Transient Radiative Transfer Research Articles

Effect of fractional derivatives on transient MHD flow and radiative heat transfer in a micro-parallel channel at high zeta potentials

By using the Caputo–Fabrizio time fractional derivative, unsteady flows of an incompressible viscous through a circular tube are developed. Flows are generated due to the combination of electroosmotic, pressure and magnetic forces. The derived fractional momentum equation incorporating the electromagnetic body force resulting from the electric double layer (EDL) field was solved using the Laplace transform technique, Riemann-sum approximation method, and the Stehfest’s algorithm. The solution obtained is validated by assenting comparisons between the Riemann-sum approximation method and Stehfest’s algorithm. Based upon the velocity field solution, the energy equation is analyzed by taking the viscous dissipation, thermal radiative, the volumetric heat generation due to Joule heating effect and electromagnetic couple effect into account. Numerical simulations and graphical illustrations were carried out using the software package Mathcad. The results highlights that, fractional models of fluid-flow and heat transfer with fractional derivatives bring significant differences compared to the ordinary model. The variations of fluid velocity, fluid temperature, skin friction and Nusselt number with related parameters are interpreted and the results are discussed.

Experimental research on noninvasive reconstruction of optical parameter fields based on transient radiative transfer equation for diagnosis applications

The noninvasive reconstruction of optical parameter fields in participating phantom is investigated experimentally based on the measured time-resolved radiative signals, which are detected by the time-correlated single-photon counting system. The discrete ordinate method is employed to solve the forward transient radiative transfer equation to simulate the time-resolved radiative transfer in the physical phantom exposed to ultra-short pulse laser irradiation. On top of that, the sequential quadratic programming algorithm based on the generalized Gaussian Markov random field is applied to solve the inverse problem. To improve the computational efficiency, an adjoint equation technique is adopted to determine the gradient of objective function. Good agreement was obtained between the predicted optical parameter fields and realistic ones. All the reconstruction results demonstrate that the proposed reconstruction methods are proved to be accurate and efficient experimentally.

Multiscale solutions of radiative heat transfer by the discrete unified gas kinetic scheme.

The radiative transfer equation (RTE) has two asymptotic regimes characterized by the optical thickness, namely, optically thin and optically thick regimes. In the optically thin regime, a ballistic or kinetic transport is dominant. In the optically thick regime, energy transport is totally dominated by multiple collisions between photons; that is, the photons propagate by means of diffusion. To obtain convergent solutions to the RTE, conventional numerical schemes have a strong dependence on the number of spatial grids, which leads to a serious computational inefficiency in the regime where the diffusion is predominant. In this work, a discrete unified gas kinetic scheme (DUGKS) is developed to predict radiative heat transfer in participating media. Numerical performances of the DUGKS are compared in detail with conventional methods through three cases including one-dimensional transient radiative heat transfer, two-dimensional steady radiative heat transfer, and three-dimensional multiscale radiative heat transfer. Due to the asymptotic preserving property, the present method with relatively coarse grids gives accurate and reliable numerical solutions for large, small, and in-between values of optical thickness, and, especially in the optically thick regime, the DUGKS demonstrates a pronounced computational efficiency advantage over the conventional numerical models. In addition, the DUGKS has a promising potential in the study of multiscale radiative heat transfer inside the participating medium with a transition from optically thin to optically thick regimes.

Transient thermal radiation heat transfer in a reinforced plastic coating with anisotropic optical properties

Advanced fiber reinforced plastics, such as carbon fiber reinforced polymers (FRP), offer many advantages over more traditional materials such as metals. Their characteristics make them ideal for use in many sensitive applications. To maximize the use of these materials, there is a need to gain a better understanding of heat and temperature distribution in these materials under different boundary conditions. In this study transient radiative and conductive heat transfer in a FRP medium with anisotropic optical properties is investigated. The solution includes the radiative transfer equation (RTE) within the material coupled to a transient energy equation that contains both radiative and conductive terms. Two different kinds of boundary conditions are treated: when the temperatures imposed on the boundaries vary with time and when the medium is subject to a radiation source which varies with time. It is shown that radiative heat transfer has significant effect on heat transfer and temperature distribution within the layer.

Non-destructive testing of ceramic materials using mid-infrared ultrashort-pulse laser

The non-destructive testing (NDT) of ceramic materials using mid-infrared ultrashort-pulse laser is investigated in this study. The discrete ordinate method is applied to solve the transient radiative transfer equation in 2D semitransparent medium and the emerging radiative intensity on boundary serves as input for the inverse analysis. The sequential quadratic programming algorithm is employed as the inverse technique to optimize objective function, in which the gradient of objective function with respect to reconstruction parameters is calculated using the adjoint model. Two reticulated porous ceramics including partially stabilized zirconia and oxide-bonded silicon carbide are tested. The retrieval results show that the main characteristics of defects such as optical properties, geometric shapes and positions can be accurately reconstructed by the present model. The proposed technique is effective and robust in NDT of ceramics even with measurement errors.

Model reduction for experimental thermal characterization of a holding furnace

Vacuum holding induction furnaces are used for the manufacturing of turbine blades by loss wax foundry process. The control of solidification parameters is a key factor for the manufacturing of these parts. The definition of the structure of a reduced heat transfer model with experimental identification through an estimation of its parameters is required here. Internal sensors outputs, together with this model, can be used for assessing the thermal state of the furnace through an inverse approach, for a better control. Here, an axisymmetric furnace and its load have been numerically modelled using FlexPDE, a finite elements code. The internal induction heat source as well as the transient radiative transfer inside the furnace are calculated through this detailed model. A reduced lumped body model has been constructed to represent the numerical furnace. The model reduction and the estimation of the parameters of the lumped body have been made using a Levenberg-Marquardt least squares minimization algorithm, using two synthetic temperature signals with a further validation test.

Transient/time-dependent radiative transfer in a two-dimensional scattering medium considering the polarization effect.

Transient/time-dependent radiative transfer in a two-dimensional scattering medium is numerically solved by the discontinuous finite element method (DFEM). The time-dependent term of the transient vector radiative transfer equation is discretized by the second-order central difference scheme and the space domain is discretized into non-overlapping quadrilateral elements by using the discontinuous finite element approach. The accuracy of the transient DFEM model for the radiative transfer equation considering the polarization effect is verified by comparing the time-resolved Stokes vector component distributions against the steady solutions for a polarized radiative transfer problem in a two-dimensional rectangular enclosure filled with a scattering medium. The transient polarized radiative transfer problems in a scattering medium exposed to an external beam and in an irregular emitting medium are solved. The distributions of the time-resolved Stokes vector components are presented and discussed.

Numerical Study of Transient Convection With Volumetric Radiation Using an Hybrid Lattice Boltzmann Bhatnagar–Gross–Krook–Control Volume Finite Element Method

In this paper, a new hybrid numerical algorithm is developed to solve coupled convection–radiation heat transfer in a two-dimensional cavity containing an absorbing, emitting, and scattering medium. The radiative information is obtained by solving the radiative transfer equation (RTE) using the control volume finite element method (CVFEM), and the density, velocity, and temperature fields are calculated using the two double population lattice Boltzmann equation (LBE). To the knowledge of the authors, this hybrid numerical method is applied at the first time to simulate combined transient convective radiative heat transfer in 2D participating media. In order to test the efficiency of the developed method, two configurations are examined: (i) free convection with radiation in a square cavity bounded by two horizontal insulating sides and two vertical isothermal walls and (ii) Rayleigh–Benard convection with and without radiative heat transfer. The obtained results are validated against available works in literature, and the proposed method is found to be efficient, accurate, and numerically stable.

Wavelength selection of bidirectional laser transmission based on Monte Carlo method

The laser detection technology in uncertain and dynamic environments is of utmost importance in many fields. A model of transient radiative transfer of bidirectional path laser based on Monte Carlo method is developed to investigate the optimum wavelength of active detector at complex atmospheric conditions. The radiative parameters of atmosphere are calculated by HITRAN database and Mie theory at several typical atmospheric conditions including the standard atmosphere, urban aerosol, and radiation fog. Transmission characteristics for five spectral bands at the above atmospheric conditions are calculated by this model. The optimal transmission ability occurred in bands 0.2–0.5, 1.4–1.6, and 0.75–1.25μm on the condition of standard atmosphere, urban aerosol, and radiation fog, respectively. All results provide effective reference and basic support for choosing the optimal spectral band for active detection.

Transient polarized radiative transfer analysis in a scattering medium by a discontinuous finite element method.

Transient (time-dependent) polarized radiative transfer in a scattering medium exposed to an external collimated beam illumination is conducted based on the time-dependent polarized radiative transfer theory. The transient term, which persists the nanosecond order time and cannot be ignored for the time-dependent radiative transfer problems induced by a short-pulsed beam, is considered as well as the polarization effect of the radiation. A discontinuous finite element method (DFEM) is developed for the transient vector radiative transfer problem and the derivation of the discrete form of the governing equation is presented. The correctness of the developed DFEM is first verified by comparing the DFEM solutions with the results from the literature. The DFEM is then applied to study the transient polarized radiative transfer induced by a pulsed beam. The time-dependent Stokes vector components are calculated, plotted and analyzed as functions of the axis coordinate and discrete direction. Effects of the diffuse/specular boundary and the incident beam polarization state with respect to the Stokes vector components are further analyzed for cases of different boundary reflection modes and incident beam illuminations.

Thermal analysis of laser-irradiated tissue phantoms using a novel separation of the variables-based discrete transfer method

ABSTRACTThermal analysis of tissue phantoms subjected to short pulse laser irradiation has been presented. The transient radiative transfer equation (RTE) has been solved using a novel separation of variables-based discrete transfer method (DTM) recently developed by the present authors (Nirgudkar et al. [21]). As an advancement, the solution of RTE has been coupled with Pennes’ bioheat transfer equation for determining the temperature distribution. Homogenous as well as phantoms embedded with optical inhomogeneity have been considered. The numerical model has been verified against the results available in the literature. This study clearly reveals the influence of the nature of the embedded inhomogeneity and its relative contrast on the resultant temperature distribution inside the body of the tissue phantom.

Analysis of transient radiative transfer induced by an incident short-pulsed laser in a graded-index medium with Fresnel boundaries

Transient radiative transfer induced by a short-pulsed laser in a one-dimensional graded-index medium is investigated by the discontinuous finite element method (DFEM). The boundaries of the medium are Fresnel reflectors, and the incident pulse is considered as the combination of the collimated and the diffuse parts after its first interaction with the medium. The correctness and accuracy of the DFEM solutions for time-resolved reflectance and transmittance are first validated by comparisons with the results obtained by the Monte Carlo method, and the DFEM is then employed to investigate the transient radiative transfer in a graded-index medium with Fresnel boundaries. Effects of the refractive index distributions, the pulse width, the optical thickness, and the scattering phase functions on the transient radiative signals are examined. Several meaningful trends on the time-resolved reflectance and transmittance are observed and analyzed.

Estimation of radiative parameters in participating media using shuffled frog leaping algorithm

The transient radiative transfer in 1-D homogeneous media with ultra-short Gaussian pulse laser irradiated was investigation by the finite volume method. The concept of optimal detection distance was proposed. The radiation characteristic was studied thoroughly. Afterwards, a memetic meta-heuristic shuffled frog leaping algorithm was introduced to inverse transient radiative problems. It is demonstrated that the extinction coefficient and scattering albedo can be retrieved accurately even with noisy data in a homogeneous absorbing and isotropic scattering plane-parallel slab. Finally, a technique was proposed to accelerate the inverse process by reducing the searching space of the radiative parameters.

Analysis of polarized pulse propagation through one-dimensional scattering medium

This paper analyzes the polarized light propagation in a one-dimensional scattering medium with the upper surface subjected to an oblique incident short-pulsed laser beam using the natural element method (NEM). The NEM discretization scheme for the transient vector radiative transfer equation (TVRTE) is presented in detail. The accuracy of the natural element method for transient vector radiative transfer in the scattering medium is assessed. Numerical results show that the NEM is accurate, and effective in solving transient polarized radiative problems. We examine a square short-pulsed laser transport firstly in the atmosphere with Mie scattering and then within aerosol scattering medium. We then investigate the transient polarized radiative transfer problem in the atmosphere-ocean system. The time-resolved signals and the polarization state of the Stokes vector are presented and analyzed. It is found that the scattering types of the medium make greatly influence on the transient transportation of the polarized light. Critically, the polarization states of the backward and forward scattered photons show significantly different time varying trends. For the two-layer system with dissimilar refractive index distributions, due to the total-reflection effect, the existence of a Fresnel interface significantly changes the polarization state of the light, and discontinuous distribution features are observed on the interface.

Implementation of a numerical holding furnace model in foundry and construction of a reduced model

Vacuum holding induction furnaces are used for the manufacturing of turbine blades by loss wax foundry process. The control of solidification parameters is a key factor for the manufacturing of these parts in according to geometrical and structural expectations. The definition of a reduced heat transfer model with experimental identification through an estimation of its parameters is required here. In a further stage this model will be used to characterize heat exchanges using internal sensors through inverse techniques to optimize the furnace command and the optimization of its design. Here, an axisymmetric furnace and its load have been numerically modelled using FlexPDE, a finite elements code. A detailed model allows the calculation of the internal induction heat source as well as transient radiative transfer inside the furnace. A reduced lumped body model has been defined to represent the numerical furnace. The model reduction and the estimation of the parameters of the lumped body have been made using a Levenberg-Marquardt least squares minimization algorithm with Matlab, using two synthetic temperature signals with a further validation test.

Numerical Investigation of the Transient Radiative Heat Transfer inside a Hexagonal Furnace Filled with Particulate Medium

The transient radiative heat transfer in two 2D irregular geometry filled with particulate media is numerically investigated. The radiative transfer equation is solved with FTn finite volume method. Non-orthogonal mesh is used to discretize the computational domain and the high resolution CLAM scheme is utilized to relate the facial intensities to the nodal values. Various cases of scattering in media with real indices of refraction (dielectric particles) and complex indices of refraction (absorbing particles) are considered. Both Mie theory and equivalent isotropic approximation are used to account for the scattering behavior of the media. The difference between these two methods is found insignificant, especially for the steady state solutions and for media with complex indices of refraction, while the complexity and computational cost of the equivalent isotropic approximation is much lower than those of Mie theory.

Transient Radiative Transfer in a Graded Index Slab with Fresnel Surfaces

One-dimensional transient radiative transfer in a graded index slab with Fresnel surfaces subject to a short-pulse laser irradiation is investigated by the lattice Boltzmann method. In the scattering medium having Fresnel surfaces, the radiative intensity includes two parts: the collimated intensity, and scattered or diffuse intensity. The contribution of the collimated pulse to the transient process is considered as a source term in the transient radiative transfer equation. First, lattice Boltzmann method solutions for time-resolved signals are validated by comparison with results obtained by Monte Carlo method. The investigations are mainly focused on the medium with linearly changing graded index, and the commonalities and differences of the time-resolved signals resulting from the slab with diffuse reflected surfaces or Fresnel surfaces are discussed. The effects of the gradient of the linearly varying refractive index on transmittance and reflectance signals are examined. Then, transient radiative transfer with two graded index distributions with a singular point is analyzed. Finally, by setting the right boundary of the slab as a diffusely reflecting surface, the transient radiative transfer in the graded index medium under the combined optical boundary conditions is examined.

Transient radiative transfer in two-dimensional graded index medium by Monte Carlo method combined with the time shift and superposition principle

ABSTRACTTransient radiative transfer (TRT) in a two-dimensional scattering medium with graded refractive index distribution subjected to a collimated short-pulse irradiation is solved by a modified Monte Carlo (MMC) method coupled with the time shift and superposition (TSS) principle. The boundaries are considered as Fresnel surfaces, the refractive index at the boundary mismatches with that of the surroundings, making the reflectivity at the boundary change with the incident directions. The incident pulse consists of two parts when it hits the boundary: bundles directly reflected by the outside boundary and bundles refracted into the medium. The accuracy of the present algorithm is confirmed first. Numerical results show that by using the TSS principle, the computational efficiency is greatly improved. Afterward, the TRT in the media with different graded refractive index distributions is investigated. The time-resolved reflectance and transmittance at different locations are given. Several trends on the time-resolved signals are observed and analyzed.

Thermal analysis of laser-irradiated tissue phantoms using dual phase lag model coupled with transient radiative transfer equation

The present work is concerned with the development and application of dual phase lag (DPL) based heat conduction model for investigating the thermal response of laser-irradiated biological tissue phantoms. The developed heat transfer model has been coupled with the transient form of radiative transfer equation (RTE) that describes the phenomena of light propagation inside the tissue phantom. The RTE has been solved using the discrete ordinate method (DOM) to determine the 2-D distribution of light intensity within the tissue phantom, while finite volume method (FVM) based discretization scheme has been employed for solving the heat transfer model. The developed numerical model has first been verified against the results available in the literature. The results obtained in the form of temperature distribution through DPL model have been compared with conventional Fourier heat conduction model as well as with hyperbolic model. The effects of two phase lags terms in the form of relaxation times i.e. τT and τq associated with DPL model on the resultant thermal profiles have been investigated. Thereafter, the temperature distribution inside the biological tissue phantom embedded with optical inhomogeneities of varying contrast levels have been determined using the DPL-based model. Here the optical inhomogeneities represent the malignant (absorbing inhomogeneity) and benign (scattering inhomogeneity) cells present in an otherwise homogeneous medium. Results of the study reveal that the hyperbolic heat conduction model consistently predicts high temperature values and also the associated thermal profiles exhibit the largest amplitude of oscillations throughout the body of the tissue phantom. The DPL-based model results into relatively lesser oscillations due to the coupled effects of τT and τq. The conventional Fourier model, on the other hand, results into the lowest temperature values without any oscillations in the temperature profiles. The effect of the presence of varying nature of optical inhomogeneities is also brought out quite clearly using the developed DPL-based heat conduction model.

Evaluation of the FTn Finite Volume Method for Transient Radiative Transfer in Anisotropically Scattering Medium

In this paper, we formulated, applied, and tested the FTn Finite Volume Method (FTn FVM) for transient radiative transfer in three-dimensional absorbing, emitting, and anisotropically scattering medium. Both the STEP and the Curved-Line Advection Method (CLAM) are introduced for spatial discretization of the transient radiative transfer equation. The results show that FTn FVM reduces largely the ray effects and it is more accurate than the standard FVM. Also, using both STEP and CLAM schemes, FTn FVM has smaller convergence time than the standard FVM for all cases. On the contrary, the STEP scheme is faster than the CLAM scheme but it has less accuracy. Then, the effects of optical thickness, scattering albedo, and anisotropy factor on incident radiation and radiative flux are presented and discussed.