Time-dependent Heat Research Articles

Memory response in quasi-static thermoelastic stress in a rod due to distributed time-dependent heat sources

PurposeTo find the quasi-static thermoelastic stress and displacement, the proposed model looks at how the microstructures interact with each other and how the temperature changes inside a rod. It uses the fractional-order dual-phase-lag (FODPL) theory to derive analytical solutions for one-dimensional problems in nonsimple media within the MDD framework. The dimensionless equations are used to analyze a finite rod experiencing the heat sources continuously distributed over a finite portion of the rod which vary with time according to the ramp-type function with other sectional heat supplies kept at zero temperature. The study introduces a technique using integral transforms for exact solutions in the Laplace transform domain for different kernel functions.Design/methodology/approachA novel mathematical model incorporating dual-phase-lags, two-temperatures and Riesz space-fractional operators via memory-dependent derivatives has been established to analyze the effects of thermal stress and displacement in a finite rod. The model takes into account the continuous distribution of heat sources over a finite portion of the rod and their time variation according to the ramp-type function. It incorporates the finite Riesz fractional derivative in two-temperature thermoelasticity with dual-phase-lags via memory effect, and its solution is obtained using Laplace transform with respect to time and sine-Fourier transform with respect to spatial coordinates defined over finite domains.FindingsIn memory-dependent derivatives, thermal field variables are strongly influenced by the phase-lag heat flux and temperature gradient. The non-Fourier effects of memory-dependent derivatives substantially impact the distribution and history of the thermal field response, and energy dissipation may result in a reduction in temperature without heat transfer. The temperature, displacement and stress profile exhibit a reduced magnitude with the MDD effect compared to when the memory effect is absent (without MDD). To advance future research, a new categorization system for materials based on memory-dependent derivative parameters, in accordance with the principles of two-temperature thermoelasticity theory, must be constructed.Research limitations/implicationsThe one-dimensional assumption introduces limitations. For example, local heating of a one-dimensional plate will not extend radially, and heating one side will not heat the surrounding sides. Furthermore, while estimating heat transfer, object shape limits may apply.Originality/valueThis paper aims to revise the classical Fourier law of heat conduction and develop analytical solutions for one-dimensional problems using fractional-order dual-phase-lag (FODPL) theory in nonsimple media in the context of MDD.

A fully implicit, asymptotic-preserving, semi-Lagrangian algorithm for the time dependent anisotropic heat transport equation

In this paper, we extend the operator-split asymptotic-preserving, semi-Lagrangian algorithm for time dependent anisotropic heat transport equation proposed in Chacón et al. (2014) [18] to use a fully implicit time integration with backward differentiation formulas. The proposed implicit method can deal with arbitrary heat-transport anisotropy ratios χ∥/χ⊥⋙1 (with χ∥, χ⊥ the parallel and perpendicular heat diffusivities, respectively) in complicated magnetic field topologies in an accurate and efficient manner. The implicit algorithm is second-order accurate temporally and demonstrates an accurate treatment at boundary layers (e.g., island separatrices), which was not ensured by the operator-split implementation. The condition number of the resulting algebraic system is independent of the anisotropy ratio, and is inverted with preconditioned GMRES. We propose a simple preconditioner that renders the finite-dimensional linear operator compact, resulting in mesh-independent convergence rates for topologically simple magnetic fields, and convergence rates scaling as ∼(NΔt)1/4 (with N the total mesh size and Δt the timestep) in topologically complex magnetic-field configurations. We demonstrate the accuracy and performance of the approach with test problems of varying complexity, including an analytically tractable boundary-layer problem in a straight magnetic field, and a topologically complex magnetic field featuring magnetic islands with extreme anisotropy ratios (χ∥/χ⊥=1010).

Theoretical study of solidification phase change heat and mass transfer with thermal resistance and convection subjected to a time-dependent boundary condition

The solidification of phase-change materials (PCMs) is a key process that occurs commonly in materials science and metallurgy, such as in the casting of alloys and energy management systems. There is a lot of literature in this area that assumes the PCMs are in close contact with the heat source or sink. However, a non-freezing wall frequently encloses them in practical situations. This work presents a phase change problem that describes the solidification of a semi-infinite PCM with thermal resistance. We assume that time-dependent heat flux drives the solidification process. The PCM first convert into mush and then into solid, which leads to a three-region problem. The current study accounts for both conduction as well as convection heat transfer mechanisms. Unfortunately, the exact solution to such problems with time-dependent flux-type boundary conditions may not be possible. Thus, there is considerable interest in deriving the analytical solution. The space–time transformation yields the analytical solution to the problem. A numerical example of Al−Cu alloy with 5%Cu is presented to demonstrate the current study. Thermal resistance shows a pronounced impact on the temperature field. Lower thermal resistance offers faster solidification rate. It is found that as the heat transfer constant increases, the rate of propagation of solid–mush and mush–solid interfaces gets enhanced. In addition, the growth of thermal resistance is of linear nature, with variation in the value of Q. The solidified region has higher concentration than the mush region. The current study is applicable to both eutectic systems and solid solution alloys.

Entropic thermodynamic analysis and radiative performance of unsteady magnetized squeezing hybrid nanofluid flowing via two disks with time-dependent heat generating

Entropic thermodynamic analysis and radiative performance of unsteady magnetized squeezing hybrid nanofluid flowing via two disks with time-dependent heat generating

Investigation of the unsteady MHD fluid flow and heat transfer through the porous medium asymmetric wavy channel

This paper uses three analytical methods to find the novel results in the two-dimensional time-dependent MHD oscillatory flow and heat transfer in an asymmetric wavy porous channel. The corresponding constitutive equations become complex by considering the pressure gradient as a complex function. This results in the existence of both real and imaginary solutions for fluid velocity and temperature. The changes in parameters like the Hartmann number, wavelength, Grashof number, and porous medium shape factor will affect the real fluid velocity. Still, only radiation parameter changes will affect the real fluid velocity and temperature. Increasing the Hartmann number, porous medium shape factor, and radiation parameter will drastically reduce real fluid velocity. The Reynolds number should theoretically affect the imaginary velocity, but according to the boundary condition definition, the imaginary velocity value becomes zero. Altering the frequency of the wavy walls and the Peclet number will only affect the imaginary temperature component, and increasing these parameters will increase the average imaginary temperature profile. The uniqueness of this study lies in the resolution of complex differential equations in a way that has not been attempted before. The results indicated that each set of three solutions was nearly identical, highlighting the outcomes' precision.

Impact of various heat sources on the transient heat transfer rate in a 3D cylinder consisting of parts with different thermal conductivity coefficients

Numerical analysis of time-dependent conductive heat transfer in three-dimensional solid bodies with a heat source is important in their use in various industries. In this article, an attempt has been made to investigate this issue for a cylinder consisting of four equal pieces with different thermal conductivity coefficients and heat sources, and conclusions have been drawn. The geometry of the cylinder consists of two lower (first) and upper (second) layers. In the lower layer of two solid bodies, one is a piece of rubber with a thermal conductivity coefficient of K1=0.16 w/m○k and the other is a piece of walnut wood with a thermal conductivity coefficient of K2=0.077 w/m○k and two solid objects are used in the upper layer. One is a piece of polyurethane with a thermal conductivity coefficient of K3=0.02 w/m○k and the other is a piece of cork with a thermal conductivity coefficient of K4=0.04 w/m○k. There are four heat source mechanisms: constant value, linear, quadratic, and sinusoidal or periodic heat source with a certain frequency. All the surfaces of the cylinder walls in the time interval 0 ≤ t ≤ 10 s10, T=0 are assumed. The obtained results show that the temperature distribution when the value of the heat source is constant affects a larger area, and the highest increase in temperature in the direction of the z-axis belongs to the constant, quadratic, sinusoidal and linear heat source, respectively.

Numerical Investigation of Nanofluid’s Heat Transfer Performance in Passive Residual Heat Removing System of AP1000 Nuclear Reactor

The Passive Heat Removal system (PHRS) is designed to remove the residual heat from the core in case of a station blackout, failure of emergency core cooling system, or failure of feedwater supply through the Passive Residual Heat Removal Heat Exchanger (PRHR HX). PRHR HX consists of a C-shaped tube bundle as a heat exchanger and the In-Containment Refueling Water Storage Tank (IRWST) as a heat sink. A temperature distribution of this passive heat removal system of an AP1000 Reactor is generated using COMSOL Multiphysics and the heat transfer coefficient is calculated to illustrate the effectiveness of the PHRS. A comparison of the heat transfer coefficient between the IRWST filled with water and nanofluid has been generated using the PRHR HX design. Thermophysical properties of nanofluids have been calculated in the process of calculating the heat transfer coefficient. Numerical results show the difference in temperature reduction of Al2O3, TiO2, and Ag as opposed to water in the IRWST. Time-dependent heat conduction of water and nanofluid results contribute to the effective analysis of passive heat removal systems and provide information for the safe operation of AP1000 reactors. By the end of 2024/2025, two VVER-1200 power stations with a combined capacity of 2400 MW will be operating in Bangladesh. For safety and licensing reasons, heat transfer simulation of VVER-1200 can be performed using COMSOL software.

Numerical analysis and experimental verification of time-dependent heat conduction under the action of ultra-short pulse laser

Numerical analysis and experimental verification of time-dependent heat conduction under the action of ultra-short pulse laser

Computational investigation of methanol-based hybrid nanofluid flow over a stretching cylinder with Cattaneo–Christov heat flux

Abstract This study investigates heat transfer rates in (AA7075-AA7072/Methanol) hybrid nanofluid flows, considering non-uniform heat sources and Cattaneo–Christov heat flux, with significant implications for aerospace engineering by enhancing thermal management in aircraft engines. The findings could revolutionize automotive cooling system efficiency, optimize heat dissipation in electronic devices, and advance the design of renewable energy systems such as concentrated solar power plants. The study aims to conduct a comparative analysis of (AA7075/Methanol) nanofluid and (AA7075-AA7072/Methanol) hybrid nanofluid flow, examining heat transfer rates, non-uniform heat sources, and Cattaneo–Christov heat flux theory around a stretching cylinder. Thermal radiation and the Biot number are also evaluated. Two different nanoparticles, AA7072 and AA7075, are used with methanol to create AA7075/Methanol nanofluid and AA7075-AA7072/Methanol hybrid nanofluid. The study compresses the resultant non-linear partial differential equation system and applies suitable similarity transformations to reduce the governing partial differential equations with boundary conditions to dimensionless form. The BVP4C shooting method in MATLAB is employed to numerically and graphically solve these dimensionless ordinary differential equations. The results indicate that higher curvature parameter values correlate with increased velocity and temperature distribution profiles. A rise in nanoparticle volume fraction reduces the radial velocity profile but increases the temperature profile. Temperature distribution profiles increase with higher thermal radiation parameter and Biot number values, while higher thermal relaxation parameter values decrease temperature. Additionally, thermal distribution profiles rise with increasing values of both the time-dependent heat source constant and space-dependent heat source parameter.

NUMERICAL ANALYSIS OF TRANSIENT SOIL TEMPERATURE VARIATION DURING WILDFIRES

In this study, transient behavior of soil temperature during large forest fires is analyzed using the Comsol© software package. The increase in soil temperature during large wildfires can be very critical, especially when oil or gas pipelines have been laid at a certain depth in the soil in or near forests. During forest fires, the temperature of the soil surface can reach extreme levels that penetrate deep into the ground if the fire is not extinguished within a short period of time. This increase in temperature on the soil surface can lead to extremely dangerous situations if the laying depth of the pipeline is not sufficient, since the heat conducted through the soil causes the surface temperature of the pipeline and therefore that of the fluid inside to also reach very high values. This can lead to a sudden rupture of the pipeline and ultimately lead to catastrophic consequences. Although the present study is conservative due to the assumptions made in structuring the numerical model, it is believed to provide invaluable information about the considerations in selecting gas pipeline locations and pipeline laying depths, while also taking into account extreme temperatures due to wildfires, seismic impacts and traffic loads. Future research could include extensive study on the energy content of different species of forest trees, considering their time-dependent heat release rates (HRR) during a forest fire, as well as experimental work if a realistic setup could be designed.

Time-dependent heating problem of the solar corona in fractal dimensions: A plausible solution

The coronal heating problem is considered one of the most puzzling problems in solar physics. It is based on the question of why the corona temperature reaches a temperature of over 2×106K whereas the temperature of the surface of the sun has about 103-104K. Since the corona is far away from the source of heat, it is realistic that the outer surface should be cooler. Solar physicists and astrophysicists have tried for several decades to solve this puzzle by supplying heat to the corona, despite several advances in MHD theory, computational and numerical simulations. Although these candidates’ sources of energy hold a number of drawbacks, the problem is still open. A motivating approach has been proposed by Walsh which consists of supplying a time-dependent sinusoidal heating function to the heat to preserve the loop at coronal temperature. Yet, the loop temperature at ∼2×106K is preserved and cools only if a critical frequency is exceeded. In this study, it was found that the MHD formulation of the Walsh approach in fractal dimensions may offer a potential solution to the problem. In particular, oscillations of the temperature in the space-fractal dimension close to unity relax quicker than those with smaller values. For time-fractal dimensions much smaller than unity, the temperature enters a state of steady state oscillations after a long time. Our analyses also reveal irregularities in the propagation of temperature over a long period of time. For low frequency and space-fractal dimensions close to unity and low time-fractal dimensions, the temperature enters a cycle of an oscillating phase by rising and falling gradually. It is probable that the loop will stay hot after a series of cycles, and extended periods of no heating are not possible for small frequencies. Additional features related to the propagation of the magnetic field in low-Reynolds numbers are discussed.

Modeling transient temperature coupled pressure behaviour for waterflooding well with induced fractures: Semi-analytical model, numerical model, and case studies

Waterflooding is a widely used technique for developing unconventional reservoirs. Long-term waterflooding can lead to the formation of multiple induced fractures. Accurately tracking the location, extent, and dynamic behavior of these induced fractures is crucial. To enhance monitoring capabilities, data obtained from distributed temperature sensors are used to track temperature variations within the wellbore and at the bottom of the well. Combining temperature and pressure inversion techniques helps mitigate the issue of multiple solutions while offering a more comprehensive characterization of multi-induced fractures from various perspectives. In this study, this work presents a model for temperature coupled pressure (TCP) transient analysis. Additionally, this work utilizes COMSOL Multiphysics software to develop and solve a dynamic wellbore temperature (DWT) model. This work proposes a workflow that describes the dynamic behaviour of multi-induced fractures. During model development and solution, this work employs both pressure and temperature transient analysis methods, examining time-dependent non-linear pressure drop and heat transfer variations. Our results reveal that induced fractures exhibit convective heat exchange with the wellbore, resulting in significantly higher temperatures at the induced fracture locations compared to other wellbore locations. By analyzing temperature-wellbore location curves, this work can accurately identify the locations of induced fractures. The TCP model successfully extracts characteristic parameters of induced fractures, while the DWT model allows for monitoring the locations and heights of these fractures. By combining the workflows of both models, this work achieves a comprehensive characterization of the physical properties of induced fractures. In conclusion, this advancement empowers engineers to manage the development of such fractures effectively, thereby averting potential adverse effects on production well performance and preventing the need for well abandonment.

Unsteady MHD oblique stagnation point slip flow of maxwell fluid over an oscillating–stretching cylinder with Cattaneo–Christov double diffusion model

The unsteady oblique stagnation point slip flow of a Maxwell fluid over an oscillating–stretching cylinder with convective heat transfer is investigated. The evaluation of this phenomenon is facilitated by employing the Cattaneo–Christov double diffusion model. According to the oblique stagnation point flow characteristics, an ordinary differential equation about pressure is derived, and pressure terms can be corrected by solving this equation. The equations are subjected to the similarity transformation, resulting in a set of dimensionless equations. The homotopy analysis method (HAM) is subsequently utilized to obtain their solutions. The effects of various parameters on the velocity, temperature, and concentration are analyzed. It is observed that slip boundary conditions accelerate fluid flow by reducing resistance. Elevating the Schmidt number means a reduction in the mass diffusion, leading to a diminished concentration. The temperature distributions of different thermal relaxation time parameters intersect at a thermal equilibrium point. Moreover, three-dimensional plots depicting the evolution of velocity and temperature over time demonstrate excellent agreement with the flow behavior and boundary conditions. They contribute to the comprehension and prediction of time-dependent flow and heat transfer phenomena.

Introducing an accurate thermodynamic modified model regarding time-dependent heat transfer for [formula omitted]-type Stirling engines

The biggest concerns of researchers and developers of Stirling engine is providing an accurate, fast and low-cost thermodynamic model. Second-order methods despite high speeds and low costs, still require increased accuracy. In present study, in order to provide high accuracy modeling, a new model based on second-order methods was developed. For this purpose, the effectiveness of cooler and heater is calculated according to the instantaneous velocity of piston and mass flow at each moment of Stirling engine movement, and its effects on the working fluid temperature are considered coupled in the main equations. Other heat and work losses including hysteresis, shuttle effect, wall heat transfer, leakage and pressure drop are calculated separately and added to the main model. The sum of mentioned item converges by using a new solution algorithm and forms a Modified model. In order to validate the Modified model and its result, it was implemented on GPU-3 engine. Modified model Estimates the efficiency and performance of GPU-3 with an error of 3.4% and 0.2%, respectively compared to the experimental results.

A study on modeling of boiling heat transfer in core debris bed of SFR

In case of a hypothetical severe accident in a Sodium-cooled Fast Reactor (SFR), coolability of the debris bed in the post-accident phase plays a vital role in mitigating the accident and ensuring the structural integrity of the reactor vessel. Few numerical studies are reported in literature, in which the boiling heat transfer in debris bed is expressed as equivalent heat conduction using similarity law between heat conduction and two-phase heat transfer. However, these studies assumed steady state mass conservation for the boiling zone and neglected the gravity force. Hence, a detailed study has been carried out for various particle sizes and porosities of SFR debris to investigate the influence of above considerations. The effect of gravity on debris bed coolability is studied using steady state model of Lipinski, which showed that gravity has a non-negligible effect, for particle size of 0.3 mm and porosity of 0.5. However, the gravitation force was found to have a negligible effect in dryout heat flux estimation for the bottom cooled configuration. A transient numerical model is developed for simulating the boiling phenomena in debris beds and validated with the published experimental results. The assumption of steady state mass conservation is verified by carrying out transient analysis, which indicated early prediction of the dryout inception. For time dependent heat generation case, the unsteady mass conservation predicted higher DHF compared to constant heat generation.

A new analytical method for transient heat conduction in composite disks applied to thermal plug and abandonment of oil wells

A new hybrid method for transient heat conduction problems is developed and applied to simulate a Plug and Abandonment (P&A) operation of oil wells. An oil well is approximated by concentric disks in a one-dimensional configuration, which allows for use of polar coordinates. The application of the Separation of Variables Method (SVM) is used as the analytical framework for the solution of the conductive heat transfer arising from a volumetric heat source located in the center of the disks. The SVM is able to solve only time-independent boundary conditions. However, using the Duhamel's theorem, the solution determined with the SVM can be used to achieve the solution when both time-dependent boundary conditions and internal heat generation are prescribed. Lastly, for verification purposes, a commercial software that solves the transient temperature field by means of numerical procedures, providing reliability to the analytical method proposed in this work.

Heat transfer through a three-layer wall considering the contribution of phase change: A novel approach to the modelling of the process

A novel analytical solution to the time-dependent heat transfer equation for a multi-layer wall considering the contribution of phase change is obtained. Based on this solution a new numerical algorithm is developed for the analysis of variations in temperature and heat flux in a three-layer wall of a building in the presence of transient ambient temperature. In this algorithm, the new analytical solution at the end of the previous time step is used as the initial condition for the following time step with adjusted values of input parameters (ambient temperature). The novel algorithm is verified based on a comparison of the predictions of COMSOL Multiphysics (version 6.1) with its predictions for the same input parameters assuming that the time dependence of the ambient temperature follows the sine law. The new code is used for the analysis of heat transfer through a three-layer building wall assuming typical continental climate conditions. The inner and outer layers were filled with polyurethane foam, while a thin middle layer, located in the centre of the wall, was filled with the phase-change material (paraffin). Using the new numerical algorithm it is demonstrated that the presence of the thin paraffin layer in the wall leads to two orders of magnitude reduction in the amplitude of temperature oscillations on the room side of the wall compared to those on its outer side. It is shown that the presence of paraffin layer in the wall leads to an increase in the phase shift between the temperature on the outer side of the wall and the heat flux on the room side from about 1 hour (homogeneous wall) to about 5.5 hours (wall with the paraffin layer).

Determination of Timewise-Source Coefficient in Time-Fractional Reaction-Diffusion Equation from First Order Heat Moment

This article aims to determine the time-dependent heat coefficient together with the temperature solution for a type of semi-linear time-fractional inverse source problem by applying a method based on the finite difference scheme and Tikhonov regularization. An unconditionally stable implicit finite difference scheme is used as a direct (forward) solver. While by the MATLAB routine lsqnonlin from the optimization toolbox, the inverse problem is reformulated as nonlinear least square minimization and solved efficiently. Since the problem is generally incorrect or ill-posed that means any error inclusion in the input data will produce a large error in the output data. Therefore, the Tikhonov regularization technique is applied to obtain stable and accurate results. Finally, to demonstrate the accuracy and effectiveness of our scheme, two benchmark test problems have been considered, and its good working with different noise levels.

Fractional derivative modelling for consolidation of multilayered saturated soils with interfacial thermal contact resistance subjected to time-dependent heating and loading

In this paper, the one-dimensional rheological consolidation characteristics of multilayered saturated soil foundations under time-dependent loading and heating are investigated by considering the semi-permeability and the interface thermal resistance. By introducing the fractional derivative model and the thermos-elastic theory, a thermo-mechanical coupling model is established to describe the rheological properties of saturated soils. Semi-analytical solutions for strain, temperature increment, pore water pressure and settlement were derived through the Laplace transform and its inverse. The accuracy of the solutions proposed in this paper has been verified by comparing with existing solutions. The effects of different thermal contact models of the interface on the rheological properties of saturated soils under semi-permeable boundary are discussed, and the effects of fractional derivative order, constitutive material parameters, and thermal conductivity of soil on the thermal consolidation process are investigated. The results show that: neglecting the thermal resistance effect can result in an overestimates of the impact of rheological properties on the thermal consolidation process of saturated soils under semi-permeable boundaries; As the thermal resistance coefficient increases, the influence of soil thermal conductivity on settlement decreases.

Dynamic behavior of mixed convection heat transfer among horizontal co-axial fixed pipes at varying temperatures: Efficiency of cylindrical heat sink

The aim of the current research is to highlight the time-dependent properties of laminar convective thermal transmission inside a semi-infinite pipe, with an emphasis on flow frequencies that impact inter-fluid momentum and energy. The implicit finite difference approach is used to solve two-dimensional mathematical model composed of nonlinear partial differential equations. The research includes forecasting thermal performance of time-dependent flow in a pipe over several parameter ranges relevant to the flow model. The obtained forecasts were emphasized graphically. The numerical solutions were separated into steady and unsteady components, with the steady component yielding findings that were then used to determine the time dependent surface shearness and energy shearness in the time dependent phase. The stable component of the investigation revealed that raising the buoyancy force parameter and the impact of viscous dissipation significantly improved the flow velocity pattern and heat distributions throughout the flow domain. While the amplitude of time dependent surface shearness varied somewhat across various buoyancy force parameter values, the amplitude of time dependent heat transmission rates varied significantly. This study sheds light on the interaction of several characteristics, such as buoyancy force effects and internal energy loss, on time-dependent thermal energy flow inside a semi-infinite pipe subjected to laminar convective flow. It is worth noting that the amplitude of the time dependent rate of heat transmission shows more noticeable variations with different values of the buoyancy force parameter, in contrast to the minute change in the amplitude of the time dependent surface sheerness.