Phase-change heat transfer during cyclic heating and cooling with internal radiation and temperature-dependent properties

This paper contains the results of a numerical investigation of the effects of internal radiation on heat transfer during cyclic heating and cooling of a phase-change energy–storage system. The effects of internal radiation, temperature distribution and energy stored and extracted were investigated. An absorbing, emitting, and isotropically scattering, finite, and semi-transparent, gray, phase-change medium bounded between two concentric cylinders was studied. The phase-change medium was a fluoride salt with LiF (41.27%), MgF₂ (48.76%) and KF (8.95% by weight). Radiative heat transfer affects the dynamics of phase changes significantly for low values of the conduction–radiation interaction parameter.     

Coupled radiation and solidification heat transfer inside a graded index medium by finite element method

Effects of thermal radiation on solidification heat transfer must be considered inside semitransparent media. This paper investigates coupled heat transfer of solidification and radiation within a two-dimensional rectangular semitransparent medium having gradient index. Solidification process is supposed to happen at some temperature range, and accordingly three zones including liquid-, solid- and mushy-zones exist in phase-change media. In different phase field, parameters of thermophysical property are assumed different and those of radiative property are assumed same. Governing equation includes conduction, radiation and phase-change terms, and radiation and phase-change are treated as source terms in the equation, respectively. A Galerkin finite element method is used to solve energy equation of coupled radiation and phase-change heat transfer. This paper analyzes effect of thermal radiation on phase-change heat transfer and those of refractive index distributions on temperature fields and liquid fraction distributions during radiation–solidification coupled heat transfer. From the results, we can find that refractive index gradient has a major influence on phase-change process and compared with the case of smaller index gradient, bigger gradient can speed up phase-change heat transfer in semitransparent media.     

A Conduction–Radiation Mixture Model for Laser-Assisted Phase Change of Semitransparent Material

A one-dimensional transient coupled conduction-radiation numerical model is developed to investigate the laser melting of semitransparent material under a continuous collimated laser pulse in a convective cooling environment. The medium is considered absorbing, emitting, and scattering. The thermophysical properties are taken to be different for different phase fields. Volumetric radiation is incorporated in the proposed model. The radiation information is obtained by solving the equation of transfer. The temperature field is obtained by solving the energy equation with internal radiation source. The finite-volume method is used to discretize both the equation of transfer and the energy equation. The enthalpy formulation is adopted to capture the continuously evolving solid–liquid interface during the phase change. The laser source is approximated with the collimated radiation source. Collimated intensity is captured directly (without splitting the total intensity into two parts: diffuse and collimated) by adjusting the control angles. The present model is first validated with the existing phase-change model in the literature. Then the effects of different parameters such as optical thickness, scattering albedo, and the conduction–radiation parameter on the liquid fractions and temperature distribution in the medium are studied. It is observed that when the radiation is dominant, the temperature in the medium is high and hence the liquid fraction is more, in contrast to conduction-dominated phase change.     

Low Rayleigh number flow in a heat generating porous media

A numerical analysis has been performed for the steady-state temperature and stream function distributions in a short cylinder, having an isothermal side and top, an insulated bottom, for a uniform heat generating porous medium. The analysis uses the stream function formulation of Darcy's equation in cylindrical coordinates and the Boussinesq approximation. A single energy equation was used for the fluid and solid, since conduction was the expected mode of heat transfer at low heat generation rates for a lead sphere air porous media system. The solution of the non-dimensionalized momentum and energy equations resulted in small Rayleigh numbers (2×10⁻⁶ to 0.2) indicating the heat transfer is by conduction. Solutions for the stream lines and isotherms were obtained using a transient explicit finite-difference approximation using a mean bed thermal conductivity.     

Two-dimensional transient conduction and radiation heat transfer with temperature dependent thermal conductivity

This paper deals with the effect of the temperature dependent thermal conductivity on transient conduction and radiation heat transfer in a 2-D rectangular enclosure containing an absorbing, emitting and scattering medium. The thermal conductivity of the medium is assumed to vary linearly with temperature. The radiative part of the energy equation was solved using the collapsed dimension method. To facilitate solution of the energy equation, which is a highly nonlinear one, time linearization was done first and then the equation was solved using the alternating direction implicit scheme. Results for the effects of the variable thermal conductivity were found for temperature and heat flux distributions.     

Estimation de la résistance thermique de contact durant la solidification du verre

Estimation of the thermal contact resistance during glass solidification. This paper presents an experimental study of thermal contact conditions during glass moulding. Our goal was to develop an experimental setup to simulate the real contact conditions during the glass solidification and to build a numerical procedure to estimate the thermal parameters characterizing heat transfer at the contact interface (mould–glass). The semi-transparent character of glass was taken into account when building the theoretical heat transfer model. Thus a heat radiation–conduction model was built to simulate heat transfer at the interface during the glass cooling. The study shows that when the coupled conduction–radiation effect is taken into account, the parameter estimation is better. Thermal contact resistance mold–glass was estimated and the quality of heat transfer at the interface was analyzed.     

Transient and non-Darcian effects on natural convection flow in a vertical channel partially filled with porous medium: Analysis with Forchheimer–Brinkman extended Darcy model

The present study addresses the transient as well as non-Darcian effects on laminar natural convection flow in a vertical channel partially filled with porous medium. Forchheimer–Brinkman extended Darcy model is assumed to simulate momentum transfer within the porous medium. Two regions are coupled by equating the velocity and shear stress in the case of momentum equation while matching of the temperature and heat flux is taken for thermal energy equation. Approximate solutions are obtained using perturbation technique. Variations in velocity field with Darcy number, Grashof number, kinematic viscosity ratio, distance of interface and variations in temperature distribution with thermal conductivity ratio, distance of interface are obtained and depicted graphically. The skin-friction and rate of heat transfer at the channel walls are also derived and the numerical values for various physical parameters are tabulated.     

Combined conduction and radiation heat transfer with variable thermal conductivity and variable refractive index

This article deals with the solution of conduction–radiation heat transfer problem involving variable thermal conductivity and variable refractive index. The discrete transfer method has been used for the determination of radiative information for the energy equation that has been solved using the lattice Boltzmann method. Radiatively, medium is absorbing, emitting and scattering. To validate the formulation, transient conduction and radiation heat transfer in a planar participating medium has been considered. For constant thermal conductivity and constant and variable refractive indices, results have been compared with those available in the literature. Effects of conduction–radiation parameter and scattering albedo on temperature have been studied for variable thermal conductivity and constant and/or variable refractive index. Lattice Boltzmann method and the discrete transfer method have been found to successfully deal with the complexities introduced due to variable thermal conductivity and variable refractive index.     

TRANSIENT CONDUCTION AND RADIATION HEAT TRANSFER WITH VARIABLE THERMAL CONDUCTIVITY

The effect of variable thermal conductivity on transient conduction and radiation heat transfer in a planar medium is investigated. Thermal conductivity of the medium is assumed to vary linearly with temperature, while the other thermophysical properties and the optical properties are assumed constant. The radiative transfer equation is solved using the discrete transfer method, (DTM) and the nonlinear energy equation is solved using an implicit scheme. Transient as well as steady state results are found for an absorbing, emitting, and anisotropically scattering gray medium. Thermal conductivity has been found to have significant effects on both transient as well as steady state temperature and heat flux distributions. Some steady state results are compared with the results reported in the literature.     

Radiative heat transfer in semitransparent solidifying slab considering space–time dependent refractive index

Radiative heat transfer in semitransparent phase-change media is of great interest in many engineering fields. Its essence is the transient coupled heat transfer of radiation and conduction along with liquid–solid phase change. The difficulty is to solve radiative heat transfer with the consideration of time–space dependent radiative properties. Especially when the refractive index is considered to vary with space and time in phase change, the problem becomes more complicated. This paper investigates the problem of the variable radiative properties with space and time during phase change in semitransparent media. The phase-change medium is assumed to have solid, mushy and liquid zones, and the solid/mushy and liquid/mushy interfaces are considered to be semitransparent and diffuse reflecting. In different zones, there are different physical property parameters. Phase interfaces are always moving in phase change, while the interfaces of control volumes are fixed. Therefore, the interfaces of control volumes and phase interfaces are not always coincided, which will bring errors into the simulation of radiative transfer in phase-change media. However, the errors can be reduced by dividing the medium into enough sub-layers. As long as the number of sub-layers is big enough, the errors can be limited in a very small range. Then using the multilayer radiative transfer model, we can solve the radiative transfer problem in the semitransparent phase-change medium. Considering time–space dependent refractive index, this paper analyzes coupled radiative and conductive heat transfer in semitransparent solidifying media. The results show that the effects of variable refractive index with time and space on transient coupled heat transfer are significant and could not be neglected inside the semitransparent phase-change medium under some conditions.     

NUMERICAL CALCULATIONS FOR COMBINED CONDUCTION AND RADIATION TRANSIENT HEAT TRANSFER IN A SEMITRANSPARENT MEDIUM

A numerical computer code was developed for calculating the combined conduction and radiation transient heat transfer in cylindrical, semitransparent materials that have temperature-dependent thermal properties. The radiative component is combined with the equation of conduction heat transfer by adding it as a heat source. The finite element method (FEM) was used for calculating the radiative component and for solving the temperature field in the medium. Very good agreement was observed between results obtained by using our code and those that exist in the literature for several steady-state cases. The advantage of the code is due to the fact that it incorporates temperature-dependent properties; thus it leads to more realistic and accurate results. The code was applied to calculate the cooling path of a large cylindrical sapphire boule while using varying, transient, temperature-dependent, combined heat transfer coefficients.     

Performance Analysis of Heat Sinks With Phase-Change Materials Subjected to Transient and Cyclic Heating

Phase-change cooling technique is a suitable method for thermal management of electronic equipment subjected to transient or cyclic heat loads. The thermal performance of a phase-change based heat sink under cyclic heat load depends on several design parameters, namely, applied heat flux, cooling heat transfer coefficient, thermophysical properties of phase-change materials (PCMs), and physical dimensions of phase-change storage system during melting and freezing processes. A one-dimensional conduction heat transfer model is formulated to evaluate the effectiveness of preliminary design of practical PCM-based energy storage units. In this model, the phase-change process of the PCM is divided into melting and solidification subprocesses, for which separate equations are written. The equations are solved sequentially and an explicit closed-form solution is obtained. The efficacy of analytical model is estimated by comparing with a finite-volume-based numerical solution for both transient and cyclic heat loads.     

Efficiency analysis of radiative slab heating in a walking-beam-type reheating furnace

The thermal efficiency of a reheating furnace was predicted by considering radiative heat transfer to the slabs and the furnace wall. The entire furnace was divided into fourteen sub-zones, and each sub-zone was assumed to be homogeneous in temperature distribution with one medium temperature and wall temperature, which were computed on the basis of the overall heat balance for all of the sub-zones. The thermal energy inflow, thermal energy outflow, heat generation by fuel combustion, heat loss by the skid system, and heat loss by radiation through the boundary of each sub-zone were considered to give the two temperatures of each sub-zone. The radiative heat transfer was solved by the FVM radiation method, and a blocked-off procedure was applied to the treatment of the slabs. The temperature field of a slab was calculated by solving the transient heat conduction equation with the boundary condition of impinging radiation heat flux from the hot combustion gas and furnace wall. Additionally, the slab heating characteristics and thermal behavior of the furnace were analyzed for various fuel feed conditions.     

Transient natural convective heat transfer in porous medium with solidification of binary mixture

In this paper an enthalpy porosity method associated with finite control volume scheme and SIMPLE iteration was employed to solve Navier–Stokes equation coupled with energy equation through Ergun equation and Boussinesq approximation for studying the effect of two-dimensional transient natural convective heat transfer from a closed region of porous medium with the different porosity on solidification in carbon–iron system. As shown in the results, it is fund that the thickness of solidification layer is increased with time due to thermal coupled flow induced by natural convection; and the wall temperature is faster changed in porous medium with larger porosity, which corresponds to slow the growth of the solidification layer in binary system.     

Heating/melting of a fused silica particle by convection and radiation

The effect of internal absorption and emission of radiation on the heating/melting process of small fused silica particles is analyzed. The particle is considered to be semitransparent to radiation, and the radiative transfer theory is used to predict the local volumetric absorption/emission rate. The transient energy equation with conduction and radiation accounted for is solved to predict the temperature distribution in the particle and the solid–liquid interface position after the melting has started. The radiative transfer calculations are carried out on the spectral basis using published spectral optical property data for fused silica. Results of parametric calculations for different diameter particles, surroundings temperatures and external flow conditions are reported and discussed.     

Heat transfer analysis of solar-driven high-temperature thermochemical reactor using NiFe-Aluminate RPCs

Converting solar energy efficiently into hydrogen is a promising way for renewable fuels technology. However, high-temperature heat transfer enhancement of solar thermochemical process is still a pertinent challenge for solar energy conversion into fuels. In this paper, high-temperature heat transfer enhancement accounting for radiation, conduction, and convection heat transfer in porous-medium reactor filled with application in hydrogen generation has been investigated. NiFe-Aluminate porous media is synthesized and used as solar radiant absorber and redox material. Experiments combined with numerical models are performed for analyzing thermal characteristics and chemical changes in solar receiver. The reacting medium is most heated by radiation heat transfer and higher temperature distribution is observed in the region exposed to high radiation heat flux. Heat distribution, O₂ and H₂ yield in the reacting medium are facilitated by convective reactive gas moving through the medium's pores. The temperature gradient caused by thermal transition at fluid-solid interface could be more decreased as much as the reaction chamber can store the transferred high-temperature heat flux. However, thermal losses due to radiation flux lost at the quartz glass are obviously inevitable.     

Thermal diffusivity measurement of glass at high temperature by using flash method

A measurement of the thermal diffusivity of a semi-transparent material (glass) by means of the "Flash Method" is investigated in the present work. By taking into account the heat losses on the two faces of the sample, and using a new experimental technique design, an improvement of the determination of the thermal diffusivity of the semi-transparent material (glass) at high temperature is realized. The experimental design presented here is an original technical concept that enables a significant reduction in heat loss during the experiments. A very simple model based on the quadrupole method is used to theoretically determine the thermal diffusivity of the semi-transparent material by taking into account both conduction and radiation. Theoretical results clarify the effect of the absorption coefficient and the thickness of the sample on the heat transfer in the semi-transparent medium.     

RADIATION-CONDUCTION INTERACTION IN A PLANAR,ANISOTROPICALLY SCATTERING MEDIUM WITH FLUX BOUNDARY

Steady, combined radiation and conduction heat transfer in an absorbing, emitting, and anisotropically scattering planar medium is investigated theoretically. The problem is considered with a constant net heat flux imposed at one boundary and a constant temperature at the other. Both specular and diffuse reflectivities are included. The influence of radiation heat transfer is obtained by solving the exact integral equations of radiative transfer with the nodal approximation technique. The technique reduces the integral equations into a discrete system of algebraic equations and permits obtaining exact numerical solutions for any scattering-phase function. Temperatures are obtained from the energy equation with an iterative procedure. The effects of scattering anisotropy as well as radiation parameters such as albedo and wall reflectivities on temperatures are analyzed.     

Analysis of transient heat transfer in multilayer thin films with nonlinear thermal boundary resistance

Transient energy transport in thin-layer films with a nonlinear thermal boundary resistance is analyzed theoretically within the framework of the dual-phase-lag heat conduction model. An iterative finite difference numerical method is used and is verified using a derived semi-analytical solution of the problem. Effects of the thermo-physical properties on energy transport when a two-layer film is exposed to a thermal pulse of certain duration and strength are presented. The thermal boundary resistance, the heat flux and temperature gradient phase lags and the thermal conductivities and heat capacities all are important factors that characterize energy transport through the interface and the temperature distribution in the two layers. The maximum interfacial temperature difference that takes place in the transient process of thermal pulse propagation is found to be the proper choice to measure the perfect-ness of the interface with a finite thermal boundary resistance. The results show that even with high values of the thermal boundary resistance the maximum interfacial temperature difference can be very small when the thermal pulse propagates from a high-thermal conductivity and heat capacity layer to a low-thermal conductivity and heat capacity layer. For a certain range of the thermal conductivities and heat capacities, the maximum interfacial temperature difference approaches zero even with high values of the thermal boundary resistance. Thermal conductivities and heat capacities are much more important in characterizing transient heat transfer through the imperfect interface than the phase lags of the heat flux and temperature gradient.     

Thermal response of a packed bed of spheres containing a phase-change material

A computational model of the transient thermal response of a packed bed of spheres containing a phase-change material (PCM) is presented. A one-dimensional separate phases formulation is used to develop a numerical analysis of the dynamic response of the bed which is subject to the flow of a heat transfer fluid, for arbitrary initial conditions and inlet fluid temperature temporal variations. Phase-change models are developed for both isothermal and nonisothermal melting behaviours. Axial thermal dispersion effects are modelled, including intraparticle conduction (Biot number) effects. Regenerative thermal storage applications involve flow reversals to recover the stored energy; this aspect of operation is included in the present model. Results from the model for a commercial sized thermal storage bed for both the energy storage and recovery periods are presented. Experimental measurements of transient temperature distributions in a randomly packed bed of uniform spheres containing a PCM for a step-change in inlet air temperature are reported for a range of Reynolds number.