SOLVING A THERMAL REGENERATOR MODEL USING IMPLICIT NEWTON-KRYLOV METHODS

Laser tissue welding and soldering with use of short laser pulses are proposed. The transient radiation heat transfer in the picosecond time scale is numerically investigated for the first time using the discrete ordinate method for cylindrical geometries. The numerical method developed incorporates the propagation of radiation with the speed of light. The temporal radiation fields of tissue cylinders under the irradiation of short laser pulses are obtained. The use of short laser pulses for tissue welding and soldering is found to have reduced thermal damage to the healthy tissue and improves the uniformity of heating in the tissue closure region in both the depth and radial directions. The addition of absorbing solders in tissue soldering results in a well-confined radiation energy deposition field in the proximity of the solder-stained region and lessens the outgoing radiative heat flux at the laser incident surface. Comparisons of radiation heat transfer are made between the spatially square-variance and Gaussian-variance laser inputs and between the temporally Gaussian-profile and skewed-profile pulses, respectively.     

Development and comparison of the DTM,the DOM and the FVM formulations for the short-pulse laser transport through a participating medium

The present article deals with the analysis of transient radiative transfer caused by a short-pulse laser irradiation on a participating medium. A general formulation of the governing transient radiative transfer equation applicable to a 3-D Cartesian enclosure has been presented. To solve the transient radiative transfer equation, formulations have been presented for the three commonly used methods in the study of radiative heat transfer, viz., the discrete transfer method, the discrete ordinate method and the finite volume method. To show the uniformity in the formulations in the three methods, the intensity directions and the angular quadrature schemes for computing the incident radiation and heat flux have been taken the same. To validate the formulations and to compare the performance of the three methods, effect of a square short-pulse laser having pulse-width of the order of a femtosecond on transmittance and reflectance signals in case of an absorbing and scattering planar layer has been studied. Effects of the medium properties such as the extinction coefficient, the scattering albedo and the anisotropy factor and the laser properties such as the pulse-width and the angle of incidence on the transmittance and the reflectance signals have been compared. In all the cases, results of the three methods were found to compare very well with each other. Computationally, the discrete ordinate method was found to be the most efficient.     

SLA (Second-law analysis) of transient radiative transfer processes

This paper concerns a SLA (second-law analysis) of transient radiative heat transfer in an absorbing, emitting and scattering medium. Based on Planck’s definition of radiative entropy, transient radiative entropy transfer equation and local radiative entropy generation in semitransparent media with uniform refractive index are derived. Transient radiative exergy transfer equation and local radiative exergy destruction are also derived based on Candau’s definition of radiative exergy. The analytical results are consistent with the Gouy–Stodola theorem of classical thermodynamics. As an application concerning transient radiative transfer, exergy destruction of diffuse pulse radiation in a semitransparent slab is studied. The transient radiative transfer equation is solved using the discontinuous finite element based discrete ordinates equation. Transient radiative exergy destruction is calculated by a post-processing procedure.     

Indirect heating strategy for laser induced hyperthermia: An advanced thermal model

A novel heating strategy based on laser irradiation of surrounding tissues as an alternative to direct irradiation of superficial tumors is proposed and analyzed for the first time. The computational analysis is based on two-dimensional axisymmetric models for both radiative transfer and transient heat transfer in the human body. A diffuse component of the radiation field is calculated using P₁ approximation. Coupled transient energy equations and kinetic equations for composite human tissue take into account the metabolic heat generation and heat conduction, blood perfusion through capillaries, the volumetric heat transfer between arterial blood and tissue, the thermal conversions in blood and tumor tissue, the periodic laser heating, and also heat exchange between a human body and ambient medium. An example problem for a superficial human cancer has been solved numerically to illustrate the relative role of the problem parameters on the transient temperature field during hyperthermia treatment. In particular, the effect of embedded gold nanoshells which strongly absorb the laser radiation is analyzed. It is shown that required parameters of tumor hyperthermia can be also reached without gold nanoshells.     

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.     

An Insight Into The Modeling of Short-Pulse Laser Transport Through A Participating Medium

Thermal radiation is a time-dependent process in the analysis of a short-pulse laser irradiation. The numerical modeling of the radiative phenomenon considers a finite number of intensity directions over a spherical space. Thus, in time-dependent radiative transfer problems, radiative intensities take different times to reach a particular location in the medium, and accordingly, collectively they remain available for durations different than the laser pulse width. The present work proposes that the above aspect be taken into account in the analysis of transient radiative transfer problems. To validate this concept, transport of a short square-pulse laser in a plane-parallel participating medium is studied. It is found that the magnitude of the transmittance signals differ for higher values of the extinction coefficient and also that the signals remain available for a longer duration. Reflectance signals are found to be less affected.     

Transient Radiative Transfer in a Graded Index Medium with Specularly Reflecting Surfaces

A modified Monte Carlo (MC) method has been developed for solving transient radiative transfer in a one-dimensional scattering medium with a graded refractive index. The accuracy and computational efficiency of the algorithm are validated initially. With the introduction of time shift and superposition principle into the MC model, the computational efficiency is greatly improved. We make a comparative analysis of the time-resolved incident radiation (and radiative heat flux) distributions in the media with diffuse and specular reflection boundaries. Results show that the temporal and spatial radiative signals of the medium with specular reflection boundaries greatly differ from those having diffuse reflection boundaries.     

RADIATION MODELING OF STATIONARY FUSED SILICA RODS AND FIBERS HEATED BY CO2 LASER IRRADIATION

This study presents a heat transfer model for a stationary fused silica rod heated by a CO₂ laser. During laser heating, the effect of fused silica being modeled to be opaque or semitransparent to laser irradiation is studied. The radiative heat transfer caused by the emission of fused silica is modeled using the zonal method, and compared to the Rosseland diffusion approximation. The spectral dependence of the fused silica absorption coefficient in semitransparent wavelengths is approximated by a two-band model. The weighted-sum-of-gray-gas (WSGG) method is used to calculate the radiative source term. The governing equation with conduction and radiation heat transfer is solved by the finite-volume method. The importance of modeling the effects of laser energy penetration below the fused silica surface during heating, especially for small diameter fibers, is discussed. The importance of radiative heat transfer in fused silica is also discussed. Around 25 K in temperature difference is observed when the diffusion approximation is used in place of the zonal method to model the radiative transfer in fused silica.     

Improved Finite Volume Method for Three-Dimensional Radiative Heat Transfer in Complex Enclosures Containing Homogenous and Inhomogeneous Participating Media

The paper presents a modified finite volume method for the solution of the radiative transport equation, which implements the FTn angular discretization along with the bounded high-resolution curved line advection method to alleviate ray effect and false scattering, respectively, and consequently improve the accuracy of the final results. Using the blocked-off-region procedure, the present formulation is capable of treating blockage effects caused by inner/outer obstructing bodies. The developed methodology based on the combination of the above methods is evaluated against five three-dimensional test cases considering either homogenous or inhomogeneous participating media. For all cases, the predictions reveal the mitigation of false scattering and ray effects consequently the improvement of accuracy, employing this model for solving radiation heat transfer in industrial applications. In industrial application, the radiative heat transfer problem is solved for a unity boiler furnace where an inhomogeneous medium is assumed. The effects of the scattering albedo, walls emissivity and walls temperature are investigated.     

Conduction and radiation in a rectangular isotropic scattering medium with black surfaces by the RTNAM

The ray tracing-node analyzing method (RTNAM) has been successfully developed to solve 1-D coupled heat transfer in isotropic and anisotropic scattering media in the past, and in this paper it is further extended to solving the 2-D coupled heat transfer in a rectangular isotropic scattering medium. Using the control-volume method, the partial transient energy equation is discretized in implicit scheme. The effect of radiation on heat transfer is considered as a radiative source term (RST) in the discretized energy equation, and in combination with spectral band model, the RST is calculated using the radiative transfer coefficients (RTCs), which are deduced by the ray tracing method. The Patankar’s linearization method is used to linearize the RST and the opaque boundary condition, and the linearized equations are solved by the ADI method. Before solving the RTCs for isotropic scattering media, the RTCs without considering scattering must be solved at first. And then, the RTCs without considering scattering are normalized according to their integrality relationships. In addition, the correctness of the results obtained by the RTNAM is validated, and effects of scattering albedo and refractive index on transient temperature distribution are investigated.     

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.     

Participating media exposed to collimated short-pulse irradiation – A Laguerre–Galerkin solution

A new method is developed for the solution of radiative transfer in a one-dimensional absorbing and isotropically scattering medium with short-pulse irradiation on one of its boundaries. The time-dependent radiative intensity is expanded in a series of Laguerre polynomials with time as the argument. Moments of the radiative transfer equation, as well as of the boundary conditions, then yield a set of coupled time-independent radiative transfer problems. This set, in turn, is reduced to a set of algebraic equations by the application of the Galerkin method. The transient transmittance and reflectance of the medium are evaluated for various values of the optical thickness, scattering albedo and pulse duration. It is demonstrated that the Laguerre–Galerkin method is not only easier to implement and more efficient but also yields more accurate results compared to the direct application of the Galerkin method. The results are in very good agreement with those available in the literature.     

Evaluation of an improved hybrid six-flux/zone model for radiative transfer in rectangular enclosures

An improved model for the calculation of radiative transfer in enclosures filled with an absorbing, emitting and scattering medium is presented. The model is denoted by a hybrid six-flux/zone model since it combines features of both the zone method and (three-dimensional) six-flux models. Compared to the zone method, computation time is considerably reduced and reaches approximately the same order as the faster flux-type models. The accuracy of the hybrid six-flux/zone model presented here is drastically improved without increasing computation time. This is achieved by introducing a correction for the directional characteristics of the propagation of radiation through adjacent zones. The thus improved hybrid model is evaluated for a realistic recognized test problem and found to be an efficient and accurate tool for calculating radiative transfer in enclosures filled with a participating medium.     

Ultrafast Radiative Heat Transfer in Three-Dimensional Highly-Scattering Media Subjected to Pulse Train Irradiation

Transient radiative transfer in highly-scattering media subjected to time-dependent pulse train heating conditions is scrutinized. A basic problem in which a cube is exposed to a unit step irradiation is first solved via the transient discrete-ordinates method, and the influences of the spatial grid and time step are examined. The temporal solutions for the basic problem are then used for constructing the responses of the same cube subjected to the irradiation of pulse trains via the superposition method. The effects of the pulse width and time interval between the pulses are studied. The characteristics of pulse train irradiation are revealed. The present approach is simple because only one basic solution is needed to construct the solutions for various problems with different pulse widths and/or pulse intervals.     

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.     

Radiative slab heating analysis for various fuel gas compositions in an axial-fired reheating furnace

A transient radiative slab heating analysis was performed to investigate the effect of various fuel mixtures on the performance of an axial-fired reheating furnace. The various fuel mixtures tested were assumed to be attained by mixing COG (coke oven gas) and BFG (blast furnace gas), which are the two main byproduct gases found in the integrated steel mill industry. The numerical prediction of radiative heat transfer was calculated using an FVM radiation solving method, which is a well-known and efficient method for curvilinear coordinates. The WSGGM (weighted sum of gray gas model) was also adopted to calculate the radiative heat transfer in composition dependent media. The entire furnace was divided into fourteen sub-zones to calculate the radiative thermal characteristics of the furnace without flow field calculations. Each sub-zone was assumed to have homogeneous media and wall temperatures. All of the medium and wall temperatures were computed by calculating the overall heat balance using some relevant assumptions. The overall heat balance was satisfied when the net heat input equaled the three sources of heat loss in each sub-zone, wall loss, skid loss, and slab heating loss.     

Modeling of the radiative contribution to heat transfer in porous media composed of spheres or cylinders

A theoretical model for evaluating the radiative conductivity tensor of a porous media is developed in this paper. The porous media is composed of a transparent fluid and opaque particles with characteristic lengths longer than the radiation wavelength. The main features of the proposed approach are (i) take into account the interaction between conduction and radiation heat transfers, (ii) allow the modeling of the radiative transfer in anisotropy system such as an assembly of cylinders, and (iii) have an easy numerical implementation into the energy equations of the porous media. In order to study the accuracy of the approach, the paper evaluates the model for porous media composed of spheres or cylinders. The predictions of the model agree well with experimental data and with results obtained from finite element simulations. The numerical results also show that the radiative conductivity can be strongly influence by the effect of temperature distribution across the particle surface and by the effect of the multiple scattering of radiation in the porous media.     

Monte Carlo simulation of transient radiative transfer in a medium with a variable refractive index

In this work, a Monte Carlo method is developed to simulate transient radiative transfer in a refractive planar medium exposed to a collimated pulse irradiation. The time of flight in closed form is derived for a medium with a linearly varying refractive index. The time-resolved reflectance and transmittance of the slab are obtained by tracing photon bundles and calculating the time of flight. There is a very satisfying correspondence between the present results and the discrete ordinates solutions. The magnitude of numerical uncertainty decreases with the increase of bundles. To simulate transient radiative transfer in an optically thick medium, we need a large number of bundles. The reflectance decreases with the increase of the positive gradient of the refractive index considered. The appearance instant of the transmittance peak postpones as the refractive index increases. Influence of the optical thickness, the scattering albedo and the anisotropically scattering coefficient on the time-resolved reflectance and transmittance is also investigated.     

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.