Volumetric Radiative Information Research Articles

Simultaneous estimation of parameters in analyzing porous medium combustion—assessment of seven optimization tools

ABSTRACTSimultaneous estimation of the gas velocity, scattering albedo, and downstream pore diameter in a two-layer planar porous matrix involving combined mode conduction, convection, and radiation heat transfer with combustion is reported. Non-local thermal equilibrium between the gas and the solid phase is accounted by separate energy equations for the two phases. Performances of the genetic algorithm, genetic algorithm parallel, simulated annealing, multiple starting point algorithm parallel, pattern search algorithm, pattern search algorithm parallel, and global search algorithm in the simultaneous estimation of three parameters are analyzed. All the algorithms utilize a priori knowledge of the axial gas temperature distribution, and the magnitudes of the convective and the radiative heat fluxes at the outer surface of the porous matrix. With volumetric radiative information needed in the solid phase energy equation computed using the discrete transfer method, the two energy equations are simultaneously solved using the finite volume method. Pattern search algorithm provides better estimation, and computationally it is also the fastest.

Analysis of Conduction and Radiation Heat Transfer in a Differentially Heated 2‐D Square Enclosure

Radiative heat transfer with and without conduction in a differentially heated 2‐D square enclosure is analyzed. The enclosure with diffuse gray boundaries contains radiating and/or conducting gray homogeneous medium. Radiatively, the medium is absorbing, emitting and scattering. On the south boundary, four types of discrete heated regions, viz., the full boundary, the left one‐third, left two third and middle one third, are considered. In the absence of conduction, distributions of heat flux along the south boundary are studied for the effect of extinction coefficient. In the presence of conduction, distributions of radiation, conduction and total heat fluxes along the south boundary are analyzed for the effects of extinction coefficient, scattering albedo, conduction–radiation parameter, and south boundary emissivity. Effects of these parameters on centerline temperature distribution are also studied. To assess the performance of three commonly used radiative transfer methods, in all cases, the radiative transfer equation is solved using the discrete ordinate method (DOM), the conventional discrete ordinate method (CDOM) and the finite volume method (FVM). In the combined mode problem, with volumetric radiative information known from one of the three methods, viz., DOM, CDOM, and FVM, the energy equation is solved using the finite difference method (FDM). In all cases, the results from FDM‐DOM, FDM‐CDOM, and FDM‐FVM are in good agreement. Computationally, all three sets of methods are equally efficient.

Analysis of Dual-Phase-Lag Non-Fourier Conduction and Radiation Heat Transfer in a Planar Slab

This article deals with the analysis of combined mode conduction and radiation heat transfer in a planar conducting-radiating medium. Radiatively, the medium is absorbing, emitting, and scattering. Finite propagation speeds of thermal perturbations owing to fluctuations in temperature and heat flux are accounted for in conduction heat transfer. The governing equation is solved using the lattice Boltzmann method. The volumetric radiative information needed in an energy equation is calculated using the discrete transfer method. Effects of lag ratio, extinction coefficient, scattering albedo, and conduction-radiation parameter on transient temperature distributions are analyzed. In the absence of radiation, at different lag ratios, results are compared with those available in the literature. Radiation is found to help in the faster establishment of the thermal field. Wave fronts are found to reflect from the boundaries until steady state is attained.

Simultaneous Estimation of Properties in a Combined Mode Conduction–Radiation Heat Transfer in a Porous Medium

Simultaneous estimation of thermophysical and optical properties such as the thermal conductivity, the scattering albedo, and the emissivity of a 1‐D planar porous matrix involving combined mode conduction and radiation heat transfer with heat generation is reported. Coupled energy equations for the gas and solid phase account for the nonlocal thermal equilibrium between the two phases. Performances of the genetic algorithm (GA) and the global search algorithm (GSA) in simultaneous estimation of three properties are analyzed. Both the GA and the GSA utilize a priori knowledge of the axial gas temperature distribution, and the magnitudes of the convective and the radiative heat fluxes at the outer surface of the porous matrix. With volumetric radiative information needed in the solid‐phase energy equation computed using the discrete transfer method, the two energy equations are simultaneously solved using the finite volume method. GSA provides better estimation, and computationally, it is much faster than the GA.

Combined Mode Conduction and Radiation Heat Transfer in a Porous Medium and Estimation of the Optical Properties of the Porous Matrix

This article deals with the analysis of combined mode conduction and radiation heat transfer in a porous medium, and simultaneous estimation of the optical properties of the porous matrix. Simultaneous solution of the gas- and solid-phase energy equations encompasses local thermal nonequilibrium, while the convective heat exchange term couples the gas- and the solid-phase energy equations. A localized uniform volumetric heat generation zone is the source of heat transfer in the porous matrix. With volumetric radiative information needed in the solid-phase energy equation computed using the discrete transfer method, the solid- and gas-phase energy equations are simultaneously solved using the finite difference method. For a given set of boundary conditions and operating parameters, the computed temperature distribution serves as the exact temperature profile necessary in the estimation of parameters. In the estimation of parameters using inverse analysis, the objective function is minimized using the genetic algorithm. Effects of measurement error, number of generations, population size, crossover probability, and mutation probability are studied in regard to the accuracy of results and the computational time required. Reasonably accurate estimations of extinction coefficient, scattering albedo, and emissivity of the porous matrix are obtained.

Analysis of Conduction-Radiation Heat Transfer in a 2D Enclosure Using the Lattice Boltzmann Method

Application of the lattice Boltzmann method (LBM) recently extended by Pietro et al. [P. Asinari, S. C. Mishra, and R. Borchiellini, A Lattice Boltzmann Formulation to the Analysis of Radiative Heat Transfer Problems in a Participating Medium, Numer. Heat Transfer B, 57(2), 126–146, 2010] for calculation of volumetric radiative information is extended for the analysis of a combined mode transient conduction and radiation heat transfer in a 2D rectangular enclosure containing an absorbing, emitting and scattering medium. Unlike all previous studies, with volumetric radiative information computed using the proposed LBM, the energy equation is formulated and solved using the LBM. In the combined mode conduction–radiation problem, to assess the computational advantage of computing the radiative information too using the LBM, the same problem is also solved using the LBM–finite volume method (FVM) formulation. In this LBM–FVM formulation, the FVM is used to calculate the volumetric radiative information needed for the energy equation, and the energy equation is solved using the LBM. Comparisons are made for the effects of the extinction coefficient, the scattering albedo and the conduction–radiation parameter on the temperature distributions in the medium. Although the number of iterations for the converged solution in LBM–LBM is much more than that of the LBM–FVM, computationally, the LBM–LBM is faster than the LBM–FVM.

Numerical Analysis of Rayleigh-Bénard Convection with and Without Volumetric Radiation

This article reports the numerical study of Rayleigh–Bénard convection in a 2-D rectangular channel in the presence of volumetric radiation. Momentum and energy equations are formulated and solved using the lattice Boltzmann method (LBM). Volumetric radiative information needed in the energy equation is computed using the finite volume method. The approach of the double population scheme is adopted in the LBM to compute the velocity and the temperature fields. Effects of optical properties such as the extinction coefficient, the scattering albedo, and the convection-radiation parameter on streamlines, isotherms, and Nusselt number distributions are analyzed for a wide range of Rayleigh numbers. Radiation is found to significantly alter the velocity and thermal fields in the medium.

Analysis of non-Fourier conduction and volumetric radiation in a concentric spherical shell using lattice Boltzmann method and finite volume method

Application of the lattice Boltzmann method (LBM) has been extended to formulate and solve the energy equation of a non-Fourier conduction and radiation heat transfer problem in a concentric spherical shell. The enclosed conducting-radiating medium is absorbing, emitting and scattering. The non-Fourier conduction effect is induced by thermally perturbing one of the boundaries and incorporating the finite propagation speed of the thermal wave front in Fourier’s law of heat conduction. The volumetric radiative information needed in the energy equation has been computed using the finite volume method (FVM). To establish the accuracy of the LBM approach, with volumetric radiative information obtained from the FVM, the energy equation is also solved using the FVM. Effects of extinction coefficient, scattering albedo, conduction–radiation parameter, emissivity, radius ratio and the magnitude of thermal perturbations are studied on transient temperature distributions. Effects of the aforesaid parameters on the steady-state conduction, radiation and total energy flow rates are also studied. Steady-state LBM and FVM results are compared. In all the cases, the LBM results compare exceedingly well with the FVM results, and LBM has a faster convergence than the FVM.

Analysis of non-Fourier conduction and radiation in a cylindrical medium using lattice Boltzmann method and finite volume method

Combined mode heat transfer in a conducting–radiating participating medium bounded by a concentric cylindrical enclosure is studied. The finite propagation speed of heat transfer by conduction is accounted by modifying the Fourier’s law of heat conduction. The energy equation is formulated and solved using the lattice Boltzmann method. The finite volume method is used to compute the volumetric radiative information needed in the energy equation. Radial distributions of temporal temperature and the steady-state conductive, radiative and total energy flow rates are analyzed for a wide range of parameters, such as the extinction coefficient, the scattering albedo, the conduction–radiation parameter, the emissivity and the radius ratio. With volumetric radiative information computed using the finite volume method, in all cases, the steady-state temperature distributions from the lattice Boltzmann method are compared with those obtained by solving the energy equation using the finite difference method. An excellent comparison is obtained.

Combined mode conduction and radiation heat transfer in a spherical geometry with non-Fourier effect

This article deals with the analysis of combined mode non-Fourier conduction and radiation heat transfer in a concentric spherical enclosure containing a conducting–radiating medium. The finite volume method (FVM) has been employed to calculate the volumetric radiative information and also to solve the governing energy equation, which is of hyperbolic nature. The non-Fourier effect which manifests in the form of a sharp discontinuity in the temporal temperature distribution and propagates with a finite speed has been investigated. As time progress, the discontinuity in the temperature distribution decays and in the steady-state, results with and without non-Fourier effect are the same. Detailed study of the effect of various parameters such as the extinction coefficient, the scattering albedo, the conduction radiation parameter, the emissivity and the anisotropy factor has been carried out. Results of the present work have been compared with the steady-state response of the combined mode Fourier conduction–radiation problems available in literature. Results have been found to agree well.

Lattice Boltzmann Method and Modified Discrete Ordinate Method Applied to Radiative Transport in a Spherical Medium with and without Conduction

This article deals with the application of the modified discrete ordinate method (MDOM) to calculate volumetric radiative information with and without conduction in a concentric spherical enclosure containing a participating medium. With radiative information known from the MDOM, the energy equation of the combined mode transient conduction and radiation heat transfer is formulated and solved using the lattice Boltzmann method (LBM). Without conduction, for pure radiation case, two benchmark problems, representing nonradiative and radiative equilibrium situations are taken up. In the case of non-radiative equilibrium, an isothermal medium is bounded by cold walls and medium is the source of radiation, while in the case of radiative equilibrium, nonisothermal medium is confined between a hot and a cold wall, and the hot (inner sphere) wall is the radiation source. Depending upon the problem, heat flux, energy flow rate, emissive power, and temperature distributions in the medium are calculated for different values of parameters such as the extinction coefficient, the scattering albedo, the conduction-radiation parameter, the boundary emissivity, and the radius ratio. To validate the MDOM and the LBM-MDOM formulations, problems are also solved using the finite volume method (FVM) and the finite-difference method (FDM)–FVM approach, in which the FVM is used to calculate the volumetric radiation and the energy equation is also solved using the FDM. Results of the MDOM, LBM–MDOM, FVM and FDM–FVM are also benchmarked against those available in the literature. MDOM and LBM–MDOM have been found to provide accurate results.

Analysis of radiative transport in a cylindrical enclosure—An application of the modified discrete ordinate method

Application of the modified discrete ordinate method (MDOM) proposed by Mishra et al. [ Mishra SC, Roy HK, Misra N. Discrete ordinate method with a new and simple quadrature scheme. J Quant Spectrosc Radiat Transfer 2006;101:249–262.] has been extended for calculation of volumetric radiative information in a cylindrical enclosure. Radiatively, the medium inside a diffuse gray 1-D concentric cylinder is absorbing, emitting and scattering. Three types of problems, viz., an isothermal medium representing non-radiative equilibrium case, a non-isothermal medium representing radiative equilibrium situation and the case of a combined mode conduction and radiation heat transfer have been used to test the robustness of the MDOM. Temperature/emissive power and heat flux/energy flow rate distributions in the medium have been found for the effects of various parameters like the extinction coefficient, the scattering albedo, the boundary emissivity and the conduction–radiation parameter. To check the accuracy of the results of the MDOM, results have been compared with those available in the literature and also by obtaining the radiative information using the finite volume method. MDOM has been found to provide accurate results.