Unsteady Temperature Distribution Research Articles

Unsteady heat transfer in porous fiber composite cylinders with compressible fluid

The study of heat transfer behavior in porous fiber composite cylinders is vital for optimizing efficient thermal management, insulation materials, and heating equipment design, with applications spanning fields like materials drying, atomization equipment, and aerospace. However, the existing research in this area faces challenges including inadequate experimental data and a lack of clarity regarding fluid-porous material interactions, particularly under the influence of compressible fluids, which demand a more nuanced investigation. This study has developed a model to depict the unsteady heat transfer behavior of porous fiber composite cylinders containing compressible fluid. Consequently, a momentum equation describing the gradual diffusion of compressible fluid within the porous medium is established based on the Darcy-Brinkman-Forchheimer equation. For the purposes of this investigation, the air is treated as a compressible fluid. Concurrently, the corresponding energy equation is formulated, assuming Local Thermal Equilibrium. Ultimately, the devised model is solved by employing the finite volume method. Additionally, a temperature measurement experiment is designed to furnish boundary conditions and verify the model's reliability. The findings indicate that omitting the influence of compressible fluid yields a maximum predicted temperature deviation of approximately 5.6 K at a heating temperature of 420 K. The temperature deviation gradually expands as the heating temperature rises. Furthermore, the parametric analysis is conducted to investigate the impact of porosity, thermal conductivity, geometric size, and the type of heat source on the non-steady heat transfer behavior of composite cylinders. This novel model contributes to a more accurate prediction of the unsteady temperature distribution within porous fiber composite structure cylinders.

SIMULATION OF FLOW AND HEAT EXCHANGE IN A HEAT ACCUMULATOR TANK

The article deals with the research of thermal energy storage tanks. It is proposed to use a «thermal core» to minimize the effects of thermal stratification and high thermal inertia. The thermal core consists of a binary tube placed along the central axis of the tank, filled with a paraffin mixture with a melting point of 45 to 65oC and a density of 0,880 to 0,915g/cm3 at 15oC. In the study the Fluent software package was used to model the temperature distribution in the tank under free convection conditions, the data was then converted to the Transient Thermal module of the ANSYS software package for further calculations of the unsteady temperature distribution in the thermal core. The study showed that a 1400-liter thermal energy storage device, heated for 1 hour by a heat-transfer fluid at 115oC, cools down to 50oC in 4 hours. The research also revealed the need to improve the tank design based on the analysis of the hydrodynamic structure of the flow in the tank, as evidenced by the trajectory distribution of free convective flows. The authors concluded that the use of a heat core, regardless of the type of paraffin used to form it, helps to reduce temperature stratification by height in the tank and that the type of paraffin used has no significant effect on the overall cooling of the tank. However, using ceresin as a core filler results in a slightly higher average tank temperature. Based on the results of the study, the time of complete cooling of the tank was determined by the non-uniform temperature field of all elements of the tank.

Two-Dimensional FEM Approach of Metabolic Effect on Thermoregulation in Human Dermal Parts During Walking and Marathon

The physiological mechanisms conduction, convection, and radiation exchange the heat energy in bi-directional routes between the body and the temperature field. Metabolism and evaporation are the uni-directional routes for the exchange of heat energy. In the metabolic process, the body creates internal heat energy, whereas the body loses excess heat energy through the evaporation process and maintains the body temperature. This study has shown steady and unsteady state temperature distribution in three skin layers: epidermis, dermis, and subcutaneous tissue, during walking and marathon. The results have analyzed that each skin layer temperature is higher during a marathon compared with walking due to more metabolic effects. The computation has been carried out for the two-dimensional Pennes’ bio-heat equation using a finite element approach. The generated results have been exhibited graphically.

Unsteady temperature distribution in a cylinder made of functionally graded materials under circumferentially-varying convective heat transfer boundary conditions

Abstract A novel model on 2D unsteady conductive heat transfer in an infinite hollow cylinder is proposed. The cylinder is made of functionally graded material (FGM) that has variable properties both in radial and angular directions. Volumetric heat capacity and thermal conductivity coefficient are changed according to the power function of the radius. In the presence of variable coefficients, the governing equations of unsteady heat transfer in FGMs have caused the complexity. The Laplace transform method is used to transfer the energy equation from time to frequency domain whereas the meromorphic function is used for the inverse Laplace transform to obtain the desired solutions. The closed form solutions have been well validated and the results have been presented for different values of functionally graded indices for thermal conductivity coefficients and volumetric heat capacity. Two different FGM cases with different complicated thermal boundary conditions have been investigated. The first case has a constant temperature in the inner radius and a variable heat flux along with the convection condition in the outer radius. In the second case, the inner radius has a specific harmonic temperature and the outer radius is exposed to the convective conditions. It was observed that in both cases, the temperature value in the cylinder decreases with the increase of the FG index for the conductivity coefficient. The presented analytical solution provides a good tool for validating unsteady numerical solutions presented in the field of heat transfer in FGMs.

Thermal-structural reduced order models for unsteady/dynamic response of heated structures in large deformations

This paper focuses on applications of recently developed thermoelastic reduced order models (ROMs) for the geometrically nonlinear response and temperature of heated structures. In these ROMs, both displacements and temperature fields with respect to the undeformed, unheated configuration are expressed in a reduced order modeling format, i.e., as modal-type expansions of the spatial and temporal variables with constant basis functions. Accordingly, the time varying generalized coordinates of the response and temperature expansions satisfy a generic set of coupled nonlinear differential equations derived from finite deformations thermoelasticity using a Galerkin approach. Finally, the coefficients of these governing equations, which characterize the structure considered and its loading conditions, are determined from structural and thermal finite element models non intrusively so that commercial finite element software can be used. This approach is considered here for the prediction of the displacements and stress fields in the presence of unsteady temperature distributions to enrich previous investigations limited to steady temperature distributions. Specifically considered here are: (i) a panel undergoing rapid heating and (ii) an oscillating flux on a panel. These problems not only demonstrate the extension of the thermal-structural reduced order framework to unsteady problems but also show the importance of the selection of the basis functions. It is also noted that the temperature dependence of the linear stiffness coefficients on temperature can induce in the unsteady situation the existence of a parametric-type excitation of the structure. This behavior is studied in the oscillating flux example and a strong sub-harmonic resonance is in particular found. The computational benefit of using ROMs is discussed and demonstrated.

Performance comparison using different multilayer perceptron input–output formats to predict unsteady indoor temperature distribution

AbstractComputational fluid dynamics (CFD) is widely used to predict the indoor thermal environment; however, large time cost represents a significant disadvantage. Several deep learning approaches have been introduced to reduce prediction time in steady‐state predictions, though their feasibility under unsteady ones has yet to be investigated. Considering the flexibility of the multilayer perceptron (MLP) input–output format, this study compared the performance of two MLP input–output formats, MLP‐A (simultaneously outputting the values for all cells in a space in a single calculation run) and MLP‐B (outputting the values for a cell in each calculation run), when used to predict unsteady indoor temperature distribution in three scenarios: time interpolation, time extrapolation, and varying boundary conditions. The two considered input–output formats resulted in different prediction patterns in the time interpolation scenario: MLP‐B accurately predicted the spatiotemporal development of airflow compared to the CFD results, whereas MLP‐A did not. Both MLP‐A and MLP‐B performed poorly in the time extrapolation scenario but exhibited different error patterns. Finally, MLP‐A also generally provided a correct prediction of airflow development as well. This study contributes to an understanding of the prediction patterns provided by different MLP input–output formats for unsteady indoor airflow prediction.

Experimental And Numerical Investigation Of A Multi-Jet Impingement Cooling Configuration

In order to protect turbine blades from thermal damage or thermally induced aging, internal impingement cooling has found common use throughout engine design, both in stationary gas turbines as well as aircraft engines, but also finds applications in other areas requiring cooling. The present investigation is focused on a generic impingement cooling configuration that can be easily modelled with CFD and at the same time can be studied in detail experimentally. The acquired experimental data can be directly used for the validation of the CFD simulations, ultimately allowing their application in more complex, realistic configurations where experimental investigations become prohibitively expensive or otherwise impossible. The investigated configuration consists of 9 evenly spaced jets of Reynolds number Re_D = 10000 issuing into a square channel that is sealed at one end. The jets directly impinge on a uniformly heated target plate. With previous work on similar configurations well described in literature, the focus of the present contribution is to further exploit the potentials offered by snap-shot based and time-resolved measurements. The flow field within the channel is characterized with both conventional, snap-shot particle image velocimetry (PIV) as well as with high-speed, time-resolved PIV to, respectively, capture overview data as well as detailed information on temporally evolving flow structures. In addition, measurements of the unsteady surface temperature distribution on the heated channel wall are performed by means of a newly developed unsteady temperature-sensitive paint measurement technique (iTSP). The interaction of the turbulent jets with the wall and with its neighbors is studied in detail using correlation and spectral analysis as well as modal decomposition. Where possible, this is supplemented with corresponding data obtained from numerical modelling.

An approach for computing the specific heat capacities of logs stored for a long time in an open warehouse

ABSTRACT This paper describes an approach for computing the specific heat capacities of logs stored for long in an open warehouse. It includes the heat capacities of the wood of non-frozen and frozen zones in the logs and of both the frozen free and bound water in these zones, also the capacities formed by the release of the latent heat of both the free and bound water during their crystallization, as well as the effective specific heat capacities of logs stored in an open warehouse at periodically changing air temperature. The approach is based on the solutions of 2D models of the temperature distribution in logs during their alternating heating and cooling. Results from a simulative study of 2D unsteady temperature distribution and all types of the specific heat capacities of beech logs with a diameter of 0.4 m, length of 0.8 m, moisture content of 60%, and initial temperature of 0°C and 20°C during their 5 days and nights continous alternating heating, cooling, freezing and defrosting in an open warehouse at sinusoidal change of the ambient air temperature with various initial and different amplitudes in the range from –25°C to 40°C are graphically presented and analyzed.

Predicting Unsteady Indoor Temperature Distributions by POD-DNN

In this study, to predict unsteady temperature distributions, POD-DNN was utilized, where DNN was trained to predicted coefficients of POMs. Two strategies, flatten POD-DNN and nested POD-DNN were compared. The flatten POD-DNN provided high accuracy if training data is sufficient, but otherwise very inaccurate. The nested POD-DNN roughly predicted the development of temperature fields even training data was small. The results showed their different sensitivities to the training data size.

A semi-analytical model based on unsteady conductive heat transfer in steam-assisted gravity drainage (SAGD)

Steam-assisted gravity drainage (SAGD) is one of the most successful in-situ recovery methods for bitumen reservoirs. Seeking the function of oil production with parameters of steam injection is significant for rapid performance evaluation of the SAGD process in fields. In this study, a new semi-analytical model based on unsteady conductive heat transfer is developed to estimate SAGD performance and describe the evolution of the steam chamber synchronously. These are implemented by interface velocity of steam chamber, as the function of the parameters of steam with the exponent-shape assumption and energy balance to link the oil output and chamber growth. It is worth mentioning that the equation of oil production is obtained based on the assumption of unsteady temperature distribution along with the interface, which is close to the real condition of the reservoir in fields. Then, the model is validated by using the Phase B, UTF project of the Athabasca reservoir. Finally, the impacts of steam injection parameters on SAGD oil production are discussed in this paper. Initial higher rate of heat injection to reach the production peak quickly and the subsequent lower rate for maintaining peak should be adopted to achieve the efficient target of oil production.

Unsteady numerical simulation and optimization of 499.8 MHz superconducting cavity cooling process at the High Energy Photon Source (HEPS)

Superconducting 499.8 MHz β single cell ellipsoidal cavities of quarter-wave geometry have been chosen for the High Energy Photon Source (HEPS). The cooling process of the superconducting cavity from the room temperature to 4.2 K is an unsteady forced convective heat transfer process. Its heat transfer mechanism analysis and efficient cooling strategy in the cooldown process is insufficient in present studies. In this paper, a three-dimensional coupled heat-flow model of 499.8 MHz superconducting cavity was built. The unsteady temperature distributions of the superconducting cavity in different inlet temperature condition were studied, serving as the training samples for the neural networks. The agent models based on the two sets of Back-Propagation (BP) neural networks (BPNet1 and BPNet2) were designed to obtain a set of quick calculation model. Genetic algorithm (GA) was used to perform the results optimization. The cooling time of the optimized cooling method could be reduced from 480 min to 290 min, with a reduction of about 40% compared the traditional cooling method. The standard deviation σsk of the modified cooling method was 0.56. The maximum temperature difference in each cooling stage approximately approached the allowed temperature difference 20 K, indicating the potential of the cooling method was maximized. The modified cooling method could shorten the total cooling time and greatly improve the efficiency during the cooldown process.

Simultaneous Flow of n-Immiscible Fractional Maxwell Fluids with Generalized Thermal Flux and Robin Boundary Conditions

In a rectangular region, the multilayered laminar unsteady flow and temperature distribution of the immiscible Maxwell fractional fluids by two parallel moving walls are studied. The flow of the fluid occurs in the presence of Robin’s boundaries and linear fluid-fluid interface conditions due to the motion of the parallel walls on its planes and the time-dependent pressure gradient. The problem is defined as a mathematical model which focuses on the fluid memory, which is represented by a constituent equation with the Caputo time-fractional derivative. The integral transformations approach (the Laplace transform and the finite sine-Fourier transform) is used to determine analytical solutions for velocity, shear stress, and the temperature fields with fluid interface, initial, and boundary conditions. For semianalytical solutions, the algorithms of Talbot are used to calculate the Laplace inverse transformation. We used the Mathcad software for graphical illustration and numerical computation. It has been observed that the memory effect is significant on both fluid motion and temperature flow.

Enhancement of Fin Efficiency: a New Proposal

The heat dissipation by fins is very important in many technological systems. The thermal efficiency of fins can be improved depending on many characteristics; one of them is the surface area. This work presents a new fin shapes model used to increase the surface area, keeping the same volume. However, three different fin geometries are used (cylinder, a new fin geometry consisting of cutting cone with hemisphere and an egg (oval) shape fin). A numerical investigation is used to analyze the thermal efficiency of these three types of fins under free convection consideration. The Finite Element Method (FEM) is used as a numerical analysis in order to compute unsteady temperature distribution and heat flux on the surface, based on Ansys Ver.16.1. The new fin shape presented in this study can increase the efficiency by 4%, compared with classical types. The thermal results show that the egg fins have the best thermal efficiency. Moreover, the result is validated and approved by other researchers.

Three‐dimensional computational fluid dynamics modeling of baking of chhana podo (milk cake)

AbstractComputational Fluid Dynamics (CFD) modeling was used to study the air velocity distribution and analyze the unsteady heat transfer and temperature distribution pattern during baking of chhana podo (milk cake). At first, a 3‐D geometry of the baking oven was created, and discrete ordinates (DO) radiation model was employed to predict the distribution of temperature. The data on progressive changes in thermal properties of chhana podo dough during baking were fed into the CFD model. The DO model was found to be adequate to predict the distribution of temperature in the product, with root mean squared error (RMSE) of 1.122 and mean percent relative deviation modulus (%P) of 0.70. Similarly, the DO model was found to be adequate to predict the air temperature distribution in the oven, with RMSE of 1.842 and %P of 1.61. The distribution of air velocity inside the oven was predicted using k‐ω turbulence model. The air velocity near the oven door was 0.505 m/s, whereas it was 5.002 m/s near the fan. Simulation results provided some insights on the effect of spatial location on air velocity. The placement of chhana podo inside the oven was optimized based on this simulation. This CFD simulation has potential application in the design of ovens with enhanced heat transfer and thermal efficiency.Practical ApplicationsThe present work models the heat transfer during baking of chhana podo. Even though a lot of research works related to CFD to products such as bread are available, many studies have not comprehensively considered temperature distribution in the oven, air velocity distribution and heat transfer in the product. The thermo‐physical properties of the product were modeled with respect to temperature and given as inputs into the CFD model. The CFD simulation of air velocity distribution inside the baking chamber will be useful in optimizing the placement of product or dough for uniform baking. The air velocity and heat transfer simulations quantified the diffusion of heat inside the product. This CFD simulation study could be useful in optimization and design of baking ovens for various products. Also, simulation of the baking conditions of a product could be advantageous from the economic perspective.

Analytical solution of heat conduction of a multilayered annular disk and associated thermal deflection and thermal stresses

In this article, a three dimensional multilayered annular disk with internal heat generation under unsteady temperature distribution is considered. Finite integral transform method is used to eliminate the partial derivatives with respect to r, while Fourier series and Fourier transform are used to deal with the variables and z, respectively. Exact solution for the temperature distribution is obtained. The thermal bending moments, thermal deflection and the resulting thermal stresses are obtained and analyzed. The results obtained in series form are numerically evaluated and analyzed by using graphical illustrations.

Unsteady theory of heat transfer and fluid flow during instantaneous transition to film boiling

The paper deals with the problem of unsteady convective heat transfer during instantaneous transition to film boiling over a flat vertical surface, when heat flux is suddenly switched on. This heat flux exceeds the critical value, which corresponds to the onset of the film boiling regime. As a result, instantaneous transition to film boiling takes place. To solve the problem, two sets of the initial and boundary conditions were used. The first set was used in the classical solution of the film condensation problem derived by Nusselt. The second set was proposed by Ellion for a stationary liquid at the vapor-liquid interface. The analytical solution of the problem enabled obtaining unsteady temperature distributions, Nusselt numbers, velocity profiles and friction coefficients. Results obtained based on the Laplace transform and the self-similar solution are analyzed.

The effect of thermal contact resistance on the temperature distribution in a WC made cutting tool

The temperature of a cutting tool during machining process has a direct effect on its lifespan. Manufacturing the tool from materials with high thermal conductivities or cooling the tool during the machining is common ways to avoid the cutting tool overheating. The thermal resistance between assembled parts of a cutting tool is a very important factor, which plays a significant role in the temperature of a cutting tool. In the present work, the effect of thermal resistance between cutting tool and its supports on the temperature of a cutting tool is investigated numerically. The governing equations are solved by COMSOL Multiphysics software to obtain the unsteady temperature distribution and especially the maximum temperature. The cutting device consists of the tool, the shim, and the holder. The tool and the shim are made of WC while the holder is manufactured from AISI 1045 carbon steel. The gap between the assembled parts are filled with four different materials including air, aluminum (Al) foil, copper (Cu) foil, and silicone oil, and the results are compared with the case that there is no thermal resistance between these parts (zero resistance). The case of using air, as a gap filling material, showed the highest maximum temperature. This is attributed to higher thermal resistance of air which prevents proper heat dissipation through the all parts of cutting device. Using copper and aluminum foils considerably decrease the tool maximum temperature and give results close to the case of zero thermal resistance.

Determination and validation of transient temperature fields within a cylindrical element using the inverse heat conduction method

The article aims to determine and experimentally validate the transient temperature fields in a cylindrical component. The applied in-house algorithm, which is based on the inverse heat conduction method, is solved by means of the finite volume method. On the basis of temperature measurements on the outer surface of the element, the algorithm enables thermomechanical analysis of the element. In order to perform experimental validation of the algorithm, the existing laboratory set-up was modernized. During the experiment, the thick-walled steam manifold was heated up rapidly with dry saturated steam. To reconstruct the unsteady temperature distribution within the element, 19 thermocouples were used and 3 thermocouples were inserted inside the wall of the element. The 3 thermocouple locations correspond with nodal positions in the numerical algorithm, thus allowingvalidation of the unstable temperature fields. The analysis of the time-step selection and of the influence of the accidental temperature measurement error on the accuracy of the solution have also been analyzed. Moreover, the algorithm has been validated based on the analytical method. The algorithm does not require knowledge of the boundary conditions on the element’s barely accessible internal surface – a highly valued feature in industrial applications.

Theoretical Investigation into the Thermo-Mechanical Behaviours of Tunnel Lining During RABT Fire Development

Safety assessment of tunnel lining after fire is a compulsory work and should be performed based on thermo-mechanical analysis. In this paper, a theoretical method is presented to investigate the thermo-mechanical behaviours of tunnel lining during fire development. The RABT curve is considered in this model, which includes three stages, i.e. temperature rising, temperature holding and cooling. By employing the Laplace transform and series solving method for ordinary differential equations, solutions for the time-dependent temperature and thermo-mechanical stresses are obtained. The unsteady temperature and stress distributions of the tunnel lining are discussed. Based on the limit state analysis, the fire-induced damage of tunnel lining is evaluated. All of the results are presented and discussed in detail.

Dielectric Loss Model for Asphalt Mixture Based on Microwave Heating

ABSTRACTThe proposed functional equation is established using a two-dimensional dielectric loss model with an unsteady temperature distribution inside the asphalt mixtures to obtain the temperature field when the asphalt mixture is heated by a horn antenna. Furthermore, the boundary conditions are built. The stiffness matrix of overall temperatures is obtained by the discretization of the solution region. The temperature value of each node can be obtained by solving the stiffness matrix. The temperature distribution is achieved in the direction of the electric and magnetic fields by using the -spline function to fit each node temperature. Results show that the temperature gradient in the direction of the electric field is smaller than that in the direction of the magnetic field. The maximum temperature occurs near the center of the horn surface. The simulation and experiment results are consistent, which are significant in solving the stiffness matrix of the overall asphalt mixture temperature.