The BFGS method for estimating the interface temperature and convection coefficient in ultrasonic welding

An inverse heat transfer problem is investigated in the present study by the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method to predict the unknown time-dependent heat generation at the weld interface and convection heat transfer coefficient during an ultrasonic metal welding process based on the knowledge of temperature measurements taken on the horn. With known temperature data at some locations on the horn, the inverse solution was rapidly obtained by solving nonlinear direct problem, Central Finite Difference and Simple Step Method. The proposed method which did not need solving adjoint and sensitivity problem revealed the characteristics of high efficiency, lower iterations for a computational algorithm and high accuracy for estimating values even when measurement error was considered. Besides, a comparison of the BFGS method with some previous methods (i.e. CGM, SCGM) was established. These results show that an excellent estimation on interfacial heat generation (or temperature), as well as a convection heat transfer coefficient, can be simultaneously obtained in this study. The current methodology will provide a useful tool to optimize welding conditions in ultrasonic welding.     

铝材退火炉退火过程的传热分析

根据箱式退火炉退火过程的传热特点,分析了铝箔退火炉退火过程各阶段炉膛内传热形式,建立了铝卷导热的数学模型,着重分析和计算了影响炉内空气与铝材间传热的重要参数——对流换热系数,并模拟计算了铝卷的退火过程和温度变化。结果表明,铝卷退火曲线计算值与实测值结果比较吻合。     

Complete heat transfer solutions of an insulated regular polyhedron by using an RPSWT model

The heat transfer characteristics for an insulated regular polyhedron (including sphere) are analyzed by using the same RPSWT model in the present study as that used by Wong and Chou previously [Energy Convers. Manage. 44 (2003) 3015]. The thermal resistance of the inner convection term and the wall conduction term in the heat transfer rate are not neglected in the present study. Thus, the complete heat transfer solution will be obtained. The present results can be applied more extensively to practical situations, such as an insulated gas tank. The results of the critical thickness t_cr and the neutral thickness t_e are independent of the values of J (generated by the effect of the inner convection term and the wall conduction term). However, the heat transfer rates are dependent on the values of J. The present study shows that the thermal resistance of the inner convection term and the body conduction term cannot be neglected in the heat transfer equation in situations of low to medium inner convection coefficients h_i and/or low to medium wall conductivities K and/or great wall thickness t₁, especially in situations with small body sizes or/and great outer convection coefficients h_o.     

Natural convection and radiation heat transfer in a vertical porous layer with a hexagonal honeycomb core (Part 1: numerical analysis)

Combined heat transfer characteristics were obtained numerically for three-dimensional natural convection and thermal radiation in a long and wide vertical porous layer with a hexagonal honeycomb core. We assumed that the porous layer was both homogeneous and isotropic. The pure Darcy law for fluid flow and Rosseland's approximation for radiation were used. The numerical methodology was based on an algebraic coordinate transformation technique and the transformed governing equations were solved using the SIMPLE algorithm. The effect of radiation on the heat transfer characteristics was investigated over a wide range of radiation numbers and temperature ratios for two Darcy-Rayleigh number values (Ra^* = 100 and 1000) and for a fixed aspect ratio of H/L = 1. The results are presented in the form of combined radiation and convection heat transfer coefficients and are compared with the corresponding values for pure natural convection. © 1999 Scripta Technica, Heat Trans Asian Res, 28(4): 278–294, 1999     

Weld Pool Shape Identification by Using Bezier Surfaces

This paper deals with the heat transfer analysis in a welding process: A method is developed to determine the shape of the three-dimensional (3-D) phase change front and to estimate the temperature field within the solid part of the work piece. The problem is formulated and solved as an inverse phase-change problem by using an optimization method. The direct problem is solved in the torch frame and so formulated as an Eulerian approach. The interface between the weld pool and the solid region is parameterized by Bezier surfaces. The most important feature of the presented approach is that the liquid–solid interface as well as the temperature distribution within the solid region can be obtained from additional temperature data available in the solid region, without considering heat transfer and fluid flow in a molten zone. The estimate of these thermal characteristics then allows a thermomechanical calculation of the welded joint (calculation of the deformations and residual stresses). The validity of the numerical solution of the inverse problem is checked by comparing the results with the direct solution of the problem.     

Thermal response of a flat heat pipe sandwich structure to a localized heat flux

The temperature distribution across a flat heat pipe sandwich structure, subjected to an intense localized thermal flux has been investigated both experimentally and computationally. The aluminum sandwich structure consisted of a pair of aluminum alloy face sheets, a truncated square honeycomb (cruciform) core, a nickel metal foam wick and distilled water as the working fluid. Heat was applied via a propane torch to the evaporator side of the flat heat pipe, while the condenser side was cooled via natural convective and radiative heat transfer. A novel method was developed to estimate experimentally, the heat flux distribution of the torch on the evaporator side. This heat flux distribution was modeled using a probability function and validated against the experimental data. Applying the estimated heat flux distribution as the surface boundary condition, a finite volume analysis was performed for the wall, wick and vapor core regions of the flat heat pipe to obtain the field variables in these domains. The results were found to agree well with the experimental data indicating the thermal spreading effect of the flat heat pipe.     

Melting effect on mixed convective heat transfer with aiding and opposing external flows from the vertical plate in a liquid-saturated porous medium

In this paper, melting effect on mixed convective heat transfer from a porous vertical plate with uniform wall temperature in the liquid-saturated porous medium with aiding and opposing external flows is numerically examined at steady state. The resulting boundary value problems (BVPs) are comprehensively solved by Runge–Kutta–Gill method and Newton’s iteration for similarity solutions. As shown in the results, for aiding and opposing external flows, it is all found that the rate of convective heat transfer at the interface of solid and liquid phases is reduced with increasing melting strength. Additionally, the melting phenomenon decreases the thermal boundary layer regions of mixed convection in a porous medium. With melting effect, the heat transfer rate is also shown to be asymptotically approaching the forced or free convection as the value of Gr/Re approaches the limits of zero and infinity for aiding external flow; and the criteria for pure forced and mixed convection from an isothermal vertical flat plate in porous media with aiding and opposing external flows are established in melting process.     

Combined mixed convection and radiation heat transfer in rectangular ducts rotating about a parallel axis

The study of combined heat transfer of convection and radiation in rectangular ducts rotating in a parallel mode was investigated numerically in detail. The coupled momentum and energy equations are solved by the DuFort–Frankel numerical scheme to examine the interactions of convection with radiation. The integro-differential radiative transfer equation is solved by the discrete ordinates method. Results are presented over a wide range of the governing parameters. The present results reveal that the rotational effect in a square duct is more significant than that in a rectangular one. The predictions also demonstrate that the radiation presents significant effects on the axial distributions of the total Nusselt number, Nu_t, and tends to reduce the centrifugal-buoyancy effects. The effect of rotation on the Nu_t is restricted in the entrance region, however, the radiation affects the heat transfer through out the channel. Additionally, the Nu_t increases with the decrease in the conduction-to-radiation parameter N_C.     

Entropy generation due to natural convection in discretely heated porous square cavities

Optimization of industrial processes for higher energy efficiency may be effectively carried out based on the thermodynamic approach of entropy generation minimization (EGM). This approach provides the key insights on how the available energy (exergy) is being destroyed during the process and the ways to minimize its destruction. In this study, EGM approach is implemented for the analysis of optimal thermal mixing and temperature uniformity due to natural convection in square cavities filled with porous medium for the material processing applications. Effect of the permeability of the porous medium and the role of distributed heating in enhancing the thermal mixing, temperature uniformity and minimization of entropy generation is analyzed. It is found that at lower Darcy number (Da), the thermal mixing is low and the heat transfer irreversibility dominates the total entropy generation. In contrast, thermal mixing is improved due to enhanced convection at higher Da. Friction irreversibility is found to dominate the total entropy generation for higher Prandtl number (Pr) fluids at higher Da, whereas the heat transfer irreversibility dominates the total entropy generation for lower Pr fluids. Based on EGM analysis, it is established that larger thermal mixing at high Darcy number may not be always recommended as the total entropy production is quite large at high Darcy number. Overall, it is found that the distributed heating methodology with multiple heat sources may be an efficient strategy for the optimal thermal processing of materials.     

Double diffusive LTNE porous convection with Cattaneo effects in the solid

The impact of Cattaneo heat flux law in the solid on the onset of double‐diffusive Darcy porous convection with local thermal nonequilibrium temperatures is investigated. The Fourier law of heat transfer is invoked for the fluid, whereas the Cattaneo heat flux law used to transfer heat in solid skeleton alters the temperature equation from parabolic to hyperbolic. The results are obtained for porous skeletons of aluminum and copper oxides. Both Cattaneo and solute concentration effects reinforce in controlling the onset of oscillatory convection and some novel consequences are observed. Compared with the results perceived in the absence of solute concentration, a manifestation of oscillatory convection with scaled‐interphase heat transfer coefficient as well as solid thermal relaxation time parameter initiates earlier in its presence. The effect of increasing interphase heat transfer coefficient and the Lewis number is to delay and hasten the onset of stationary and oscillatory convection. Besides, the increase in the value of solid thermal relaxation time parameter advances the oscillatory onset. Although the increase in the solute Darcy–Rayleigh number is to delay the stationary onset, it shows a twofold behavior on the onset of oscillatory convection. Before the onset of oscillatory convection, the size of the convection cell gets narrower and after which it becomes much wider. The existing results are retrieved as limiting cases from the current study.     

Dual influence of temperature and gas composition of selected helium-based binary gas mixtures on the thermal convection enhancement in Rayleigh–Bénard enclosures

This paper addresses the potential augmentation of natural convection heat transfer in Rayleigh–Bénard enclosures when filled with a certain type of binary gas mixture. To form the binary gas mixtures, helium (He) is the primary gas and the secondary gases are nitrogen (N₂), oxygen (O₂), carbon dioxide (CO₂) and methane (CH₄). Each of the thermo-physical properties participating in the binary gas mixtures viscosity η_m, thermal conductivity λ_m, density ρ_m, and heat capacity at constant pressure C_p,m depends on the molar gas composition, temperature and pressure. Results are presented in terms of the maximum allied heat transfer coefficient h_m,max/B at the optimal mole gas composition w_opt, in the w-domain [0, 1] for the entire range of laminar and turbulent conditions. In the conduction regime, He provides the best heat transfer regardless of temperature. In the convection regime at 300 K a He–CO₂ mixture usually provides the maximum heat transfer, whereas at 1000 K pure methane CH₄ is the optimum. In addition, a detailed thermo-fluidic structure of the thermal convection patterns in the Rayleigh–Bénard enclosure was analyzed by performing 2-D numerical simulations.     

Convective‐radiative fins with simultaneous variation of thermal conductivity,heat transfer coefficient,and surface emissivity with temperature

This paper is a numerical study of thermal performance of a convective‐radiative fin with simultaneous variation of thermal conductivity, heat transfer coefficient, and surface emissivity with temperature. The convective heat transfer is assumed to be a power function of the local temperature between the fin and the ambient which allows simulation of different convection mechanisms such as natural convection (laminar and turbulent), boiling, etc. The thermal conductivity and the surface emissivity are treated as linear functions of the local temperature between the fin and the ambient which provide a satisfactory representation of the thermal property variations of most fin materials. The thermal performance is governed by seven parameters, namely, convection–conduction parameter Nc, radiation–conduction parameter Nr, thermal conductivity parameter A, emissivity parameter B, the exponent n associated with convective heat transfer coefficient, and the two temperature ratios, θ_a and θ_s, that characterize the temperatures of convection and radiation sinks. The effect of these parameters on the temperature distribution and fin heat transfer rate are illustrated and the results interpreted in physical terms. Compared with the constant properties model, the fin heat transfer rate can be underestimated or overestimated considerably depending on the values of the governing parameters. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20408     

Heat transfer in the evaporator section of moderate-speed rotating heat pipes

Experiments were performed to investigate the heat transfer mechanism in the evaporator section of non-stepped rotating heat pipes at moderate rotational speeds of 2000–4000 rpm or accelerations of 40g–180g, and evaporator heat fluxes up to 100 kW/m². The thermal resistance of the evaporator section as well as that of the condenser section was examined by measuring the axial temperature distributions of the flow in the core region of the heat pipe and along the wall of the heat pipe. The experimental results indicated that natural convection heat transfer occurred in the liquid layer of the evaporator section under these conditions. The heat transfer measurements were in reasonable agreement with the predictions from an existing rotating heat pipe model that took into account the effect of natural convection in the evaporator section.     

Numerical study on coupled fluid flow and heat transfer process in parabolic trough solar collector tube

A unified two-dimensional numerical model was developed for the coupled heat transfer process in parabolic solar collector tube, which includes nature convection, forced convection, heat conduction and fluid-solid conjugate problem. The effects of Rayleigh number (Ra), tube diameter ratio and thermal conductivity of the tube wall on the heat transfer and fluid flow performance were numerically analyzed. The distributions of flow field, temperature field, local Nu and local temperature gradient were examined. The results show that when Ra is larger than 10⁵, the effects of nature convection must be taken into account. With the increase of tube diameter ratio, the Nusselt number in inner tube (Nu₁) increases and the Nusselt number in annuli space (Nu₂) decreases. With the increase of tube wall thermal conductivity, Nu₁ decreases and Nu₂ increases. When thermal conductivity is larger than 200 W/(m K), it would have little effects on Nu and average temperatures. Due to the effect of the nature convection, along the circumferential direction (from top to down), the temperature in the cross-section decreases and the temperature gradient on inner tube surface increases at first. Then, the temperature and temperature gradients would present a converse variation at θ near π. The local Nu on inner tube outer surface increases along circumferential direction until it reaches a maximum value then it decreases again.     

Radiation and mass transfer effects on flow of an incompressible viscous fluid past a moving vertical cylinder

The interaction of free convection with thermal radiation of a viscous incompressible unsteady flow past a moving vertical cylinder with heat and mass transfer is analyzed. The fluid is a gray, absorbing-emitting but non-scattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing equations are solved using an implicit finite-difference scheme of Crank-Nicolson type. Numerical results for the transient velocity, the temperature, the concentration, the local as well as average skin-friction, the rate of heat and mass transfer are shown graphically. It is found that at small values of the Prandtl number and radiation parameter N, the velocity and temperature of the fluid increases sharply near the cylinder as the time t increase, which is totally absent in the absence of radiation effects.     

A numerical study of film condensation on a metallic foam-sintered plate with considering convection and super-cooling effects

A numerical solution was presented for film condensation on a vertical plate sintered with metallic foam. In the metallic foam region, the Brinkman-Darcy model was employed to establish the fluid flow equation, and the thermal equilibrium model was used to describe local heat transfer. Through introduction of dimensionless distance, namely, the ratio of the coordinate normal to the plate and the local film thickness, the computational domain was regularized in a rectangular zone. The effects of convection and explicit heat of super-cooled liquid on the condensation film were considered. The temperature and velocity profile, film thickness, and the local and average Nu number were obtained. The effects of Ja and Da number on the velocity profile and heat transfer performance were investigated. The numerical model was verified through comparison of the predicted results with those in the literature, which neglected convection and explicit heat of super-cooling effects. Convection and explicit heat of super-cooling can play a positive role in reducing the velocity level in the film. The two effects played a positive role in heat transfer improvement when the dimensionless location along the gravity direction (X) was > 0.15, which was associated with reduced film thickness. The two effects also had a mild influence on the linear distribution of dimensionless temperature. The heat transfer performance deteriorated with an increase in Ja number or Da number.     

Laminar heat transfer in a porous channel simulated with a two-energy equation model

Laminar heat transfer in a porous channel is numerically simulated with a two-energy equation model for conduction and convection. Macroscopic equations for continuity, momentum and energy transport for the fluid and solid phases are presented. The numerical methodology employed is based on the control volume approach with a boundary-fitted non-orthogonal coordinate system. Fully developed forced convection in a porous channel bounded by parallel plates is considered. Solutions for Nusselt numbers along the channel are presented for laminar flows. Results simulate the effects Reynolds number Re, porosity, particle size and solid-to-fluid thermal conductivity ratio on Nusselt sumber, Nu, which is defined for both the solid and fluid phases. High Re, low porosities, low particle diameters and low thermal conductivity ratios promote thermal equilibrium between phases leading to higher values of Nu.     

Measurement of transient heat transfer in vicinity of gas–liquid interface using high-speed phase-shifting interferometer

The heat transfer process and initial stage of coupled convection at a gas–liquid interface are observed with high temporal and spatial resolutions in view of understanding phase transition dynamics such as evaporation or condensation for energy technologies. A high-speed phase-shifting interferometer is used to precisely measure the transient heat conduction and convection processes near the gas–liquid interface of a small water droplet. In the present study, the transient heat conduction around a water droplet interface during the adiabatic expansion process before the appearance of convection is visualized and examined. In the visualization experiment, transient density variations due to heat conduction in the vicinity of the gas–liquid interface are observed with temporal and spatial resolutions of 1 ms and 8.83 μm/pixel, respectively. It is determined that convection appears at approximately t = 0.25 s in a fast depressurization process, while transitions in both temperature and pressure are observed. In addition, the transient density variations and distributions of the gas phase before convection are compared with numerical simulations as an optical path length difference, and there is good agreement between the simulations and experimental results. The measurement methods developed in this study can be applied in the measurement of interfacial heat and mass transfers with high temporal and spatial resolutions.     

Influence of thermal and flow boundary perturbations on convection heat transfer characteristics: Numerical analysis based on adjoint formulation

A numerical approach based on adjoint formulation of convection heat transfer is proposed to predict the change of heat transfer characteristics for arbitrary thermal and flow boundary perturbations. In order to obtain the adjoint system of the convection heat transfer problem, we formally linearize the governing equations by the perturbation method and then derive the adjoint system for the perturbation system. As a result, it is shown that the numerical solutions of the base and the adjoint problems enable us to predict the changes of heat transfer characteristics, such as the change of total heat transfer rate or the change of temperature at a specific location, when the thermal and flow boundary conditions are perturbed. An application example is presented to demonstrate the proposed method. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(1): 1–12, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10065     

Steady state simulation for the de-bottlenecking of heat recovery networks

This work presents the use of a steady state simulator for the de-bottlenecking of heat recovery networks. It is shown how a heat exchanger network designed for fixed conditions can be de-bottlenecked when process streams undergo changes in operating conditions such as flow rate and supply temperature. A network is said to be flexible if it is capable of maintaining acceptable operation either during normal or under modified conditions. The de-bottlenecking of heat recovery networks can be considered as a special case of the design for improved flexibility. A simulation model for a single phase network of heat exchangers is presented. The model is based on the use of the thermal effectiveness (ε) parameter for heat exchangers. Any type of exchanger configuration and flow arrangement can be modeled by using the appropriate ε–number of transfer units relationships. A general methodology for improving network flexibility is proposed.