Conduction-radiation Interaction Research Articles

Heat transfer, efficiency and turn-down ratio of a dynamic radiative heat exchanger

Efficient heat transfer is critical in the design and optimization of thermal control systems. Static radiative heat exchangers are often simple and reliable systems but typically cannot be adapted to environmental changes. Adaptable radiative heat exchangers can be adjusted in response to variations in the thermal environment or operating conditions and have the potential for increased efficiency and reduced cost. Dynamic control of a radiative heat exchanger is possible through geometric manipulation of a segmented, self-irradiating fin, consisting of rigid panels that are linked by thermal hinges in an accordion arrangement. In this paper, a numerical model is described to predict the temperature profile and efficiency of a radiative heat exchanger, accounting for conduction and self-irradiation. Governing equations are cast in terms of the conduction-radiation interaction parameter, surface emissivity, actuation angle, and the thermal conductance of the hinges linking the panels. Results indicate that a turn-down ratio (largest possible heat rate divided by smallest possible heat rate) of greater than three is possible for realistic panel geometries and materials. Self-irradiation decreases the turn-down ratio, and there is evidence that an optimal number of rigid panels exists for any combination of panel geometry and device temperature. The maximum efficiency occurs when the plates are in the collapsed position, but the heat rate is at a minimum in this configuration. Finally, the properties and geometry of the plates are shown to have a more significant effect on the turn-down ratio than the properties of the thermal hinges.

Influences of radiative characteristics on free convection in a saturated porous cavity under thermal non-equilibrium condition

The present work numerically examines the effect of thermal radiation from the solid phase on the thermal and flow field inside a porous medium by investigating free convection within a saturated porous cavity. A local thermal non-equilibrium (LTNE) model is used to represent the energy transport for the solid and fluid phases. The heat flux caused by the thermal radiation is obtained by solving the radiation transfer equation (RTE), so the detailed influence of the radiative characteristics can be analyzed. All the dimensionless governing equations together with the corresponding boundary conditions are solved numerically by Chebyshev collocation spectral method. The results are reported in terms of streamlines, isotherms and average Nusselt numbers for different radiative characteristics such as the conduction-radiation interaction parameter (Pl), the optical thickness (τL), the scattering albedo (ω), and the emissivity of the walls (εW). It is found that the thermal radiation plays an important role on the fluid flow and heat transfer for the buoyancy dominated flow. Substantial changes occur in heat transfer and flow field when Pl, τL, ω and εW vary in the specified ranges. The overall heat transfer is increased with decreasing of Pl and τL, as well as the increasing of εW, however, they are not very sensitive to the change of ω.

Effects of thermal radiation on MHD flow and heat transfer in a cubic cavity

A numerical study of thermal radiation effects on MHD flow and heat transfer in the presence of an external magnetic field in a cubic differentially heated cavity is carried out. The improved projection scheme, which is based on the spectral methods, is used to deal with the coupling of the velocity and the pressure. The radiative transfer equation is angularly discretized by the discrete ordinates method with an SPAPN quadrature scheme, and all the governing equations are solved by the Chebyshev collocation spectral method using the same grid. The results are presented in graphical and tabulated form. The isothermal surfaces, the projection of streamlines and isotherms on the three different mid-plane of the cubic cavity, comparative results of heat transfer rate, and three-dimensional transverse flow show the effects of the Hartmann number, the optical thickness and the conduction–radiation interaction parameter on flow and heat transfer process.

Radiation-Conduction Interaction of Steady Streamwise Surface Temperature Variations on Vertical Free Convection

The combined effects of the steady free convective boundary-layer flow induced by a vertical heated surface in the presence of sinusoidal surface temperature variations about a constant mean value with the effect of radiation are examined. The problem is studied using fully numerical techniques. The surface rate of heat transfer eventually alternates in sign with distance from the leading edge, but no separation occurs unless the amplitude of the thermal modulation is sufficiently high. Numerical results are obtained for different values of the physical parameters, the radiation parameter Rd, the Prandtl number Pr, and the surface temperature wave amplitude a. It is found that both the local shear stress and the rate of heat transfer decrease when values of Rd increase.

The effect of conduction—radiation on the oscillating natural convection boundary layer flow of viscous incompressible fluid along a vertical plate

The natural convection boundary layer flow with conduction—radiation interaction of a viscous incompressible fluid along a vertical plate to surface temperature oscillations has been studied. Three distinct methods are used in the investigation, namely (a) the perturbation method for low frequency range and the asymptotic series expansion method for high frequency range, (b) the direct finite difference method for primitive variable formulations, and (c) the implicit finite difference method for stream-function formulation together with the Keller-box elimination technique for the entire frequency range. The effects of varying the Prandtl number Pr, the conduction—radiation parameter Rd, and the surface temperature parameter θw, are discussed in terms of amplitude and phase of the rate of heat transfer for fluid having the Prandtl number equal to 0.1. Also the effects of these parameters on the amplitude of oscillation of the transient skin-friction and transient heat transfer have been investigated.

Transient nonlinear optically-thick radiative–convective double-diffusive boundary layers in a Darcian porous medium adjacent to an impulsively started surface: Network simulation solutions

A boundary-layer model is described for the two-dimensional nonlinear transient thermal convection heat and mass transfer in an optically-thick fluid in a Darcian porous medium adjacent to an impulsively started vertical surface, in the presence of significant thermal radiation and buoyancy forces in an (X∗,Y∗,t∗) coordinate system. An algebraic approximation is employed to simplify the integro-differential equation of radiative transfer for unidirectional flux normal to the plate into the boundary-layer regime, by incorporating this flux term in the energy conservation equation. The conservation equations are non-dimensionalized into an (X,Y,T) coordinate system and solved using the Network Simulation Method (NSM), a robust numerical technique which demonstrates high efficiency and accuracy. The transient variation of non-dimensional streamwise velocity component (u) and temperature (T) and concentration (C) functions is computed for various selected values of Stark number (radiation–conduction interaction parameter) and Darcy number. Transient velocity (u) and steady-state local skin friction (τX) are also studied for various thermal Grashof number (Gr), species Grashof number (Gm), Schmidt number (Sc) and Stark number (N) values. These computations for the infinite permeability case (Da→∞) are compared with previous finite difference solutions [Prasad et al. Int J Therm Sci 2007;46(12):1251–8] and shown to be in excellent agreement. An increase in Darcy number is seen to accelerate the flow and boost velocity. A decrease in Stark number (corresponding to an increase in thermal radiation heat transfer contribution) is shown to increase the velocity values. Temperature function is observed to fall in value with a rise in Da and increase with decrease in N (corresponding to an increase in thermal radiation heat transfer contribution). Applications of the study include rocket combustion chambers, astrophysical flows, spacecraft thermal fluid dynamics in debris-laden environments (cosmic dust), heat transfer in forest fire spread, geochemical contamination and ceramic materials processing.

Conduction–radiation interaction in 3D irregular enclosures using the finite volume method

Interaction of conduction and radiation in 3D enclosures is carried out with a gray participating media. Application of block structured grid is shown with the finite volume method (FVM). Radiation modeling is performed with the FVM and is coupled with an ‘in-house’ code to solve the set of transport equations. The detailed numerical results are presented for a cubical and a cylindrical enclosure as these results are not available in the literature. The numerical simulation for the cylindrical enclosure is performed using a block-structured ‘O’ grid. Two additional geometries are considered in order to show the applicability of the present work. Results of temperature, radiative heat flux and total heat flux distributions are presented for different optical thicknesses, scattering albedoes, emissivities and conduction–radiation parameters. The 3D results are validated with the available 2D results or results with pure radiation problems as limiting cases.

An Estimate of the Temperature of Semitransparent Oxide Particles in Thermal Spraying

A considerable temperature difference in semitransparent oxide particles due to intensive heating in plasma spraying makes it difficult to interpret the optical measurements of their temperature. The problem of determining the bulk temperature of such particles from the experimental data on the color temperature is analyzed by using a recently proposed approximate model for the radiation transfer inside a nonisothermal refracting spherical particle. The same approximation is also employed for developing an improved model of particle heating, taking into account the radiation-conduction interaction inside the particle. Calculations for Al 2 O 3 and ZrO 2 particles in a typical plasma jet show that the color temperature of oxide particles may be less than or greater than their bulk temperature, depending on the spectral absorption coefficient of particle substance. This temperature difference during the melting of particles may reach the value of 200-300 K. A procedure for in situ evaluation of the absorption coefficient by comparison of color and brightness temperatures of molten particles is proposed.

A modified differential approximation for thermal radiation of semitransparent nonisothermal particles: application to optical diagnostics of plasma spraying

A modified differential approximation proposed recently by the author is formulated for nonisothermal particles. This approximation called MDP 0 (modified DP 0) is much simpler than the radiation transfer equation (RTE). Comparison with the RTE solution confirms an acceptable accuracy of MDP 0. An improved model of particle heating in plasma spraying is proposed. This model, which includes MDP 0 equations, takes into account the radiation–conduction interaction inside the particle. Calculations for metal oxide particles in a typical plasma jet show that the particle color temperature, which is usually determined in monitoring the plasma spraying, is very sensitive to the absorption index of the particle substance. This effect should be taken into account in experimental evaluations of the bulk temperature of particles.

Thermal radiation from nonisothermal spherical particles of a semitransparent material

The applicability of radiation transfer theory for calculations of the thermal radiation emitted by spherical particle of a semitransparent material, and in particular the determination of radial heat generation profiles, is analyzed. For homogeneous isothermal particles, a comparison with the exact solution based on the Mie theory shows that the radiation transfer calculations are sufficiently accurate for diffraction parameter of the particle of x ≥ 20. Numerical examples for large particles illustrate the transition from conditions of dominant radiation of the central region of the particle to conditions of the surface layer emission. A new differential approximation for radiation transfer in a refracting particle is proposed. This approximation called MDP 0 (modified DP 0) is much simpler than the radiation transfer equation. Using MDP 0, we have a chance to consider radiation–conduction interaction in nonisothermal particles without great computational efforts.

Radiation-conduction interaction on mixed convection from a horizontal circular cylinder

A mixed convection flow of an optically dense viscous incompressible fluid along a horizontal circular cylinder has been studied with the effect of radiation when the surface temperature is uniform. Using appropriate transformations, the boundary layer equations governing the flow are reduced to local nonsimilarity form. Solutions of the governing equations are obtained employing the implicit finite difference method. Effects of varying the pertinent parameters, such as, the Planck number, R w the surface temperature parameter, θw and the buoyancy parameter, α on the local skin-friction and local heat transfer coefficients are shown graphically as well as in tabular form against the curvature parameter ξ, while taking Prandtl number Pr = 1.0. It is found that an increase of R d,θw or α leads to increases in the values of the local skin-friction and the local rate of heat transfer coefficients. At the stagnation point asymptotic solutions for large value of α are also obtained and the effect of the other pertinent parameters on the formation of the flow separation are studied.

Thermal radiation effects on the natural convection flow over an isothermal horizontal plate

The natural convection boundary layer flow with conduction-radiation interaction of a viscous incompressible fluid along an isothermal horizontal surface has been studied. The equations valid in the upstream, downstream as well as in the entire regime are obtained. Solutions of the non-similar equations governing the flow for the entire regime and the downstream regime are obtained by employing an efficient implicit finite difference approximation together with the Keller box method, for a Prandtl number of 0.73. Also, the effects of the pertinent parameters, R d, the radiation-conduction parameter and θw, the surface heating parameter are shown graphically in terms of the local skin-friction and the local rate of heat transfer. Comparison of the results obtained for the upstream and the downstream regimes shows good agreement over the entire regime. Effects of R d and θw are also shown on the streamlines and the isotherms.

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%), MgF 2 (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.

Radiation-Conduction Interaction on Mixed Convection Flow Along a Slender Vertical Cylinder

Nomenclature = Rosseland mean absorption coefficient specific heat at constant pressure dimensionless stream function Grashof number acceleration because of gravity Nusselt number Prandtl number surface heat flux Planck number radial and axial coordinates temperature of the fluid temperature of the heated surface temperature of the ambient fluid velocities in the x and r directions coefficient of thermal diffusivity coefficient of cubical expansion scaled streamwise coordinate similarity variable scaled temperature surface temperature ratio to the ambient fluid coefficient of thermal conductivity curvature parameter v = kinematic viscosity £ = nondimensional axial coordinate p = density of the fluid cr = Stefan—Boltzmann constant crs = scattering coefficient

Radiation-conduction interaction in mixed convection along rotating bodies

This paper investigates the interaction of the steady mixed convection boundary layer flow past a rotating impermeable body placed in a uniform stream moving opposite to the gravitational force and parallel to the axes of the body of revolution with uniform surface temperature and thermal radiation. The fluid considered here is a gray, absorbing-emitting but non-scattering medium, and the Rosseland approximation is used to describe the radiative heat flux in the analysis. The difficulty of having a unified mathematical treatment of this problem is due to the nonsimilarity nature of the governing equations arising from the buoyant force-field and the transverse curvature of the bodies. The important parameters of this problem are the radiation-conduction parameter Rd and the wall to free stream temperature ratio θw, for the case of a heated surface. Numerical simulations of the boundary layer equations are performed using the local nonsimilarity method as well as an implicit finite-difference method. The theory is applied to a rotating sphere for the gases with Prandtl number of 0.7. The results are shown graphically in terms of the local skin-friction coefficients and the local rate of heat transfer. Effects of the pertinent parameters Rd and θw are also shown on the components of the velocity distribution as well as on the temperature distribution in the boundary layer.

Radiation-conduction interaction: an investigation on silica aerogels

Thermal transport in low density silica aerogels was studied theoretically and experimentally over a wide range of optical thickness and ratio of radiative to conductive heat transfer. Measurements on the combined heat transfer were performed for aerogel densities between 5 and 220 kg m −3, for temperatures from 100 to 650 K, for internal gas pressures between 10 −4 and 1000 hPa and two boundary emissivities of 0.04 and 0.77. A high precision numerical method for the calculation of the temperature profile and the total (combined) heat flux in these semi-transparent, non-scattering, non-grey media is presented.

Conduction-radiation interaction in absorbing, emitting, and anisotropically scattering media with variable thermal conductivity

The problem of simultaneous conduction and radiation heat transfer through absorbing, emitting, and anisotropically scattering media with temperature-dependent thermal conductivity is numerically investigated. The temperature dependence of thermal conductivity is found to have significant effects on heat flux and temperature distribution. Positive gamma increases the temperature, while negative gamma decreases it. The effects of variable conductivity is more significant as omega is increased. The differential-discrete-ordinate method is found to be an accurate and powerful method for dealing with the radiative transfer problem. 5 refs.

Asymptotic Analysis of a Uniform Area Radiating Fin

The present study considers in detail the problem of a uniform area radiating fin for large values of the radiation conduction interaction parameter N. A method is developed for improving the previously known asymptotic solution to make it applicable for relatively smaller values of N. While the method yields the exact solution in the case of linearized radiation, it leads to a close form solution, valid for all N, in the case of a fin radiating to a sink at zero temperature. The general case of a fin radiating to a sink at a non-zero temperature needs a numerical solution of equations that do not involve N. The results show an excellent agreement between the present calculations and the exact solutions available in the literature.

ANALYSIS OF HEAT TRANSFER PROBLEMS WITH COMPUTER-EXTENDED PERTURBATION SERIES

The method of computer extension of perturbation series and its subsequent improvement are applied to four problems in nonlinear heat conduction. The nonlinearities involve temperature-dependent thermal properties, temperature-dependent heat generation, and simultaneous conduction-radiation interaction. The series are improved by techniques such as the extraction of singularity. Fade approximants, and Euler and Shanks transformations. The improvement achieved highlights the usefulness of the approach.

Analysis Of Heat Transfer Problems With Computer-Extended Perturbation Series

The method of computer extension of perturbation series and its subsequent improvement are applied to four problems in nonlinear heat conduction. The nonlinearities involve temperature-dependent thermal properties, temperature-dependent heat generation, and simultaneous conduction-radiation interaction. The series are improved by techniques such as the extraction of singularity. Fade approximants, and Euler and Shanks transformations. The improvement achieved highlights the usefulness of the approach.