Temperature-dependent Heat Transfer Coefficient Research Articles

Heat transfer and thermal analysis in a semi-spherical fin with temperature-variant thermal properties: an application of Probabilists’ Hermite collocation method

Finned surfaces are utilized in several industrial and technological applications including radiators in cars, air conditioning systems, and computer CPU heat sink to dissipate heat through convection or radiation. In this regard, the heat transfer enhancement utilizing the fins has received more attention in the scientific field. Motivated by this, the present research explicates temperature variation through a convective-radiative semi-spherical fin (SSF) with internal heating by taking into consideration of linear and nonlinear temperature-dependent heat transfer coefficient and thermal conductivities. Furthermore, the efficiency and heat transfer aspects of the fin are elaborated. The Rosseland approximation is used in this study to analyze radiation heat exchange. The developed energy equation is converted to a nonlinear ordinary differential equation (ODE) using dimensionless terms, and the probabilists’ Hermite collocation method (PHCM) is used to solve this problem. The governing parameters have been varied in their appropriate ranges to illustrate their impact on the thermal profile, and the results have been portrayed graphically. Some notable key findings of the current analysis are that as the scale of the convection–conduction and the radiation number upsurges, the thermal distribution through SSF drops. On the other hand, thermal distribution escalates for heat generation and thermal conductivity parameters.

Numerical investigation on the thermal response of an unsteady magnetohydrodynamics straight porous fin

Fins are frequently used in many heat transfer applications and also for the control and prevention of thermal damage in electronic and mechanical equipment. Thus, the current investigation focuses on estimating the thermal performance, efficiency, and effectiveness of MHD straight porous fin with temperature-dependent heat transfer coefficient, thermal conductivity, and emissivity. The finite-difference approximation is utilized to solve the governing nonlinear differential equation and numerical solutions are endorsed by analytical solutions of the steady-state model using the partial Noether method, Adomian decomposition method, and homotopy perturbation method. From the model predictions, it is noticed that the rise in geometry parameter, magnetic parameter, Rayleigh number, time, and Biot number rises the heat transfer rate of the system. In addition, fin efficiency and effectiveness are directly correlated with boiling parameter, thermal conductivity parameter, and porosity.

Cooling Capacity of Oil-in-Water Emulsion under wet Machining Conditions

Many industrial machining operations are carried out under wet machining conditions. Modelling and simulating fluid-structure-interactions and conjugate heat transfer are still a challenge nowadays. In this paper, temperature dependent heat transfer coefficients (HTC) h(T) are experimentally estimated for wet machining-like conditions in a jet cooling experiment. The transient temperature is thereby used to solve an Inverse Heat Transfer Problem for HTC function estimation. Determined HTC are applied as input in related jet cooling simulation using the Finite-Pointset-Method (FPM) to validate the modeling approach. Additionally, wet cutting simulations numerically highlight the influence of determined HTC h(T) on turning.

Thermal-shock experiments for separate-effects validation of UO[formula omitted] fuel fracture models

Because of the important role that fracture plays in the behavior of ceramic UO2 fuel in a nuclear reactor environment, fracture models are a major component of fuel performance codes. As with any aspect of fuel performance, it is crucial to validate these fracture models against experimental data; however, obtaining well-controlled data for conditions representative of a reactor environment is difficult. Quenching is proposed here as a relatively simple approach for using in a laboratory environment to achieve conditions that approximate those of a reactor environment. In this paper, an experimental apparatus containing a single instrumented fuel pellet in a sealed section of copper tubing is developed and applied to a series of seven experiments in which the apparatus is first heated to a high temperature (580–680 °C) by immersion in a molten salt bath, then quenched in a cold bath (-10–4 °C). Development of these experiments was guided by numerical simulations, and post-test simulations were performed to aid in understanding the experimental behavior and assessing the accuracy of the predictions of fracture initiation and propagation. In addition, similar experiments were performed on solid copper rods to provide temperature-dependent heat transfer coefficients for use in simulations of these experiments. This study demonstrates that quenching is a viable approach for generating thermal gradients representative of those in prototypical light-water reactor conditions at powers of about 5–10 kW/m. Fracture is expected to begin at these power levels, and moderate amounts of radial and axial cracking was observed in these quenching tests.

Thermal Analysis of the Effect of Absorber Plate Geometric Parameters on the Dynamic of an Indirect Type Solar Dryer

Abstract This paper studies the effects of the absorber plate geometry on the thermal performance of an indirect solar dryer considering temperature dependent thermal conductivity and heat transfer coefficients. The main goal was to explore the effects of the absorbers confined air as well as the absorber plate thicknesses and to provide more realistic characterizations of the thermal dynamic of an indirect solar dryer. The heat transfer process is described using highly nonlinear partial differential equations. The mathematical model accounts the contribution of the upper soil surface temperature calculated using the boundary layer similarity theory. The established mathematical equations describing heat transfer in the solar drying system are solved numerically using a developed matlab program. The investigations of heat transfer of the proposed model reveal excellent agreement of prediction responses with the experimental results from the literature. Mathematical model of indirect solar drying prototype developed with double absorber plates separated with a confined air layer operates more effectively with a thermal efficiency greater than 6% compared to the model without confined air configuration. The numerical experiments also show the non-negligible effects of the absorber plate thickness on the thermal dynamic of an indirect solar dryer.

Effect of Internal Decay Power and Surface Cooling on Nuclear Fuel Droplet Solidification During MFCI in a SFR—A Numerical Study

Melting of the nuclear core is one of the severe accident scenarios in a Sodium-cooled Fast Reactor (SFR). During such an event, molten corium may come into contact with the coolant sodium. This interaction of the molten fuel and the coolant is commonly termed molten fuel–coolant interaction (MFCI) in the nuclear industry. In this study, a numerical analysis is carried out to study the solidification of a molten fuel droplet in the liquid sodium pool. In the first part of the study, the effect of constant internal heat generation on the solidification of the droplet is evaluated with convective heat dissipation prescribed at the droplet surface. The internal heat generation (decay power) and the heat transfer coefficient are varied as parameters, and the time required for complete solidification of the molten droplet is obtained. Based on the results, the freezing of the droplet is categorized into three regimes: conduction limited, transition, and internal heat generation dominated regimes. It is observed that the solidification process of nuclear fuel droplets generated during MFCI is not influenced by internal heat generation and lies in a conduction-limited regime for decay power level prevailing in a medium-sized SFR. Hence, in the next part of the study, the numerical analysis is carried out by incorporating the time-dependent decay power and the temperature-dependent heat transfer coefficient in the computational model by developing user-defined subroutines depicting a realistic scenario of an accident. The results of the analysis show that because of the high subcooling of sodium, film boiling is ruled out; nucleate boiling with a maximum heat transfer rate occurs briefly. The heat transfer coefficient then declines as the interface temperature between the droplet and the sodium decreases rapidly until the natural convective regime is reached. A parametric study on the droplet diameter is also carried out by varying the diameter from 0.5 to 10 mm, spanning the typical particle size spectrum expected during MFCI.

Computational study to predict the thermal performance and optimal design parameters of a T-shaped fin subjected to natural convection

The present paper aims to predict the optimal design parameters of a T-shaped fin subjected to natural convection using constructal theory. Both analytical and computational investigations are performed to determine its thermal performance for a wide range of thermo-physical and geometric parameters. Power law type temperature-dependent heat transfer coefficient is assumed for natural convection. For analytical solution Adomian decomposition method is adopted to evaluate the temperature distribution in both the stem and flange part of the fin. A numerical scheme called finite difference method is implemented to validate the analytical results. The temperature distribution obtained from the computational analysis using ANSYS FLUENT 14.0 is lower than that obtained from the analytical calculations. Moreover, the actual heat transfer rate is also compared between the two methods which reveal that the computational analysis gives higher value as compared to the analytical results. Further, optimization study has also been carried out in a generalized way so that either the fin volume or the heat transfer rate can be taken as a constraint. It is found that with the increase in length ratio, the optimum effectiveness is obtained at a higher value of aspect ratio whereas the optimum efficiency is obtained at a lower value of it. Though, a decrease in thickness ratio predicts a higher value of actual dimensionless heat transfer rate.

A Coupled Multifield Estimation for Temperature Rise in a Gas Insulated Bus Bar Using ANSYS

Gas Insulated Switchgear (GIS) is an integral part of the urban power systems, which have been developed to address the substantial need for making substations more compact and reliable. The gas insulated bus bar is a crucial component of the power equipment in the substations with voltages over 100kV. In general, the ampacity of the bus bar is constrained by the maximum operating temperature, which has to be predicted, according to the demands of the standard IEC 62271. Therefore, thermal analysis of gas insulated bus bar has to be performed in the design of GIS. However, the mechanisms of heat generation and transfer in the SF6 gas and air are so complicated that it is not a simple problem to predict the temperature rise. Joule’s heat due to current in the main conductor and heat due to induced eddy currents in the tank is calculated via Magnetic Analysis. The heat transfer to the tank and atmosphere is done by means of radiation and natural convection. Heat transfer coefficients are not constant and vary on many parameters such as model geometry and material constants, making them difficult to calculate and apply to the boundaries. By considering the factors stated above, Nusselt number is used to analytically compute the temperature dependent heat transfer coefficients on the boundaries. The proposed research work presents a coupled magnetic and thermal field analysis supported by finite element analysis of extra-high voltage GIS bus bar with the help of ANSYS Maxwell and ANSYS Fluent. The results of the coupled finite element approach accord well with the values derived analytically.

Exploration of transient heat transfer through a moving plate with exponentially temperature-dependent thermal properties

The present research examines the transient temperature distribution through a moving plate with exponentially temperature-dependent thermal conductivity and heat transfer coefficient. Further, the internal heat generation, as well as convective boundary condition, is considered. The governing energy equation describing the transient heat transfer is formulated and is transformed into a non-dimensional partial differential equation (PDE) using appropriate non-dimensional terms. The resultant PDE is solved numerically with the assistance of the finite difference method (FDM). The consequence of embedding parameters on the transient thermal profile of a moving plate is explicated through a graphical description. The results reveal that the transient thermal distribution decreases remarkably with an upsurge of convection–conduction parameter and the same trend is perceived for radiation–conduction parameter. The result also manifests that as the plate moves faster, the transient thermal distribution through a moving plate enhances gradually. The higher variation in the thermal distribution is perceived for elevated values of the exponential index of thermal conductivity. Moreover, the nature of transient temperature distribution is compared for linear and exponentially temperature-dependent thermal conductivity.

Exploration of Temperature Distribution through a Longitudinal Rectangular Fin with Linear and Exponential Temperature-Dependent Thermal Conductivity Using DTM-Pade Approximant

The present study elaborates on the thermal distribution and efficiency of a longitudinal rectangular fin with exponentially varying temperature-dependent thermal conductivity and heat transfer coefficient concerning internal heat generation. Also, the thermal distribution of a fin is comparatively studied for both exponentially varying temperature-dependent thermal conductivity and linearly varying temperature-dependent thermal conductivity. Further, the thermal distribution of a longitudinal fin is examined by using ANSYS software with different fin materials. Many physical mechanisms can be explained by ordinary differential equations (ODEs) with symmetrical behavior, the significance of which varies based on the perspective. The governing equation of the considered problem is reduced to a non-linear ODE with the assistance of dimensionless terms. The resultant equation is solved analytically using the DTM-Pade approximant and is also solved numerically using Runge-Kutta Fehlberg’s fourth-fifth (RKF-45) order method. The features of dimensionless parameters influencing the fin efficiency and temperature profile are discussed through graphical representation for exponentially and linearly varying temperature-dependent thermal conductivity. This study ensures that the temperature field enhances for the higher magnitude of thermal conductivity parameter, whereas it diminishes for diverse values of the thermo-geometric parameter. Also, greater values of heat generation and heat transfer parameters enhance the temperature profile. Highlight: Thermal distribution through a rectangular profiled straight fin is examined. Linear and non-linear thermal properties are considered. The combined impact of conduction, convection, and internal heat generation is taken for modeling the energy equation of the fin. Thermal simulation is performed for Aluminum Alloy 6061 (AA 6061) and Cast Iron using ANSYS.

Results for the heat transfer of a fin with exponential-law temperature-dependent thermal conductivity and power-law temperature-dependent heat transfer coefficients

Abstract In this article, thermal behavior analysis of nonlinear fin problem with power-law heat transfer coefficient is studied to determine temperature distribution. This new supposition for the thermal conductivity, exponential-law temperature dependent, makes it to be nonlinear that is a general case in some sense. It is shown that the governing fin equation, that is, a nonlinear second-order differential equation, is exactly solvable with proper boundary conditions. To this purpose, the order of differential equation is reduced and then is converted into a total differential equation by multiplying a proper integration operant. An exact analytical solution is given to advance physical meaning, and the existence of unique solution for some specific values of the parameters of the model is demonstrated. The results are shown graphically. It is observed that fin efficiency is decreasing with respect to the power-law mode for heat transfer.

Thermal stress and temperature distribution of an annular fin with variable temperature-dependent thermal properties and magnetic field using DTM-Pade approximant

The thermal distribution within a rectangular profiled annular fin in the presence of a magnetic field and internal heat generation is examined in the present inspection. Furthermore, the linear and nonlinear temperature-dependent thermal conductivity and heat transfer coefficient are considered. The heat transfer equation is nondimensionalized using dimensionless terms, which results in a nonlinear ordinary differential equation (ODE) with related boundary conditions, which is then solved analytically and numerically using the DTM-Pade approximant and Runge–Kutta Fehlberg’s fourth-fifth order (RKF-45) approach respectively. Moreover, the effect of several non-dimensional parameters on temperature gradient, radial, and tangential thermal stresses is explained with the assistance of graphs. The significant outcomes of the investigation reveal that enhancing the heat generation parameter strengthens temperature distribution significantly, but increasing the magnitude of the thermo-geometric parameter and magnetic field parameter leads to the lessening of thermal distribution through the fin.

Variable transform-based semi-analytical methods for solving convective straight fins problem with temperature-dependent thermal conductivity

This paper presents effective algorithms to approximate solutions of nonlinear fin problem with temperature dependent thermal conductivity and heat transfer coefficient. We propose new approximate semi-analytical techniques, namely the Laplace homotopy variable transform method (LHVTM) and the differential variable transform method (DVTM), to obtain expressions for generalized convective straight fins problem. The linear dependence of thermal conductivity on temperature is considered, and fin efficiency and effectiveness are evaluated. We further analyzed the effects of the model parameters on surface heat loss, and the results are presented in tables and with graphical illustrations.

Analytical solution for temperature equation of a fin problem with variable temperature-dependent thermal properties: Application of LSM and DTM-Pade approximant

Temperature variation through a longitudinal fin with linear and nonlinear temperature-dependent thermal conductivities and heat transfer coefficient, subject to radiative heat flux and convective heat transport is explained in the present examination. For the radiative heat flux, the Rosseland approximation is incorporated and convection mode of energy transmission is accounted on the fin's surface. The associated physical problem is developed in such a manner that the steady-state heat transmission problem is governed with the help of dimensionless variables signified by a second order differential equation (ODE). To solve this equation, an analytical approach, DTM-Pade, and the LSM are implemented. Moreover, the consequence of a few non-dimensional factors on the temperature field are depicted graphically. The investigation's main findings illustrate that a significant decline in the thermal field is caused by an increment in the convection and the radiation mechanism. The internal development of heat affects the thermal distribution in the fin.

Investigation of the waste heat recovery and pollutant emission reduction potential in graphitization furnace

The graphite furnaces, which are extensively used for high-purity graphite production, inevitably discharges a large amount of waste heat that requires significant recovery for purpose of the improved energy efficiency. The paper numerically analyzed the heat transfer performance of a graphitization furnace under the electrical-heating and natural-cooling period. The temperature-dependent properties and heat transfer coefficients were used to predict the waste heat recovery potential along with on-site measurements. The results show that during the graphitization production, the core furnace temperature can reach 3000 °C while the petroleum coke surface reaches 368 °C without the combustion of the volatiles in the coke. The heat dissipation on the top coke surface accounts for 48.5% of the total electricity input and 66.9% of the total heat dissipation from the furnace, respectively. The equivalent emission reduction of CO2, SO2 and NOx are 47.5 t, 7.4 t and 3.6 t respectively per annum. The investigation of the waste heat recovery potential for graphitization furnaces can provide a reference for the heat recovery equipment and operation for graphitization furnaces.

Thermal distribution through a moving longitudinal trapezoidal fin with variable temperature-dependent thermal properties using DTM-Pade approximant

The present inspection elaborates the thermal distribution through a convective-radiative longitudinal trapezoidal moving fin with an internal heat source by considering the linear and nonlinear temperature-dependent thermal conductivities and heat transfer coefficient. The non-dimensionalization of the energy equation is carried out using dimensionless terms, and the resulting nonlinear ordinary differential equation (ODE) is solved analytically using the differential transform method (DTM) with Pade approximant approach. Furthermore, the consequence of several non-dimensional parameters, namely thermal conductivity parameter, convection-conduction parameter, Peclet number, radiation-conduction parameter, fin taper ratio, temperature ratio parameter, and internal heat generation parameter on temperature gradient and fin efficiency is explained with the help of graphs. The significant primary results of the investigation illustrate that the thermal distribution through the fin gradually decreases as the magnitude of the convection-conduction parameter, temperature ratio parameter, and radiation-conduction parameter rise. In contrast, it upsurges for heat generation and thermal conductivity parameters.

Modelling and simulation of densification and σ-phase precipitation in PM duplex steel AISI 318LN during hot isostatic pressing

Following the development of hot isostatic pressing (HIP) with integrated rapid cooling technology, it is now possible to combine consolidation of encapsulated powder and subsequent heat treatment in a single process step in a pressure vessel. Using this technology, a near-net-shape product with target microstructure can be achieved. However, qualified final products still require traditional expensive and time-consuming trial-and-error tests. To eliminate these costly trial-and-error tests and achieve the required final properties of the products, it is urged to develop a combined numerical model to precisely predict the geometrical changes of the component during the HIP process and the evolution of significant microstructural features. This is realised in this work exemplarily by using duplex stainless steel AISI 318LN. This steel was selected due to requirements coming from applications regarding precise complex shaped near-net-shape components combined with high strength and toughness by avoiding brittle σ-phase precipitation. In this study, an existing finite element model for the densification in the HIP process was supplemented by a model for σ-phase precipitation kinetics based on microscopical characterisation. Moreover, the temperature dependent heat transfer coefficient (HTC) was implemented in the developed model to simulate the evolution and the distribution of the σ-phase during cooling. The numerically simulated final component dimensions and σ-phase volume fractions were verified by comparing with experimental data obtained from specimens and components of various shapes produced by both conventional HIP process and HIP with integrated rapid cooling. The high consistency between experimental and numerical results validates the accuracy of the developed simulation approach.

Thermal conductivity of porous oxide layer: A numerical model based on CT data

This paper presents a novel method to determine the effective thermal conductivity of porous oxides formed on steel. This advanced approach enables more accurate numerical modeling of the oxide layer impact on the spray cooling of steel. Although the thermal conductivity of the oxide layer is highly influenced by the porous structure of iron oxides, the microstructure of the oxide layer was generally not considered in the studies of the thermal conductivity. In this paper a detailed 3D finite element model of the oxide layer based on a data acquired by computed tomography was created. The image acquisition and image processing are described. An unconventional method of converting image voxels directly into finite elements was used. Two distinct segmentation approaches were implemented and results of simulations were averaged. Obtained temperature-dependent results of the effective conductivity of the oxide layer was used as an input material parameter for the subsequent numerical simulation of the spray cooling of steel. The impact of the oxide layer with different thicknesses was quantified by plotting the temperature-dependent effective heat transfer coefficient. The limitations of the commonly used alternative analytical approach were identified.

Research on improved hydrostatic guideway base thermal characteristics by flattening temperature distribution

This paper proposed a new guideway base structure of hydrostatic guideways to flatten its spatial temperature variation characteristics. Four oil storage holes penetrating through the base are used to collect the hydraulic oil, which is heated by power losses after oil flows through the bearing clearances. When the heated oil flows into the four oil storage holes, the whole base is warmed and temperature distribution non-uniformity is avoided. In order to verify the effectiveness of the new structure, a physical model of the guideway base simplified from actual base was developed. A thermal model of a guideway base was developed using the finite element method (FEM). The temperature distribution of guideway bases was calculated, taking into account the temperature-dependent heat transfer coefficients of interfaces and thermal contact conductances. Analysis of temperature differences, thermal equilibrium time, and temperature uniformity of bases demonstrates the effectiveness of the new base design on its thermal characteristics and improves structural parameters. The experimental results verify the accuracy of the thermal model hydrostatic guideway bases.

Heat Transfers Coefficients of Directly and Indirectly Cooled Component Areas during Air-Water Spray Cooling

Abstract For the determination of heat transfer coefficients in air-water spray cooling, two methods are presented that are capable of characterizing multi-nozzle cooling set-ups. The methods are based on the quenching of thin-walled tubes or massive cylinders on which cooling curves are recorded at given positions with thermocouples. The temperature dependent heat transfer coefficients were calculated by an inverse calculation and the measured temperature-time-curves could be reproduced with these data in numerical cooling simulations. Next, the determined heat transfer coefficients were used for the calculation of an air-water-spray quenching process of a forging part with more challenging geometry. The calculated results were compared with thermocouple measurements. Different calculation variants for the heat transfer on component surfaces not directly exposed to the air-water spray are shown and discussed. ◼