Time-dependent Heat Research Articles

Capacitive charging rate dependence of heat from porous carbon in aqueous salt solution

Porous capacitive electrodes are applied in supercapacitors and capacitive deionization of aqueous salt solutions. In both cases, electric charge and ions are stored in the electrical double layer at the surface of the pores. Recently, we revealed that the equilibrium potential energy of the ions in the pores can be obtained from isothermal calorimetric measurements. On that basis, we now introduce a model for the time-dependent heat production at any charging or discharging rate. The model centers on a mathematical expression for the time-dependent internal energy of the double layer, which depends only on constant system parameters and the time-dependent electric potential drop across the double layer. Semiquantitative agreement is found with experiments on a porous carbon electrode in aqueous salt solution. The theory applies both in the case of abrupt application of a potential to the electrode, generating a maximum amount of Joule heat, and in cases where the potential is applied more slowly, even when charging becomes so slow that heat production is essentially reversible. These results not only provide fundamental insight into the electrical double layer of porous capacitive electrodes, but they are also a new way to describe and to predict the time-dependent generation of heat from such electrodes.

Real-time estimation of thermal boundary conditions and internal temperature fields for thermal protection system of aerospace vehicle via temperature sequence

Aerospace vehicles go through extremely aerothermal heating upon entry into the atmospheric, which need to employ the reliable thermal protection system (TPS). The boundary heat flux and inner temperature information for aerospace vehicles are required to design the TPS. The direct measurement for temperature and heat fluxes is quite difficult mission. In this study, unscented Kalman filtering, is an indirect measurement method based on inner surface temperature information and is introduced to reconstruct the transient heat flux and inner temperature fields of TPS in real-time, which is regarded as a graded index medium. The finite volume method and discrete ordinate method are utilized to solve the energy equation and radiative transfer equation to obtain measurement temperature, respectively. Based on the measurement temperature signal, the unscented Kalman filtering technique is applied to reconstruct the surface heat flux and inner temperature field of the TPS. Simulation results indicate the time-dependent boundary heat flux and inner temperature fields can be estimated using proposed method. The effects of thickness, refractive index, measurement noise, and process noise on the reconstructed results are studied in detail. Retrieval results show the proposed technique is more precise and robust than Kalman filtering method in the nonlinear system.

Improvement of a temperature response function for divertor heat flux monitoring in fusion devices

Temperature response functions have been developed to investigate sensor design and divertor heat flux estimation in magnetically confined plasmas. The time-dependent heat flux can be derived by fitting the response function to experimental thermocouple (TC) data. Because the TC signals have a time delay to transit events such as discharge start or confinement transition, the time delay is taken into account in a temperature response function. Such a function accurately describes the signal from each TC channel with time delay in a sensor test using a neutral beam injection. Measurement for commercial TCs shows that the time delay is caused by the finite heat capacity of TC wire and contact heat resistance between TC and target surface.

Determination of time-dependent coefficient in time fractional heat equation

The aim of this work is to determine the time-dependent heat coefficient in a type of inverse problem for one dimensional time-fractional heat equations defined by the Caputo operator for (0<α<1) by applying a method based on the finite difference scheme and Tikhonov’s regularization. First, a stable implicit finite difference scheme is applied to find a numerical solution to the (forward) direct problem. While the inverse problem was reformulated as a nonlinear least-square minimization problem with a simple physical bound on the unknown coefficient and solved efficiently by MATLAB routine lsqnonlin from the optimization toolbox. But the latter problem will remain ill-posed because the presence of any error in the input data will lead to a large error in the output data. So, Tikhonov’s technique is applied to obtain stable results. In the end, two numerical test examples show that the proposed method is stable, accurate, and works well with different noise levels

On the fully coupled quasi-static equations for the thermoelastic halfspace

Influence functions for fully coupled quasi-static thermoelasticity are presented. They can be used to calculate displacements, stresses as well as temperature distributions within a halfspace for arbitrarily shaped and time dependent heat sources or pressure distributions on the surface. To this end, the underlying equations are solved for a mechanically or thermally loaded rectangular element on the surface by potential theory. The solution procedure is described in detail. The obtained results are verified and may easily be transferred to the theory of poroelasticity where the underlying equations are structurally equal. Example calculations for a parabolic pressure field, heat flux and temperature field are performed and simulation results are discussed particularly in comparison to the uncoupled case. Estimations of the extent to which the Gough–Joule effect and its consequences can be neglected are given.

Study of nonlinear thermal convection of ternary nanofluid within Darcy-Brinkman porous structure with time dependent heat source/sink

&lt;abstract&gt; &lt;p&gt;The dynamical behaviour and thermal transportation feature of mixed convective Casson bi-phasic flows of water-based ternary Hybrid nanofluids with different shapes are examined numerically in a Darcy- Brinkman medium bounded by a vertical elongating slender concave-shaped surface. The mathematical framework of the present flow model is developed properly by adopting the single-phase approach, whose solid phase is selected to be metallic or metallic oxide nanoparticles. Besides, the influence of thermal radiation is taken into consideration in the presence of an internal variable heat generation. A set of feasible similarity transformations are applied for the conversion of the governing PDEs into a nonlinear differential structure of coupled ODEs. An advanced differential quadrature algorithm is employed herein to acquire accurate numerical solutions for momentum and energy equations. Results of the conducted parametric study are explained and revealed in graphs using bvp5c in MATLAB to solve the governing system. The solution with three mixture compositions is provided (Type-I and Type-II). Al&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt; (Platelet), GNT (Cylindrical), and CNTs (Spherical), Type-II mixture of copper (Cylindrical), silver (Platelet), and copper oxide (Spherical). In comparison to Type-I ternary combination Type-II ternary mixtures is lesser in terms of the temperature distribution. The skin friction coefficient is more in Type-1 compared to Type-2.&lt;/p&gt; &lt;/abstract&gt;

High-precision solidification simulation by estimating heat transfer coefficients through data assimilation

Solidification analysis is important for accurately predicting casting processes. A high-precision casting simulation requires accurate data of the physical properties of materials and heat transfer parameters. In particular, the heat transfer coefficient is a major parameter influencing the casting simulation results. Because the heat transfer coefficient is not uniquely determined by the material, it is typically estimated by trial and error, which requires considerable time for accurate estimations. Therefore, we developed a method to quickly estimate the heat transfer coefficient in a casting process by combining data assimilation and solidification simulations. With this method, the time-dependent heat transfer coefficient can be estimated in an appropriate and easy manner. To reproduce the 3D temperature distribution in a casting with high accuracy, we developed a method to estimate multiple heat transfer coefficients simultaneously by combining data assimilation and 3D solidification simulation. Al–5 mass% Si alloy was cast into a sand mold with a casting size of 30 mm × 30 mm × 100 mm, and the temperature was measured at five points in the casting to obtain a cooling curve. Two cooling curves corresponding to locations of 5 mm from the casting wall were used to estimate the two heat transfer coefficients on the side and bottom surfaces, which were simultaneously estimated by data assimilation. The results confirmed that all the five cooling curves could be reproduced with a high accuracy and that high-precision casting simulation was possible.

Revisiting “Non-Thermal” Batch Microwave Oven Inactivation of Microorganisms

Over the last few decades there has been active discussion concerning the mechanisms involved in “non-thermal” microwave-assisted inactivation of microorganisms. This work presents a novel non-invasive acoustic measurement of a domestic microwave oven cavity-magnetron operating at fo = 2.45 ± 0.05 GHz (λo ~ 12.2 cm) that is modulated in the time-domain (0 to 2 minutes). The measurements reveal the cavity-magnetron cathode filament cold-start warm-up period and the pulse width modulation periods (time-on time-off and base-time period, where time-on minus base-time = duty cycle). The waveform information is used to reconstruct historical microwave “non-thermal” homogeneous microorganism inactivation experiments: where tap-water is used to mimic the microorganism suspension; and ice, crushed ice, and ice slurry mixture are used as the cooling media. The experiments are described using text, diagrams, and photographs. Four key experimental parameters are indentified that influence the suspension time-dependent temperature profile. First, where the selected process time > the time-base, the cavity-magnetron continuous wave rated power should be used for each second of microwave illumination. Second, external crushed ice and ice slurry baths induce different cooling profiles due to difference in their heat absorption rates. In addition external baths may shield the suspension resulting in a retarding of the time-dependent heating profile. Third, internal cooling systems dictate that the suspension is directly exposed to microwave illumination due to the absence of surrounding ice volume. Fourth, four separated water dummy-loads isolate and control thermal heat transfer (conduction) to and from the suspension, thereby diverting a portion of the microwave power away from the suspension. Energy phase-space projections were used to compare the “non-thermal” energy densities of 0.03 to 0.1 kJ·m-1 at 800 W with reported thermal microwave-assisted microorganism inactivation energy densities of 0.5 to 5 kJ·m-1 at 1050 ± 50 W. Estimations of the “non-thermal” microwave-assisted root mean square of the electric field strength are found to be in the range of 22 to 41.2 V·m-1 for 800 W.

Molecular Photothermal Effects on Time-Resolved IR Spectroscopy: Solute-Solvent Intermolecular Energy Transfer.

Time-resolved IR pump-probe (IR-PP) and two-dimensional IR (2D-IR) spectroscopy are valuable tools for studying ultrafast chemical and biological processes in solutions. However, the corresponding signals at long times are obscured by the molecular photothermal effects resulting from the heat dissipation of vibrationally photoexcited molecules to the surroundings. Recently, a phenomenology model was used to describe molecular photothermal effects on IR-PP signals and the diagonal and cross-peaks of 2D-IR spectra at long pump-probe delay times. Here, we consider the thermal diffusion equation with a time-dependent heat source term to describe the solute-solvent energy transfer process. An approximate solution to the nonhomogeneous differential equation shows that the molecular photothermal effect is determined by the mean intermolecular distance between IR-absorbing molecules. We show that the time profile of heat dissipation from a vibrationally excited molecule to the surroundings, which provides information about the mechanisms involved in the solute-solvent intermolecular energy transfer process in solutions, can be directly measured by analyzing the molecular photothermal IR-PP and 2D-IR signals. We anticipate that the present work can be used to interpret local heating-induced time-resolved IR spectroscopic signals and understand the rate of and the mechanisms involved in the conversion from high-frequency molecular vibrational energy to solvent kinetic energy in condensed phases.

Uncovering the non-radiative thermal characteristics of a passive radiative cooler under real operating conditions

Passive radiative cooling (PasRadCool), which emits thermal energy from objects to deep cold space through atmospheric transparency, offers complementary and alternative green energy solutions for passive cooling of buildings, clothing, and renewable energy harvesting. Depending on the spectral emissive/absorptive properties of the unit under test (UUT), radiative heat exchanges occur between the UUT, atmosphere, and sun, while at the same time non-radiative heat exchange occurs. The performance of the PasRadCool is determined by the combined thermal and thermodynamic effects of both exchange mechanisms. Although the non-radiative heat exchange, which consists of conductive and convective processes to the outer surfaces of the UUT and the surrounding air fluid, is very sensitive to environmental changes, the actual performance is not fully determined since this feature is considered statically in many studies. Herein, we propose a method that reveals the non-radiative thermal characteristics of the PasRadCool under real operating conditions. With a photonic radiative cooler structure, which we manufacture as a proof of concept, we perform nighttime field test measurements in varying non-radiative thermal conditions. The proposed method extracts the time-dependent non-radiative heat transfer coefficient of the UUT as accurately as possible. We also confirm that our experimental result shows good agreement with both numerical and analytical methods. The proposed approach, which highlights the realistic thermal management of PasRadCool, is not specific to the circumstances of our study and can be applied to all PasRadCool situations with different geometry, material, and environmental conditions.

Multi-phase-lag model on forced vibrations of nonlocal thermoelastic diffusive cylinder with time-dependent heat flux

Multi-phase-lag model on forced vibrations of nonlocal thermoelastic diffusive cylinder with time-dependent heat flux

Impact of time-dependent heat and mass transfer phenomenon for magnetized Sutterby nanofluid flow

Due to widespread applications of nanofluid and working as most effective source of energy researchers as well as engineer paid more attention toward nanofluid, moreover nanofluid are preferred as they are environmentally friendly and having extraordinary thermal properties. . In this article, we have investigated the properties of heat and mass transfer mechanisms for incompressible Sutterby nanofluid past over a stretching non-porous surface. The d magnetic strength is incorporated into the flow regime. The effects of Brownian motion and thermophoresis are also incorporated in this work. Moreover, similarity transformations are used to change the coupled PDEs into a set of coupled ODEs and then these ordinary differential equations are solved numerically using an effective numerical technique, namely, bvp4c. For exploring, the effects of physical parameters on the leading coupled ordinary differential equations, we have presented the graphical analysis and discussed in detail. . The dimensionless thermal distribution is greater with Brownian motion, while the opposite behavior is noticed for the concentration field. The analysis further reveals that the unsteadiness parameter is decreasing functions of the velocity and the temperature field.

Fast Bayesian inference for inverse heat conduction problem using polynomial chaos and Karhunen–Loeve expansions

We present a fast Bayesian inference framework for solving inverse heat conduction problems (IHCP) for the estimation of boundary heat flux. The framework leverages the polynomial chaos expansions (PCEs) for generating computationally efficient and statistically equivalent surrogate model of the computationally expensive forward model and dimensionality reduction based on Karhunen–Loeve (K–L) expansion. We demonstrate the potential of this approach using three model problems to estimate heat flux in inverse heat conduction models. We represent the heat flux using K–L expansion to reduce the high dimensionality of the heat flux and compute the posterior probability distribution of the heat flux using the temperature measurements. The first inverse problem involves the estimation of time–varying heat flux in a one–dimensional slab using transient temperature measurements. The second problem involves the estimation of the unknown time–dependent heat flux of the disc in a realistic axisymmetric disc brake system. The third problem involves the estimation of the surface heat flux on a sounding rocket having a realistic three–dimensional geometry of the rocket module used in actual flight tests. We further obtain the inverse solution by computing the expectation of the distribution and demonstrate that this approach becomes orders of magnitude more efficient when we use the PCE surrogate model instead of the direct forward model for comparable accuracy. The numerical results show that this framework overcomes the drawback of high computational cost of Markov chain Monte Carlo (MCMC) without compromising on solution accuracy. The combination of PC–based surrogate modeling and K–L based dimensionality reduction leads to over 2000–fold speed up of numerical solution of IHCP.

Electrical resistivity of the Fe–Si–S ternary system: implications for timing of thermal convection shutdown in the lunar core

The composition of the lunar core has been suggested to be Fe-rich with varying amounts of lighter elements, such as Si and S. Presence of Si and S affects electrical and thermal transport properties and thus influences core thermal processes and evolution. Paleomagnetic observations constrain a high intensity magnetic field that ceases shortly after formation of the moon (~ 3.5–4.2 Ga year ago), and thermal convection in the core may contribute to generation of this field. In this study, the electrical resistivity of Fe-14 wt% Si-3 wt% S was measured in both solid and molten states at pressures up to 5 GPa and thermal conductivity was calculated via the Wiedemann–Franz Law from the electrical measurements. The results were used to estimate the adiabatic conductive heat flux of a molten Fe-14 wt% Si-3 wt% S lunar core and compared to a Fe-2-17 wt% Si lunar core, which showed that thermal convection of either core composition shuts down within the duration of the high intensity magnetic field: (1) 3.17–3.72 Ga year ago for a Fe-14 wt% Si-3 wt% S core; and (ii) 3.38–3.86 Ga years ago for a Fe-2-17 wt% Si core. Results favouring compatibility of these core compositions with paleomagnetic observations are strongly dependent on the temperature of the core-mantle boundary and time-dependent mantle-side heat flux.

Mathematical Study of unsteady micropolar fluid flow due to non-linear stretched sheet in the presence of magnetic field

The goal of this research is to check irregularity in heat generation, chemical reaction and thermal radiation effect an unsteady micropolar fluid flow. With the help of suitable similarity variables, the group of governing system of PDE and their associative boundary conditions are converted into the family of ODE and then solved using the HAM. The effect of various and important dimensionless parameters on the momentum, micro-rotation, energy and concentration equations have been discussed with graphical representation as well as tabular forms. It is observed that buoyancy force parameter, mixed convection parameter and permeability parameter enhance the velocity distribution while micropolar reduces the velocity profile. The temperature profiles are boosted for time and space dependent heat generation and absorption parameter respectively but reverse trend is observed for Prandtl number and unsteadiness parameter. Skin-friction factor, mass transfer rate and heat transfer rate have been listed and displayed in tables.

A Transient Resistance/Capacitance Network-Based Model for Heat Spreading in Substrate Stacks Having Multiple Anisotropic Layers

Abstract Heat spreading from local, time-dependent heat sources in electronic packages results in the propagation of temperature nonuniformities through the stack of material layers attached to the chip. Available models either predict the chip temperatures only in the steady-state or a single substrate for transient analysis, without the ability to predict the transient response in compound substrates having multiple anisotropic layers. We develop a transient resistance/capacitance network-based modeling approach capable of predicting the spatiotemporal temperature fields for this chip-on-stack geometry, accounting for in-plane heat spreading, through-plane heat conduction, and the effective convection resistance boundary conditions. The transient heat spreading resistance for an anisotropic substrate has been formulated by converting it to an effective isotropic substrate for which there is an available half-space solution. The transient heat spreading model for a step heat input to a single substrate is subsequently extended to any arbitrary transient heat input using a Fourier series and extending the half-space formulation from a step heat input to sinusoidal heat input. For obtaining the transient spreading resistance for heat inputs into multiple stacked substrates, a method has been outlined to convert the multisubstrate stack to a single substrate with effective isotropic properties by properly accounting for the in-plane and through-plane thermal conductivities, and the heat capacity. The estimates from the present model are validated with direct comparison to a finite volume numerical model for three-dimensional heat conduction. Case studies are presented to demonstrate the capabilities of the proposed network-based model and compare its estimates with the numerical conduction solution. In the presence of a step heat input, the results demonstrate that the model accurately captures the transient temperature rise across the multisubstrate stack comprising layers with different anisotropic properties. For a case where the rectangular stack is exposed to a sinusoidally varying heat input, the model is able to capture the general trends in the transient temperature fields in the plane where the heat source is applied to the multisubstrate stack. In summary, the developed resistance/capacitance network-based transient model offers a low-computational-cost method to predict the spatiotemporal temperature distribution over an arbitrary transient heat source interfacing with a multilayer stack of substrates.

Multivariate analysis for assessing the thermal performance of vertical opaque envelopes in extended regions

We introduce a statistical methodology to evaluate the thermal performance of vertical opaque envelopes and provide the most adequate design of energy-efficient buildings located across extended regions. The analytical procedure was applied to the extensive Argentinian territory with a variety of climates and a limited number of networked meteorological stations. Although the study was conducted over a full year, results are presented for January and June, when the building energy demand for heating and cooling is most significant, taking into account the local climate, the thermal properties of the walls and the effects of the daily variation in the solar radiation. By using the Fourier series expansion of the sol-air temperature and multivariate analysis, we first correlated the weather data and the steady-state and time-dependent heat fluxes transmitted by conduction through five types of typical walls facing north and south in 10 climatically differentiated cities where full weather data were recorded. Then, the mean values of the sol-air temperature and the amplitude of its time variations were interpolated throughout the territory, thus yielding the spatial distributions of these parameters for a typical day in the months of interest. Finally, the calculation of the heat fluxes exchanged through building opaque envelopes was extended to the whole country.

A computational study on diffusion-thermo and rotation effects on heat generated mixed convection flow of MHD Casson fluid past an oscillating porous plate

A finite element computational study is conducted to evaluate the impacts of diffusion-thermo and rotation on time-dependent heat generated MHD chemically reactive mixed-convection Casson fluid transport due to an oscillatory porous plate considering ramp surface temperature with thermal radiation and Hall effects. The boundary-layer equations describing the flow are formulated and altered into dimensionless form with aid of non-dimensional variables and parameters. The resulting governing boundary layer equations are numerically solved by a precise and robust finite element method. A representationary set of outcomes is exhibited graphically to exemplify the influent of emerging parameters on the profiles of temperature, concentration and velocity. The computed results of shearing stresses, Nusselt and the Sherwood numbers are displayed in the tables. We found that both velocity components decreased as magnetic field, rotation and Casson parameters increased whereas opposite result is discovered as heat generation and Hall parameter increased. Thickness of thermal and momentum boundary layers improve with increment in thermal radiation. Increasing chemical reaction parameter reduces both concentration and momentum boundary layer thickness. It is prominent to highlight in this investigation, in case of isothermal plate temperature, both velocity components, concentration and temperature are higher than in case of ramped surface temperature. Further, our results compared with earlier published works and established to be in excellent conformity.

Size determination of interior defects by reconstruction of subsurface virtual heat flux for step heating thermography

Step heating thermography is a non-destructive testing (NDT) technique that inspects interior defects by observing surface temperature rises during a long pulse heat stimulation. Due to the heat diffusion induced blurring of defect shapes, it is a challenging task to accurately determine the sizes of deep and small defects. This work focuses on estimating the size of a subsurface defect by an inversion of temperature images for the step heating thermography, to overcome the information loss during the propagation of thermal waves. We assume a space- and time-dependent virtual heat flux on the defect surface, which is reconstructed from surface temperature measurements by solving a two-dimensional inverse heat conduction problem. The local future time concept is combined with the Tikhonov's regularization to stabilize the inverse solution. A prudent choice of the regularization parameter is carried out through the L-curve. The feasibility of the proposed approach is assessed by numerical simulations and experiments. It is shown that the inversion brings an improvement in defect sizing accuracy for defects with low width-to-depth ratios and an efficient suppression of measurement noises.

Studying transient heat transfer in a cylindrical pin fin with radiation and convection

A simple experimental fin device was used to develop a laboratory procedure for undergraduate engineering students, in order to enhance their understanding of the transfer of thermal energy. This experiment exposes the student to several important concepts, namely one-dimensional, time-dependent heat transfer in extended surfaces by conduction, convection and radiation. In a few simple steps, students have the opportunity to compare the measured to the predicted temperature profiles obtained at different times using an analytical complex solution and to calculate convective and radiative heat coefficients, such as the relative predominance of convection heat transfer with respect to radiation.