Final Temperature Distribution Research Articles

Predication of nonlinear heat transfer in a convective-radiative fin with temperature-dependent properties by the collocation spectral method

ABSTRACTThe applicability of the collocation spectral method (CSM) for solving nonlinear heat transfer problems is demonstrated in a convective-radiative fin with temperature-dependent properties. In this method, the fin temperature distribution is approximated by Lagrange interpolation polynomials at spectral collocation points. The differential form of the energy equation is transformed to a matrix form of algebraic equations. The computational convergence of the CSM approximately follows an exponential decaying law; and thus, it is a very simple and effective approach for a rapid assessment of nonlinear physical problems. The effects of temperature-dependent properties such as thermal conductivity, surface emissivity, heat transfer coefficient, convection-conduction parameter, and radiation-conduction parameter on the fin temperature distribution and efficiency are discussed.

Numerical investigation to study effect of radiation on thermal performance of radiator for onan cooling configuration of transformer

In the present work, flow and temperature distribution in the radiator fins of a power transformer is studied numerically with conjugate heat transfer using commercial CFD software to study the effect of radiation on heat dissipation. The approach considered here is a complete 3D geometry of the radiator fins with average height of the flute geometry of the fins for meshing and computational time reduction. Simulations are performed for ONAN (Oil Natural Air Natural) case for one radiator configuration. The simulations also study the effect of radiation and its impact on the overall heat dissipation. These results would give a holistic picture of heat transfer phenomenon to the designers.

A computational study of mixed convective heat and mass transfer from a shrouded vertical non-isothermal fin array during dehumidification process

A computational study is made on simultaneous heat and mass transfer from a shrouded vertical non-isothermal finite thickness fin array representing dehumidification process undergoing mixed convection. Governing equations involve number of parameters, namely, dimensionless fin spacing (0.1⩽S∗⩽0.5), dimensionless clearance (0⩽tc∗⩽0.2), non-dimensional fin conductance parameter (2830.18⩽Ω⩽5660.37), thermal Grashof number (1.04×105⩽Grt⩽4.82×105), mass Grashof number (2.9×104⩽Grm⩽1.36×105), and dimensionless inlet mixed convection velocities (1123⩽Win,mix⩽2879). Induced velocity is decoupled from the mixed convection velocity and correlated with the governing parameters. Fin temperature distribution shows significant variation along the fin height as well as along the axial direction, especially near the entrance. Local thermal Nusselt number and local condensing Nusselt number show monotonic decreasing trend along the axial direction. Finally induced velocity, pressure drop, overall thermal Nusselt number, and overall condensing Nusselt number is correlated with the governing parameters.

Thermal performance characteristics of an absorber plate fin having temperature dependent thermal conductivity and overall loss coefficient

The prime objective of the present numerical study is to analyze the thermal performance characteristics of an absorber plate fin of a sheet and tube type solar flat plate collector of fixed collector area. Considering temperature dependent thermal conductivity and overall loss coefficient and assuming cubic temperature profile along the tube, pseudo-transient form of two-dimensional, highly nonlinear partial differential equation governing the steady state temperature distribution in the absorber plate fin is solved using Alternating Direction Implicit finite difference scheme. Keeping ambient temperature, fluid inlet temperature and number of tubes fixed, numerical results are presented and discussed for wide range of values of aspect ratio of the absorber plate, fluid outlet temperature, overall loss parameter and solar flux. Finally, it is found that there exists an upper limiting value of solar flux beyond which increase in heat transfer rate is insignificant. Further, it is concluded that fin efficiency remains independent of aspect ratio of absorber plate whereas it increases significantly with decrease in overall loss parameter and decreases slightly with increase in fluid outlet temperature.

Periodic Heat Transfer in Convective Fins Based on Dual-Phase-Lag Theory

Heat transfer enhancement through extended surfaces is crucial in modern engineering applications such as microelectromechanical systems and electronic components. Conduction heat transfer is the only way to achieve this objective when the mixing augmentation is not possible. This paper investigates the effects of non-Fourier thermal conduction in convective straight fins with arbitrary constant cross section under periodic boundary conditions by introducing the exact analytical solution for the dual-phase-lag heat conduction. The corresponding analytical approach is developed through the Laplace transform method and inversion theorem. To help advance the understanding of fin thermophysical behavior, a generalized model of conduction heat transfer equation is used for studying all of the interpretations to Fourier-based model, namely, parabolic thermal diffusion, hyperbolic thermal wave, and dual-phase-lag models. Heat flux and temperature gradient relaxation times are the characteristics of the dual-phase-lag model, and the simulation results are strictly a function of these two parameters. Therefore, fin temperature distributions are presented for flux precedence and gradient precedence heat flow regimes. Calculations are performed to investigate the influence of temperature gradient relaxation time on the hyperbolic heat conduction characteristics of non-Fourier fins.

Determination of Temperature Distribution for Porous Fin with Temperature-Dependent Heat Generation by Homotopy Analysis Method

In this study, highly accurate analytical methods, Homotopy Analysis Method (HAM), is applied for predicting the temperature distribution in a porous fin with temperature dependent internal heat generation. The heat transfer through porous media is simulated using passage velocity from the Darcy’s model. It has been attempted to show the capabilities and wide-range applications of the Homotopy Analysis Method in comparison with a type of numerical analysis as Boundary Value Problem (BVP) in solving this problem. The results show that the HAM is an attractive method in solving this problem.

Effect of mode stirrers in a multimode microwave-heating applicator with the conveyor belt

In this work, a numerical study is performed to know the effect of mode stirrers on the temperature distribution inside a microwave cavity with a conveyor belt system. A 3-dimensional simulation model is built and simulated using the COMSOL Multiphysics software. Since it is very difficult to simulate the mode stirrer’s motion using COMSOL, eleven still angles of the mode stirrers are considered. The final temperature distribution result is obtained by taking the average of all eleven angles results. Also to get the final temperature of a heated material after it comes out of the cavity, the average of all temperature values in the direction of conveyor belt motion is taken as it is assumed that conveyor belt motion is much slower than the speed of the mode stirrers. The simulation results show that temperature distribution is more uniform for the case with mode stirrers compared to that obtained without mode stirrers. This is confirmed by using standard deviation equation.

Convective-radiative fin with temperature dependent thermal conductivity, heat transfer coefficient and wavelength dependent surface emissivity

In this paper, we have studied heat transfer process in a continuously moving fin whose thermal conductivity, heat transfer coefficient varies with temperature and surface emissivity varies with temperature and wavelength. Heat transfer coefficient is assumed to be a power law type form where exponent represent different types of convection, nucleate boiling, condensation, radiation etc. The thermal conductivity is assumed to be a linear and quadratic function of temperature. Exact solution obtained in case of temperature independent thermal conductivity and in absence of radiation conduction parameter is compared with those obtained by present method and is same up to ten decimal places. The whole analysis is presented in dimensionless form and the effect of variability of several parameters namely convection-conduction, radiation-conduction, thermal conductivity, emissivity, convection sink temperature, radiation sink temperature and exponent on the temperature distribution in fin and surface heat loss are studied and discussed in detail.

Analytical investigation of convective heat transfer of a longitudinal fin with temperature-dependent thermal conductivity, heat transfer coefficient and heat generation

In this article, the heat transfer through a longitudinal fin is studied. The heat transfer coefficient, thermal conductivity and heat generation are variables and supposed to be temperature-dependent. The temperature distribution in fin with longitudinal rectangular profile was carried out by using the differential transformation method (DTM) which is an analytical solution technique. For validation of the analytical solution, the heat equation is solved numerically. The temperature distribution is shown for different values of the embedding parameters. The DTM results indicate that the fin tip temperature increases with an increase in the heat generation gradient. Results reveal that DTM is very effective and convenient. Comparison of the results (DTM and numerical) was shown that the analytical method and numerical data are in a good agreement with each other. Key words: Fins, temperature dependent thermal properties, heat generation, analytical solutions, differential transformation method (DTM).

Refrigeration efficiency analysis for fully wet semi-spherical porous fins

In this study, temperature distribution equation for a fully wet semi-spherical porous fin is presented by a new modified fin parameter introduced by Sharqawy and Zubair which can be calculated without needing to fin tip conditions. The driving forces for the heat and mass transfer are considered temperature and humidity ratio differences, respectively. It is assumed that heat and mass convective coefficients are temperature-dependent and heat transfer through the porous media is simulated by using the passage velocity from the Darcy’s model. After introducing the governing equation, Least Square Method (LSM) and fourth order Runge–Kutta method (NUM) are applied to predict the temperature distribution in a Si3N4 porous fin. Also, the effects of porosity, Darcy number, Rayleigh number, Lewis number, etc. on the fin efficiency are investigated. As a main outcome, results confirm that Lewis number should be significantly more than unit to make high refrigeration efficiency.

Effect of thermo-geometric parameters on entropy generation in absorber plate fin of a solar flat plate collector

The prime objective of the present numerical study is to obtain relatively more realistic values of performance parameters of a sheet and tube type solar flat plate collector of fixed collector area and number of tubes. Considering temperature dependent thermal conductivity and overall loss coefficient and assuming cubic temperature profile along the tube, pseudo-transient form of two-dimensional, nonlinear partial differential equation governing the steady state temperature distribution in the absorber plate fin is solved using Alternating Direction Implicit finite difference scheme. Numerical results are presented and discussed for wide range of values of aspect ratio of the absorber plate, overall loss parameter, and dimensionless fluid outlet temperature. On the basis of discussion of these results, it is concluded that assumption of constant thermal conductivity and overall loss coefficient results in overestimation of the total entropy generation rate with substantial error. It is also concluded that for any fixed set of values of dimensionless fluid outlet temperature and overall loss parameter, total entropy generation rate increases linearly with increase in aspect ratio of absorber plate. Further, it is found that total entropy generation rate increases with increase in overall loss parameter, the rate of increase being somewhat higher for lower values of overall loss parameter and a decrease in fluid outlet temperature results in an appreciable increase in total entropy generation rate.

Metal eFuse Test-Key Design with Electro-Thermal Modeling for 28 HKMG Technology

This paper employs a novel electro-thermal modeling methodology to assist eFuse test-key design. The temperature distribution for eFuse is simulated based on electrical Joule-heating and thermal heat conduction in eFuse and surrounding materials. The electrical Joule-heating strongly depends on the contact pads and wiring shapes. The thermal heat conduction is important for the hot-spot to reach the burn-out temperature range. The final temperature distribution and hot-spot for each type of test-key under preset electrical operation condition depend on material electrical and thermal properties. Thermal boundary conditions are applied to establish thermal equivalent surrounding effects. Test structure design splits include anode/cathode shapes, wiring sizes, and via configurations. Simulated test-key designs with hot-spots in the desired position and failing in the melting temperature range are then selected to build actual test vehicles. This electro-thermal modeling assisted test-key design methodology effectively speeds up the turnaround time and reduces the development cost.

A regularization method for solving the radially symmetric backward heat conduction problem

Abstract This work is devoted to solving the radially symmetric backward heat conduction problem, starting from the final temperature distribution. The problem is ill-posed: the solution (if it exists) does not depend continuously on the given data. A modified Tikhonov regularization method is proposed for solving this inverse problem. A quite sharp estimate of the error between the approximate solution and the exact solution is obtained with a suitable choice of regularization parameter. A numerical example is presented to verify the efficiency and accuracy of the method.

Thermal behavior of longitudinal convective–radiative porous fins with different section shapes and ceramic materials (SiC and Si3N4)

In this study, heat transfer and temperature distribution equations for longitudinal convective–radiative porous fins are presented. It is assumed that the thickness of fins varies with length, so four different shapes (rectangular, convex, triangular and exponential) are considered. Temperature-dependent heat generation, convection and radiation are considered and heat transfer through porous media is simulated using passage velocity from Darcy's model. After deriving equation for all geometries, the Least Square Method (LSM) and fourth order Runge–Kutta method (NUM) are applied for predicting the temperature distribution in the porous fins. The selected ceramic porous materials are Al, SiC, and Si3N4. Effects of porosity, Darcy number, Rayleigh number, etc. on transferred heat are examined. As a main outcome, exponential section fin with Si3N4 material has the most amount of transferred heat among other shapes and materials.

Investigation of refrigeration efficiency for fully wet circular porous fins with variable sections by combined heat and mass transfer analysis

Temperature distribution equation and refrigeration efficiency for fully wet circular porous fins with variable sections are introduced in this study by a new modified wet fin parameter presented by Sharqawy and Zubair. This parameter can be calculated without knowing the fin tip condition by considering the temperature and humidity ratio differences for the driving forces of heat and mass transfer, respectively. It's assumed that heat and mass convective coefficients vary with fin temperature and heat transfer through porous media is simulated using passage velocity from the Darcy's model. After presenting the governing equation, Least Square Method (LSM) and fourth order Runge-Kutta method (NUM) are applied for predicting the temperature distribution in the sample aluminum porous fins. After that, effects of porosity, Darcy number, Rayleigh number, Lewis number and etc. on fin efficiency are examined. As a main outcome, for reaching to high values of fin efficiency, rectangular fin should be used instead of convex and triangular sections.

Thermal performance of circular convective–radiative porous fins with different section shapes and materials

In this study, heat transfer and temperature distribution equations for circular convective–radiative porous fins are presented. It’s assumed that the thickness of circular fins varies with radius so four different shapes, rectangular, convex, triangular and exponential, are considered. The heat transfer through porous media is simulated using passage velocity from the Darcy’s model. After deriving equation for each geometry, Least Square Method (LSM) and fourth order Runge–Kutta method (NUM) are applied for predicting the temperature distribution in the porous fins. The selected porous fin’s materials are Al, SiC, Cu and Si3N4. Results reveal that LSM has very effective and accurate in comparison with the numerical results. As a main outcome, Si3N4-exponential section fin has the maximum amount of transferred heat among other fins.

The evaluation for the chromatic characteristics of LED module under electrical and thermal coupling analysis

Towards energy-saving, high efficiency, and low pollution, the lighting of light-emitting diode systems, the solid state lighting, is important for the future of green energy technology industry. It becomes the replacement of traditional lighting, such as light bulbs and compact fluorescent lamps. Because of the characteristics of semiconductor, the electrical property of light-emitting diodes is varying with operating temperature. Then, the alternation of electrical property changes the heating power and operating temperature of light-emitting diodes. This is a mutual interaction between electrical property and operating temperature until they reach the steady state. The final current and temperature distributions decide the optical and chromatic characteristics of light-emitting diodes. Besides increasing the luminous efficiency, effectively controlling electricity and thermal characteristics in the design of light-emitting diode lighting products is the key point to achieve the demand of light and color. In this paper, we designed experiments and calculation algorithm to do the temperature distribution simulation of light-emitting diode module. Then, we obtained the analysis technology to predict the reliably optical and chromatic characteristics of light-emitting diode module in practical use.

Study on the Heat Transfer of the Rectangular Fin with Dehumidification: Temperature Distribution and Fin Efficiency

This study presents a numerical investigation of the fin efficiency and temperature distribution of a plain fin with combined heat and mass transfer. Using the finite difference scheme the differential equation results from an energy balance on an element of the fin has been solved to obtain temperature distribution along the fin surface. The effects of variations in relative humidity, dry air and fin base temperatures, atmospheric pressure, and fin pitch on temperature distribution and also on fin efficiency are discussed.

Heat transfer study through porous fins (Si3N4 and AL) with temperature-dependent heat generation

In this study, three highly accurate and simple analytical methods, Differential Transformation Method (DTM), Collocation Method (CM) and Least Square Method (LS) are applied for predicting the temperature distribution in a porous fin with temperature dependent internal heat generation. The selected porous fin’s materials are Si3N4 and AL and generated heat varies linearly with temperature. The heat transfer through porous media is simulated using passage velocity from the Darcy’s model. Results reveal that DTM, CM and LS are very effective and accurate in comparison with the numerical results. Moreover the temperature distribution is depended to the Darcy and Rayleigh numbers. In addition the results show that using the AL as a porous fin’s substrate leads to higher value of temperature than Si3N4 element. A higher heat generation rate leads to higher fin temperatures since more amount of heat is dissipated to the surrounding.

Numerical Analysis of Effect of Backplate Diffusivity on the Transient Temperature in Friction Stir Welding

It is still not clearly known as to what extent the temperature field of friction stir welding joint is influenced by backplate diffusivity owing to the limitation of temperature measuring points. In the present study, therefore, the effect of backplate diffusivity on the temperature field of the workpiece was systematically investigated based on the numerical analysis. Simulated results show that the backplate diffusivity has a significant influence on not only the peak temperature but the final temperature distribution. More heat is dissipated by using a high thermal conductivity backplate during FSW. With increasing the backplate diffusivity, the peak temperature decreases gradually and the average cooling rate increases first and then slightly decreases. In addition, the time spent above 195 °C presents a nearly linear decrease with increasing the backplate diffusivity. Moreover, the width of temperature region higher than 195 °C in the transverse direction is remarkably diminished by using the backplate of a high conductivity, and changes little during the entire process.