Final Temperature Distribution Research Articles

FRACTAL MODEL OF POROUS FIN WITH TEMPERATURE-DEPENDENT HEAT GENERATION AND ITS NOVEL SOLUTION

Porous fins with temperature-dependent internal heat generation are frequently used to improve performance in a wide range of heat transfer and porous media applications. Thermal analysis of the porous fin fractal model with temperature-dependent heat generation is generated using fractal derivatives and investigated analytically using a novel Maclaurin series method (MSM). Nonlinear temperature distribution in a porous longitudinal fin is produced by the MSM. The porous fin solution is demonstrated using the Sierpinski fractal, which is based on time-dependent heat generation. The effects of the convection parameter, porosity, internal heat production, and generation number parameter on the dimensionless temperature distribution are discussed. MSM results are graphically and tabularly compared to existing solution methods such as HPM, CM, CSCM, LWCM, and GWRM. A comparison study reveals that MSM is a very reliable, accurate, and effective addition in the field of differential equations.

Calculating the effective thickness of the thermal barrier coating

The paper presents the results of numerical simulation of heat transfer at the interaction of a hot impact nitrogen jet with a ceramic thermal barrier coating 7YSZ based on ZrO2 with the addition of 7% Y2O3. The radiant component of heat transfer is shown to make a significant contribution to the final temperature distribution on the surface of the protected product.

Study of Thermoelastic behaviour, Efficiency and Effectiveness of Rectangular Fin with Fractional Order Energy Balance Equation

In this paper, the analytical solution is obtained for temperature distribution, efficiency, effectiveness and thermal stresses in convective fin of a rectangular profile with thermosensitive conductivity by implementing Homotopy Perturbation Method (HPM). This method is one of the effective tool to solve the fractional order non-linear diffussion equation with thermosensitive conductivity. The results obtained are illustrated graphically for better understanding of the effect of fractional parameter on fin effeciency and effectiveness with respect to thermogeometric fin parameter.

Solutions of fractional order differential equations modeling temperature distribution in convective straight fins design

In this paper, the problem of temperature distribution for convective straight fins with constant and temperature-dependent thermal conductivity is solved by using artificial neural networks trained by the biogeography-based heterogeneous cuckoo search (BHCS) algorithm. We have solved the integer and noninteger order energy balance equation in order to analyse the temperature distribution in convective straight fins. We have compared our results with homotopy perturbation method (HPM), variational iteration method (VIM), and homotopy perturbation Sumudu transform method (HPSTM). The results show that the ANN–BHCS algorithm gives better results than other analytical techniques. We have further checked the efficiency of the ANN–BHCS algorithm by using the performance metrics MAD, TIC, and ENSE. We have calculated the values of MAD, TIC, and ENSE for case 1 of the problem, and histograms of these metrics show the efficiency of our algorithm.

PISCES-RF: a liquid-cooled high-power steady-state helicon plasma device

Radio-frequency (RF) driven helicon plasma sources can produce relatively high-density plasmas (n > 1019 m−3) at relatively moderate powers (<2 kW) in argon. However, to produce similar high-density plasmas for fusion relevant gases such as hydrogen (H), deuterium (D) and helium (He), much higher RF powers are needed. For very high RF powers, thermal issues of the RF-transparent dielectric window, used in the RF source design, limit the plasma operation timescales. To mitigate this constraint, we have designed, built and tested a novel helicon plasma source assembly with a fully liquid-cooled RF-transparent window which allows steady state operations at high power (up to 20 kW) and successfully produces high-density plasma with both argon and H. Deionized (DI) water, flowing between two concentric dielectric RF windows, is used as the coolant. We show that a full azimuthal blanket of DI water does not prevent high-density plasma production. From calorimetry on the DI water, we measure the net heat removed by the coolant at steady state conditions. Using infra-red imaging, we calculate the constant plasma heat deposition and measure the final steady state temperature distribution patterns on the inner surface of the ceramic layer. The heat deposition pattern follows the helical shape of the antenna. We also show the consistency between the heat absorbed by the DI water, as measured by calorimetry, and the total heat due to the combined effect of the plasma heating and the absorbed RF. These results are being used to answer critical engineering questions for the 200 kW RF device materials plasma exposure experiment being designed at the Oak Ridge National Laboratory as a next generation plasma material interaction device.

An accurate approach for thermal analysis of porous longitudinal, spine and radial fins with all nonlinearity effects – analytical and unified assessment

The present study deals with a thermal analysis of porous fins subjected to internal heat generation, convection, and radiation energy transfer considering an actual system of analysis under the moving condition of the fin. The main aspiration to carryout this analysis is to establish a correct approach to derive the governing equation for energy transfer in porous fins. The physical explanation was given to require the modification of all existing analyses of porous fins to exchange heat with the surroundings. Three types of fins, namely longitudinal, annular, and spine, have been analyzed with the common mathematical expressions. The temperature distribution in fins has been obtained by employing the differential transform method for solving a high class nonlinear governing equation for all temperature dependent design variables adopted to develop an actual case study. The present approximate analytical method has been authenticated by the numerical technique based on the finite difference method. An excellent agreement of results between these two analyses has been investigated. Unlike all the published works allied with the porous fin, the present work establishes a correct thermal analysis with the key parameter porosity. A clear demonstration has been discussed to distinguish between the solid and porous fins which can be only conjunction with the porosity. The present method of analysis is equally suited for the solid fin also considering only the zero value of porosity to convert the porous fin into a solid fin directly. An optimization study has also been carried out for the maximization of heat transfer rate for a given volume of the solid fraction of a porous fin. The optimum results indicate that under a given design condition, there is an optimum value of porosity for which the heat transfer rate attains a maximum and it is always higher than the solid fin. Therefore, the enhancement of heat transfer can be significantly done by using porous fins for a constant volume of solid or weight of a fin. Finally, the results have been presented in a direction adopted to clearly visualize the superiority of the present study over that of the existing analyses, and to exhibit a difference between solid and porous fins.

Application of the Trefftz Method for Pool Boiling Heat Transfer on Open Microchannel Surfaces

In the paper, the results of tests on pool boiling heat transfer on open microchannel surfaces were discussed. Nucleate pool boiling from copper microchannel surfaces was examined using ethanol as a working fluid. Parallel microchannels fabricated by machining were about 0.2 to 0.4 mm wide and 0.2 to 0.5 mm deep. In the mathematical model the heat transfer process was in steady state. The heat transfer in copper block was assumed axisymmetric while the specimen temperature distribution was not. The temperature of the copper block and the specimen were assumed to satisfy Laplace’s equations with adequate boundary conditions. The problem was solved by the Trefftz method with two sets of Trefftz functions. Graphs were used to represent the copper block and the specimen temperature distributions, local values of heat transfer coefficients as a function of the heat flux and fin temperature distribution. Uncertainty analysis was presented.

The Development of the Temperature Disturbance Zone in the Surrounding of a Salt Cavern Caused by the Leaching Process for Safety Hydrogen Storage

This article presents an estimation of the temperature decrease in the vicinity of a salt cavern due to its leaching. The one-dimensional radially symmetry models of a salt cavern were considered and described. The initial temperature of rock salt massif was assumed as 50 ∘C and temperature of leaching water varied seasonally from 6 ∘C to 20 ∘C. A significant influence of the season of the leaching process, beginning on the final temperature distribution was found. The model takes into account: convection coefficient changes depending on temperature of brine and rock formation and heat effects caused by salt dissolution. Numerical results are compared with measurements data on the field of cavern volume increasing with time as the function of flow of leaching water and its temperature. The accuracy of the cavern volume increasing versus time was assumed as good—both quantitative and qualitative.

The effects of infill on hydrogen tank temperature distribution during fast fill

The temperature rise of hydrogen tank during fast fill poses challenge on the safety of hydrogen-powered vehicles. Researchers have been continuously looking for methods to mitigate the challenge of overheating. In this paper, we proposed an innovative solution by introducing porous infill in gas tanks to slow down gas-to-wall heat transfer. The porosity of the infill is no less than 97% to maintain the volume capacity of gas tanks. To evaluate the impact of infill heat capacity, we modelled the filling process with a lumped-parameter model and obtained various time-independent temperature evolution curves. Then, we set up a 2D and a 3D finite volume model and investigated the spatial distribution of temperature rise. Four cases with different infill properties were simulated and compared. At the end of the fast fill, the infill resulted in lower tank wall temperature at the cost of higher gas temperature. The combined effect of internal gas temperature and gas-phase effective thermal conductivity largely determines the final temperature distribution. The presence of infill effectively slowed down convective heat transfer, yet overly resistive porous infill may overly slow down the gas flow and result in thermal stratification. Further studies on infill design can be done to seek more effective solutions.

Thermal management of parabolic pin fin subjected to a uniform oncoming airflow: optimum fin dimensions

A concave-parabolic pin fin (spine) is considered within the present research. The thermal property of the spine is exhibited to be affected by a uniform oncoming airflow in an aim at improving its cooling performance. The mathematical model corresponding to one-dimensional physical layout is formulated first from the usual heat balance method. Exact and numerical solutions of the fin temperature distribution are then extracted from the model, relying upon two physical parameters: namely, the Peclet number Pe, controlling the magnitude of the airflow and the fin shape parameter $$\alpha$$ , adjusting the spine shape. It is shown that these parameters have high impacts on the performance of the parabolic pin fin towards cooling the medium it is attached to. Finally, optimum concave parabolic pin fins corresponding to a given volumetric region are identified by means of maximizing the base heat transfer rate. Interestingly, the optimum dimensions of the spine are found to be much influenced by the variation in Peclet number.

Radio frequency tempering of frozen pacific sauries (Cololabis saira) under batch and continuous mode: Temperature distribution and energy consumption evaluation

AbstractTo investigate the influences of modes and operating parameters on the radio frequency (RF) tempering uniformity of a pack of frozen pacific sauries, a 27.12 MHz RF equipment was employed for sauries tempering with different input power and electrode gaps under batch and continuous mode. Nine frozen sauries were placed in the RF chamber and tempered under different input power (200, 400, 800, 1,600 W), electrode gaps (7, 8, 9 cm) under batch and continuous tempering mode. With a target end‐point tempering temperature of −4°C. Results showed 200 W/9 cm resulted in the longest tempering time (16.44, 15.43 min) and 1,600 W/7 cm was the shortest (2.95, 3.54 min) under batch mode tempering, respectively. The processing conditions of 200 W/9 cm and 200 W/7 cm under batch mode, and 200 W/8 cm, 200 W/9 cm, 400 W/9 cm, 800 W/8 cm under continuous mode all produced a final sample surface temperature distribution within the range of −10°C to 20°C, which indicated a reasonable tempering process. The area of the high temperature zone (10°C &lt; T ≤ 20°C) of tempered sauries under 200 W/9 cm decreased from 0.28% to 0.23% when switching from batch to continuous mode. This implies that continuous RF tempering could reduce overheating and improve tempering uniformity of sauries.Practical applicationsTempering rate, temperature distribution, and energy consumption are the most important concerns to researchers and the industry since tempering temperature and time are highly correlated to fish product quality. Results in this study showed both batch and continuous mode RF tempering could achieve reasonable tempering effect to a pack of frozen sauries. The application of continuous tempering system is more desirable than the batch ones, which can be applied to the tempering industry with higher throughput and connect to the following continuous processing unit operations. This study will broaden the knowledge of food engineers and provide an alternative technology of aquatic product tempering, and the parameters used in this study can assist technologists for the development of commercial equipment.

Application of an Integral Numerical Technique for a Temperature-Dependent Thermal Conductivity Fin with Internal Heat Generation

A numerical study of convective heat transfer in a longitudinal fin with temperature-dependent thermal conductivity and internal heat generation is undertaken. Integral calculations are implemented on each generic element of the discretized problem domain. The resulting systems of nonlinear equations are solved efficiently because of the coefficient matrix sparsity to yield both the dependent variable and its flux. In order to validate the formulation, the effects of the thermogeometric parameter, nonlinearity due to the temperature-dependent thermal conductivity, and of the heat transfer coefficient on the fin temperature distribution are investigated. The results are found to be in agreement with those for similar problems described in the literature and with the physics of the problem.

A numerical study of new fractional model for convective straight fin using fractional-order Legendre functions

The Fractional-order model of fin problem in the presence of a temperature-dependent rate of internal heat generation in fin material has been studied in the proposed paper. Fractional-order Legendre functions (F-OLFs) with the Galerkin approach has been used to compute the result of the proposed fin problem. The exact solution is also calculated in a particular case of our fractional-order fin problem. The proposed fin problem has been presented in the non-dimension form. Temperature distribution in the straight fin is calculated for different values of used variables or parameters along space coordinate. The impact of different parameters such as fractional order, fin parameter, internal heat generation, generation number, etc. on the temperature profile in the fin is described in detail. The cooling process is faster in fractional order fin problem than the integer-order.

Temperature Distribution in Porous Fins, Subjected to Convection and Radiation, Obtained from the Minimization of a Convex Functional

This work proposes a convex functional endowed with a minimum, which occurs for the solution of the thermal radiation and natural convection heat transfer problem in a rectangular profile porous fin with a fluid flowing through it. The minimum principle ensures the (mathematically demonstrated) uniqueness of the solution and allows the problem simulation by employing a minimization procedure. Darcy’s law with the Oberbeck–Boussinesq approximation simplifies the momentum equation. The energy equation assumes thermal equilibrium between the porous matrix and fluid, allowing comparisons with previous authors’ models, which accounts for the effects of a porosity parameter, a radiation parameter, and a temperature ratio on the temperature. Results for very long fin and finite-length fin with insulated tip were successfully compared with previous works. Closed-form exact solutions for two limiting cases (no convection and no thermal radiation) are also presented.

Two-channel time-optimal control of induction heating process with maximum temperature constraint

The formulation and method of solution of the problem of time-optimal control of induction heating process of an unlimited plate with two control actions on the value of internal heat sources with technological constraint in relation to a one-dimensional model of the temperature field are proposed. The problem is solved under the conditions of a given accuracy of uniform approximation of the final temperature distribution over the thickness of the plate to the required. The method of finite integral transformations is used to search for the input-output characteristics of an object with distributed parameters with two control actions. The preliminary parameterization of control actions based on analytical optimality conditions in the form of the Pontryagin maximum principle is used. At the next stage reduction is performed to the problem of semi-infinite optimization, the solution of which is found using the alternance method. The alternance properties of the final resulting temperature state at the end of the optimal process lead to a basic system of relations, which, if there is additional information about the shape of the temperature distribution curve, is reduced to a system of equations that can be solved. An example of solving the problem of time-optimal control of temperature field of an unlimited plate with two offices is carried out in two stages. At first stage the case of induction heating without maximum temperature constraints is considered, at the second stage is carried out on the basis of the results of the first stage to obtain the solution subject to the limitation on the maximum temperature of the heated billet.

A novel analytical model for the thermal behavior of a fiber-reinforced plastic pulley in a front-end accessory drive

This research proposes an innovative model for calculating the temperature distribution of a composite pulley inside a belt drive. The main advantage of the proposed model is a significant reduction in the costs of calculation resources and time. This model adopts two classical theories to determine the heat generation flux and subsequent thermal flow into the pulley. Then, ordinary differential equations are developed in this model according to the irregular geometric structures of a pulley to describe the thermal flow inside this component. Afterward, analytical solutions of the ordinary differential equations are derived to provide final temperature distributions of the pulleys. Moreover, measurements of thermal properties are conducted to reduce the influence of errors. To improve the reliability of the results, experimental temperature measurements were performed on a composite pulley of a designed belt drive system in an engine dynamometer system to validate this analytical model under various operating conditions. The temperature data measured at multiple locations indicate good agreement with the corresponding analytical results. Therefore, the temperature distribution provided by this model can be utilized for the development of high-thermal resistance composite. It can also be used for thermal fatigue simulations of composites under numerous load cases.

Mathematical Model of the Solar Pyrolysis of Biomass

Abstract The paper presents a two-dimensional computational fluid dynamics (CFD) model of lab-scale fixed-bed pyrolytic reactor. The goal of the work was to verify assumptions regarding construction and operating parameters of the pyrolytic reactor and examining heat transfer conditions and the final temperature distribution in the system taking into account the endothermic pyrolysis reactions occurrence. The impact of the most important numerical parameters on simulation results was also investigated. Model was prepared in ansys fluent 18.2 software. The studies have shown large temperature gradients both in the biomass deposit and at the reactor walls. The analysis has confirmed the validity of the proposed reactor construction concept and allowed to specify the range of thermal power value necessary for obtaining the pyrolysis process in a system with given properties and dimensions. Increasing the heat flux supplying the reactor from 160 to 480 W caused acceleration and intensification of biomass thermal decomposition, while the average final bed temperature after 10 min of heating in each case was reaching similar level. Low thermal conductivity of the bed and strong heat absorption due to pyrolysis suppress heat transfer through the bed, which causes significant temperature differences between the warmest and coldest regions of the bed. However, temperature unevenness and hence the unevenness of the pyrolysis process can provide favorable conditions for measuring the gas composition leaving the reactor due to the relatively balanced time stream of pyrolysis gases.

Temperature and Stress Evaluation during Three Different Phases of Friction Stir Welding of AA 7075-T651 Alloy

The current study performs an explicit nonlinear finite element simulation to predict temperature distribution and consequent stresses during the friction stir welding (FSW) of AA 7075-T651 alloy. The ABAQUS® finite element software was used to model and analyze the process steps that involve plunging, dwelling, and traverse stages. Techniques such as Arbitrary Lagrangian–Eulerian (ALE) formulation, adaptive meshing, and computational feature of mass scaling were utilized to simulate sequence events during the friction stir welding process. The contact between the welding tool and workpiece was modelled through applying Coulomb’s friction model with a nonlinear friction coefficient value. Also, the model considered the effect of nonlinear material properties as well as heat transfer conditions such as heat losses due to convection and thermal contact conductance between the workpiece and the backing plate interface on the thermal history. To validate the computational model results, an experimental procedure was carried out to measure temperature history on both sides of the specimen as well as the plunging force throughout the whole process time. The results obtained showed that symmetrical temperature distribution throughout the workpiece width was distinguished, implying that the tool rotation has a minor effect on the final temperature distribution. In addition, asymptotic V shape with high gradient temperature value in the weld nugget region after the full plunging was distinguished. Mechanical stresses and related plastic deformations generated, while achieving the FSW samples were evaluated in addition to the tool reaction force and heat generated to protect against tool failure.

Temperature distribution inside Ising system confined by fixed boundary temperatures

In this paper, a two dimensional Ising model system in which the two boundaries of it are confined by two fixed boundary temperatures has been taken into consideration, obviously, the temperature inside the system is self-adjusting. To investigate the temperature evolutionary process of this Ising model system, the energy-exchange has been introduced in the Monte Carlo steps, and then the temperature variation of a local region is determined by the energy-exchange. Making use of above modified Monte Carlo method, a final steady temperature distribution of the system has been determined, and the obtained results suggest that this temperature distribution is nonlinear: from the constant temperature of the boundary to the critical temperature, the temperature variation is almost linear; however, lots of the local temperatures near the critical value remain almost unchanged and a temperature platform is obtained. Furthermore, the length of the temperature platform is much larger than that of the linear variation part. Meanwhile all the physical quantities and their fluctuations were also obtained by the Monte Carlo simulations, and the results show that, near the critical temperature, the fluctuations of magnetization are much larger than that of the energy, specific heat and magnetic susceptibility.

Numerical Simulation of Dual-Phase-Lag Model and Inverse Fractional Single-Phase-Lag Problem for the Non-Fourier Heat Conduction in a Straight Fin

In recent years, many studies have been done on heat transfer in the fin under unsteady boundary conditions using Fourier and non-Fourier models. In this paper, unsteady non-Fourier heat transfer in a straight fin having an internal heat source under periodic temperature at the base was investigated by solving numerically Dual-Phase-Lag and Fractional Single-Phase-Lag models. In this way, the governing equations of these models were presented for heat conduction analysis in the fin, and their results of the temperature distribution were validated using the theoretical results of Single and Dual-Phase-Lag models. After that, for the first time the order of fractional derivation and heat flux relaxation time of the fractional model were obtained for the straight fin problem under periodic temperature at the base using Levenberg-Marquardt parameter estimation method. To solve the inverse fractional heat conduction problem, the numerical results of Dual-Phase-Lag model were used as the inputs. The results obtained from Fractional Single-Phase-Lag model could predict the fin temperature distribution at unsteady boundary condition at the base as well as the Dual-Phase-Lag model could.