of Caputo–Fabrizio heat transport law, Sudip Mondal, Abhik Sur, M. Kanoria, Acta Mech 230, 4367–4384 (2019)”

Comment on the paper “Magneto-thermoelastic interaction in a reinforced medium with cylindrical cavity in the context of Caputo–Fabrizio heat transport law, Sudip Mondal, Abhik Sur, M. Kanoria, Acta Mech 230, 4367–4384 (2019)”

Generalized ballistic-conductive heat transport laws in three-dimensional isotropic materials

General constitutive equations of heat transport with second sound and ballistic propagation in isotropic materials are given using non-equilibrium thermodynamics with internal variables. The consequences of Onsager reciprocity relations between thermodynamic fluxes and forces and positive definiteness of the entropy production are considered. The relation to theories of Extended Thermodynamics is discussed in detail. We provide an explicit expression for all the components of the matrices of the transport coefficients. The expressions are cumbersome but are expected to be useful for computer programming for simulations of the corresponding physical effects.

Transient heating in a spherical tissue due to thermal therapy in the context of memory-dependent heat transport law

The objective of the present study is to formulate the bio-heat model to study the variations of temperature profile and thermal damages within a spherical living tissue subjected to a thermal therapy, whose outer surface is thermally insulated. The heat conduction equation is formulated in the context of convolution-type Dual-phase (DP) lag memory-dependent derivative, having kernels to be power functions, from which, the Lord–Shulman model can be obtained as a particular case. The Laplace transform technique is implemented to solve the governing equations. The influences of the memory-dependent derivative and effect of time-delay parameters on the temperature of skin tissues and the thermal injuries are precisely demonstrated. The thermal injuries of the tissue are assessed by the denatured protein range. The numerical inversion of the Laplace transform is performed with the help of Zakian methods. The numerical outcomes of thermal injuries and temperatures have been represented graphically. Excellent predictive capability is demonstrated to identify an appropriate therapy to select different kernel functions for effective heating in hyperthermia treatment. Significant effect of the thermal therapy is reported due to the effect of delay time also.

Memory responses in a three-dimensional thermo-viscoelastic medium

ABSTRACT Due to the shortcomings of power law distributions in the heat transfer laws of fractional calculus, some other forms of derivatives with few other kernel functions have been proposed. This literature survey focuses on the mathematical model of thermo-viscoelasticity which investigates the transient phenomena in a three-dimensional thermoelastic medium in the context of two-temperature Kelvin–Voigt three-phase-lag model of generalized thermoelasticity, defined in integral form on a slipping interval incorporating the memory-dependent heat transport law. The bounding plane is subjected to a time-dependent thermal loading and is free of tractions. Incorporating normal mode as a tool, the problem has been solved analytically in terms of normal modes and the physical fields have been depicted graphically for a copper-like material. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed. Excellent predictive capability is demonstrated due to the presence of memory-dependent derivative, effect of delay time and viscosity also.

Will direct exposure to the Sun damage all digital cameras equally?

Considerations of optical damage induced by thermal effects were initiated by an apparent paradox: small and large diameter lenses with the same f-number produce an image of the Sun with the same irradiance. Thus, if one assumes that a damage threshold is given by irradiance (or intensity, as it is specified by most laser optics companies, in relation to continuous-wave lasers), all digital cameras should have the same probability of being damaged when pointed at the Sun. However, smartphones and in general small cameras are unaffected, while optical sensor arrays of larger cameras are often overheated and irreversibly damaged by the Sun. Therefore, the temperature rise responsible for the damage is not simply due to the irradiance of the Sun’s image, but is actually related to lens size in a more subtle way. A simple thermal model shows that such a temperature rise is proportional to the linear power density (power/illuminated spot diameter) at focus. A web search shows that this important result is generally overlooked, although it is used by two renowned laser optics companies. This short article discusses the heating of an optical sensor as a practical example of applications of geometrical optics and heat transport laws at an undergraduate level.

Thermal radiation in Rayleigh-Bénard convection experiments.

An important question in turbulent Rayleigh-Bénard convection (RBC) is the effectiveness of convective heat transport, which is conveniently described via the scaling of the Nusselt number (Nu) with the Rayleigh (Ra) and Prandtl (Pr) numbers. In RBC experiments, the heat supplied to the bottom plate is also partly transferred by thermal radiation. This heat transport channel, acting in parallel with the convective and conductive heat transport channels, is usually considered insignificant and thus neglected. Here we present a detailed analysis of conventional far-field as well as strongly enhanced near-field radiative heat transport occurring in various RBC experiments. A careful inclusion of the radiative transport appreciably changes the Nu=Nu(Ra) scaling inferred in turbulent RBC experiments near ambient temperature utilizing gaseous nitrogen and sulfur hexafluoride as working fluids. On the other hand, neither the conventional far-field radiation nor the strongly enhanced near-field radiative heat transport appreciably affects the heat transport law deduced in cryogenic helium RBC experiments.

Classical 1/3 scaling of convection holds up to Ra = 1015

The global transport of heat and momentum in turbulent convection is constrained by thin thermal and viscous boundary layers at the heated and cooled boundaries of the system. This bottleneck is thought to be lifted once the boundary layers themselves become fully turbulent at very high values of the Rayleigh number [Formula: see text]-the dimensionless parameter that describes the vigor of convective turbulence. Laboratory experiments in cylindrical cells for [Formula: see text] have reported different outcomes on the putative heat transport law. Here we show, by direct numerical simulations of three-dimensional turbulent Rayleigh-Bénard convection flows in a slender cylindrical cell of aspect ratio [Formula: see text], that the Nusselt number-the dimensionless measure of heat transport-follows the classical power law of [Formula: see text] up to [Formula: see text] Intermittent fluctuations in the wall stress, a blueprint of turbulence in the vicinity of the boundaries, manifest at all [Formula: see text] considered here, increasing with increasing [Formula: see text], and suggest that an abrupt transition of the boundary layer to turbulence does not take place.

Wave propagation analysis of porous asphalts on account of memory responses

In the present literature, a new set of governing equations for a mathematical model of generalized thermoelasticity in a poroelastic asphalt have been derived in the context of the memory-dependent heat transport equation involving three phase lags in the heat transport law. The present examination overcomes the shortcomings of power law distributions in fractional derivatives, and some other forms of derivatives with few other kernel functions are proposed. Employing the Laplace transform as tool, the analytical results for the distributions of the thermophysical quantities have been derived. The numerical inversion of the Laplace transform is carried out using a suitable scheme based on the Riemann-sum approximation technique. The numerical computations are performed for a porous asphalt in which, the boundaries of the solid and fluid phases are traction-free and are subjected to prescribed thermal loadings. The numerical computations and the associated results also demonstrate how the temperature, stresses, strains, in solid and fluid phases, the displacement in the solid phase and the velocity of the fluid phases have been influenced for various set of kernel functions. Also, significant effect of the time-delay parameter is discussed in the analysis.

Graph theory-based heat current analysis method for supercritical CO2 power generation system

Supercritical carbon dioxide (sCO2) power generation system holds tremendous potential in energy utilization fields featuring with its high efficiency, compactness, and security. However, dramatic variations in sCO2 thermophysical properties make the existing constant property analysis methods imprecise. In this contribution, inlet temperature difference-based thermal resistance transforms the nonlinear governing equations of heat transfer process into linear forms, and applying the graph theory builds the heat current model of a sCO2 recompression cycle with consideration of fluid property variation, which is analogous to electric circuit. Therefore, utilizing the electric circuit principle offers the overall heat transport and conversion laws in the whole system and gives the integral mathematical relations of all independent variables, which are solved by the newly proposed iterative divide-and-conquer solution algorithm. Finally, optimization of a typical sCO2 recompression system under different boundary conditions shows the applicability and conciseness of the heat current method compared to the existing analysis methods.

Influence of Moving Heat Source on Skin Tissue in the Context of Two-Temperature Caputo–Fabrizio Heat Transport Law

Modeling and understanding heat transport and temperature variations within biological tissues and body organs are key issues in medical thermal therapeutic applications, such as hyperthermia cancer treatment. In this analysis, the bio-heat equation has been studied in the context of a new formulation using Caputo–Fabrizio (CF) heat transport law. The heat equation for this problem involving the Three-Phase (3P)-lag model under two-temperature theory. The Laplace transform technique is implemented to solve the governing equations. The influences of the CF order, the two-temperature parameter and moving heat source velocity on the temperature of skin tissues have been precisely investigated. The numerical inversion of the Laplace transform is carried out using the Zakian method. The numerical outcomes of conductive temperature and thermodynamic temperatures have been represented graphically. Excellent predictive capability is demonstrated for identification of appropriate procedure to select different CF order to reach effective heating in hyperthermia treatment. Significant effect of thermal therapy is reported due to the effect of CF order, the two-temperature parameter and the velocity of moving heat source as well.

Transient heating within skin tissue due to time-dependent thermal therapy in the context of memory dependent heat transport law

In the present analysis, the bio-heat equation has been studied in the context of memory responses which is defined in the form of convolution having kernels as power functions. The heat transport equation for this problem involving the memory dependent derivative on a slipping interval in the context of Lord-Shulman (LS) model is formulated. The thermal damage within the skin tissue during the thermal therapy is also reported in the literature. Laplace transform technique is implemented to solve the governing equations. The influences of the memory-dependent derivative and time-dependent moving heat source velocity on the temperature of skin tissues and the thermal injuries are precisely investigated. The thermal injuries to the tissue are assessed by the denatured protein range using the current formulation in which the numerical inversion of the Laplace transform is carried out using Zakian methods. The numerical outcomes of thermal injuries and temperatures have been represented graphically. Excellent predictive capability is demonstrated for identification of appropriate procedure to select different kernel functions to reach effective heating in hyperthermia treatment. Significant effect of the thermal therapy is reported due to the effect of delay time also.