Radiative heat transfer by flowing multiphase medium-part I. An analysis on heat transfer of laminar flow between parallel flat plates

The multiphase flow of gaseous suspensions of fine particles furnishes high heat transfer characteristics at high and/or extremely high temperatures and at high heat fluxes due to the radiative transfer from heat source to suspensions. The phaseshift of particulate medium improves the overall heat transfer remarkably and from the practical viewpoint there exists important relevance pertinent to the industrial applications.

It is worth having a closer look at the behaviors of the suspensions and the heat transfer mechanism in flowing multiphase media so that the discussions are held concerning the foregoing media in some details.

An analysis is carried out on the laminar flow between parallel plates by taking into account of thermal radiation and the results illustrate the temperature profiles of fluid and dispersed phase, respectively, and the heat transfer characteristics for the wide ranges of dimensionless parameters such as conduction y, and radiation interaction parameter, loading ratio of particles, optical depth of duct, heat transfer between the two phases and so forth. Reference to the temperature profiles reveals the facts that while the temperature gradient in the vicinity of the heating surface increases due to the presence of particulate phase, the cupmixing mean temperature is raised appreciably by thermal radiation through the dispersed medium. In consequence, the contributions of suspensions on heat transfer are drastic, particularly in high temperature cases. Alternatively the correlations between the foregoing dimensionless parameters are also examined in current study.     

Performance optimization of a solar driven heat engine with finite-rate heat transfer

An optimal performance analysis for an equivalent Carnot-like cycle heat engine of a parabolic-trough direct-steam-generation solar driven Rankine cycle power plant at maximum power and maximum power density conditions is performed. Simultaneous radiation-convection and only radiation heat transfer mechanisms from solar concentrating collector, which is the high temperature thermal reservoir, are considered separately. Heat rejection to the low temperature thermal reservoir is assumed to be convection dominated. Irreversibilities are taken into account through the finite-rate heat transfer between the fixed temperature thermal reservoirs and the internally reversible heat engine. Comparisons proved that the performance of a solar driven Carnot-like heat engine at maximum power density conditions, which receives thermal energy by either radiation-convection or only radiation heat transfer mechanism and rejects its unavailable portion to surroundings by convective heat transfer through heat exchangers, has the characteristics of (1) a solar driven Carnot heat engine at maximum power conditions, having radiation heat transfer at high and convective heat transfer at low temperature heat exchangers respectively, as the allocation parameter takes small values, and of (2) a Carnot heat engine at maximum power density conditions, having convective heat transfer at both heat exchangers, as the allocation parameter takes large values. Comprehensive discussions on the effect of heat transfer mechanisms are provided.     

Numerical modeling of bed-to-wall heat transfer in a circulating fluidized bed combustor based on cluster energy balance

The bed-to-wall heat transfer in a circulating fluidized bed (CFB) combustor depends on the heat transfer contributions from particle clusters, dispersed/gas phase and radiation from both of them. From the available CFB literature, most of the theoretical investigations on cluster and bed-to-wall heat transfer are based on mechanistic models except a few based on mathematical and numerical approaches. In the current work a numerical model proposed to predict the bed-to-wall heat transfer based on thermal energy balance between the cluster/dispersed phase and the riser wall. The effect of cluster properties and the thermal boundary conditions on the cluster heat transfer coefficient are analyzed and discussed. The fully implicit finite volume method is used to solve the governing equations by generating a 2D temperature plot for the cluster and the dispersed phase control volumes. From this 2D temperature profile, space and time averaged heat transfer coefficients (for cluster, dispersed phase and radiation components) are estimated for different operating conditions. The results from the proposed numerical simulation are in general agreement with published experimental data for similar operating conditions. The results and the analysis from the current work give more information on the thermal behavior of the cluster and dispersed phases, which improves the understanding of particle and gas phase heat transfers under different operating conditions in CFB units.     

Analysis of heat transfer characteristics of double-layered microchannel heat sink

Numerical analysis is performed to examine the heat transfer characteristics of a double-layered microchannel heat sink. The three-dimensional governing equations are solved by the finite volume method. The effects of substrate materials, coolants, and geometric parameters such as channel number, channel width ratio, channel aspect ratio, substrate thickness, and pumping power on the temperature distribution, pressure drop, and thermal resistance are discussed. Predictions show that the heat transfer performance of the heat sink is improved for a system with substrate materials having a higher thermal conductivity ratio. A coolant with high thermal conductivity and low dynamic viscosity also enhances the heat transfer performance. The pressure drop decreases with the channel aspect ratio and channel width ratio. Further, the thermal resistance of the microchannel heat sink can be minimized by optimizing the geometric parameters. Finally, the results show that for the same geometric dimensions, the thermal performance of the double-layered microchannel heat sink is better than that of the single-layered one, by an average of 6.3%.     

Radiation heat transfer in planar SOFC electrolytes

Because of their high operating temperatures, there has been speculation that thermal radiation may play an important role in the overall heat transfer within the electrode and electrolyte layers of solid oxide fuel cells (SOFCs). This paper presents a detailed characterization of the thermophysical and radiative properties of the composite materials, which are then used to define a simple 2D model incorporating the heat transfer characteristics of the electrode and electrolyte layers of a typical planar SOFC. Subsequently, the importance of thermal radiation is assessed by comparing the temperature field obtained using a conduction model with those obtained using two coupled conduction/radiation models. Contrary to some published literature, these results show that radiation heat transfer has a negligible effect on the temperature field within these components, and does not need to be accommodated in comprehensive thermal models of planar SOFCs.     

Effects of combined heat transfer on the thermo-economic performance of irreversible solar-driven heat engines

A thermo-economic performance analysis and optimization has been carried out for an irrversible solar-driven heat engine with losses due to heat transfer across finite temperature differences, heat leak and internal irreversibilities. In the considered heat engine model, heat transfer from the hot reservoir is assumed to be simultaneous radiation and convection mode and the heat transfer to the cold reservoir is assumed to be convection mode. The effects of the technical and economical parameters on the thermo-economic performance have been investigated in order to see the collective effects of the radiation and convection modes of heat transfer. Also the optimal performance parameters of the heat engine, such as the thermal efficiency, temperatures of the working fluid and the ratio of heat transfer areas have been discussed in detail.     

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.     

Radiation heat transfer in enclosures with discrete heat sources

The potential for the enhancement of heat transfer by thermal radiation within enclosures containing modern electronic equipment is established on the basis of a diffuse-gray analysis of the thermal radiation heat transfer in a rectangular enclosure with discrete heat sources when the medium enclosed is radiatively nonparticipating. The geometry considered is representative of a unit cell of parallel-circuit board inside of modern electronic equipment. The results are presented for heat fluxes in the range of 0.01 to 25 W/cm², emissivity values of 0.1 to 1.0, the ratios of the distance between center line of the heaters to the spacing between heaters of 1 to 3, and enclosure height-to-width (H/W) ratios of 1 to 4. For the problem considered, the results indicate the following: (1) Surface temperature reduction of at least 50°C can be achieved when emissivities of the surfaces of the enclosure are increased from 0.25 to 1.0. (2) The influence of H/W is, however less significant. (3) The surface temperature of the constant-flux heat sources is essentially uniform. Also a simple dimensionless correlation between the average temperature of the heat sources to the heat flux supplied to them is presented for use by designers for estimation purposes.     

A study on entropy generation and heat transfer in a magnetohydrodynamic flow of a couple-stress fluid through a thermal nonequilibrium vertical porous channel

The effect of local thermal nonequilibrium (LTNE) on the entropy generation and heat transfer characteristics in the magnetohydrodynamic flow of a couple-stress fluid through a high-porosity vertical channel is studied numerically using the higher-order Galerkin technique. The Boussinesq approximation is assumed to be valid and the porous medium is considered to be isotropic and homogeneous. Two energy equations are considered one each for solid and fluid phases. The term involving the heat transfer coefficient in both equations renders them mutually coupled. Thermal radiation and an internal heat source are considered only in the fluid phase. The influence of inverse Darcy number, Hartmann number, couple-stress fluid parameter, Grashof number, thermal radiation parameter, and interphase heat transfer coefficient on velocity and temperature profiles is depicted graphically and discussed. The entropy generation, friction factor, and Nusselt number are determined, and outcomes are presented via plots. The effect of LTNE on the temperature profile is found to cease when the value of the interphase heat transfer coefficient is high, and in this case, we get the temperature profiles of fluid and solid phases are uniform. The physical significance of LTNE is discussed in detail for different parameters' values. It is found that heat transport and friction drag are maximum in the case of LTNE and minimum in the case of local thermal equilibrium. We observe that LTNE opposes the irreversibility of the system. The corresponding results of a fluid-saturated densely packed porous medium can be obtained as a limiting case of the current study.     

Forced convection heat transfer in microchannel heat sinks

This paper presents an analysis of forced convection heat transfer in microchannel heat sinks for electronic system cooling. In view of the small dimensions of the microstructures, the microchannel is modeled as a fluid-saturated porous medium. Numerical solutions are obtained based on the Forchheimer–Brinkman-extended Darcy equation for the fluid flow and the two-equation model for heat transfer between the solid and fluid phases. The velocity field in the microchannel is first solved by a finite-difference scheme, and then the energy equations governing the solid and fluid phases are solved simultaneously for the temperature distributions. Also, analytical expressions for the velocity and temperature profiles are presented for a simpler flow model, i.e., the Brinkman-extended Darcy model. This work attempts to perform a systematic study on the effects of major parameters on the flow and heat transfer characteristics of forced convection in the microchannel heat sink. The governing parameters of engineering importance include the channel aspect ratio (α_s), inertial force parameter (Γ), porosity (ε), and the effective thermal conductivity ratio (k_r). The velocity profiles of the fluid in the microchannel, the temperature distributions of the solid and fluid phases, and the overall Nusselt number are illustrated for various values of the problem parameters. It is found that the fluid inertia force alters noticeably the dimensionless velocity distribution and the fluid temperature distribution, while the solid temperature distribution is almost insensitive to the fluid inertia. Moreover, the overall Nusselt number increases with increasing the values of α_s and ε, while it decreases with increasing k_r.     

Simultaneous estimation of four parameters in a combined-mode heat transfer in a 2D porous matrix with heat generation

This article reports a study on simultaneous estimation of four parameters for combined-mode conduction and radiation heat transfer in a 2D rectangular porous matrix with a localized volumetric heat generation source. Air flows at uniform velocity through the conducting and radiating porous matrix. In the heat generation zone, and its downstream, the gas temperature is higher than that of the solid, and in the upstream the reverse situation occurs. This temperature difference between gas and the solid results in heat transfer by convection between the two phases, and the analysis thus requires consideration of separate energy equations for the two phases. The solid being involved radiatively, the volumetric radiative source term, in the form of the divergence of radiative heat flux, appears only in the solid-phase energy equation. The two equations are coupled through the convective heat transfer term. Four parameters—scattering albedo, emissivity, solid conductivity, and heat transfer coefficient—are simultaneously estimated based on the solid and gas temperature distributions, and convective and radiative heat fluxes at the outer surface of the porous matrix. In both direct and inverse approaches, the energy equations are solved using the finite volume method. For a test case, determining the genetic algorithm is much more time-consuming than the global search algorithm; in other cases, parameter estimations are done using the global search algorithm. Parameters are found to be estimated accurately.     

Transient natural convection and heat transfer during the storage of granular media

Transient heat transfer in an originally isothermal cylinder filled with a porous medium after sudden change of wall temperature is studied experimentally and computationally. Lab-scale experiments with water as the interstitial fluid are used in order to imitate the conditions prevailing in large, air-filled industrial silos. The proposed model assumes isotropy of the porous medium, local thermal equilibrium between the phases, Darcy flow and applicability of the Boussinesq approximation. Its predictions are in satisfactory agreement with the experimental results. Simulations reveal the role of dimensionless parameters like the modified porous media Rayleigh number and the cylinder aspect ratio. A criterion for neglecting the influence of natural convection on heat transfer is established.     

Transient heat transfer in a silica window with phase change

A new numerical phase change model is developed here using a fixed space implicit finite difference scheme. The object of this study is to develop short time solutions for the conduction, convection, radiation and apparent phase change during high heat rate processes occurring in ceramics. It is desired to gain an understanding of the effects of each mode of heat transfer. Comparisons are made for the medium with and without latent heat. Numerous high heat rate problems utilize glasses and ceramics because of their low thermal conduction and high melting temperatures. Several papers [1–3] have included latent heat effects for glasses and ceramics; this paper shows that such effects may be negligible depending on problem parameters.     

Heat transfer through woven textiles

A mathematical model based on the principles of heat transfer to predict the thermal resistance of fabrics has been presented in this paper. The woven fabric is considered as a system of porous yarns, interlacements between warp and weft yarns and air pores and all the basic weaves can be depicted by this system. The conduction and radiation heat transfer together, was calculated based on the construction parameters of the fabric. The thermal insulation, which is equivalent to the thermal resistance, was predicted with the help of these parameters. The total heat transfer by conduction through each part was calculated using Fourier’s equation. Radiation heat transfer through the air pore was calculated with the help of net radiation method. Linear anisotropic scattering was used to model the radiation heat transfer through fibrous media. The total thermal resistance obtained was validated with actual values obtained from a standard thermal resistance measuring instrument.     

Analysis of evaporating mist flow for enhanced convective heat transfer

Enhancement of forced convective heat transport through the use of evaporating mist flow is investigated analytically and by numerical simulation. A two-phase mist, consisting of finely dispersed water droplets in an airstream, is introduced at the inlet of a longitudinally-finned heat sink. The latent heat absorbed by the evaporating droplets significantly reduces the sensible heating of the air inside the heat sink which translates into higher heat-dissipation capacities. The flow and heat transfer characteristics of mist flows are studied through a detailed numerical analysis of the mass, momentum and energy transport equations for the mist droplets and the airstream, which are treated as two separate phases. The coupling between the two phases is modeled through interaction terms in the transport equations. The effects of inlet mist droplet size and concentration on the thermal performance of the heat sink are analyzed parametrically. The results provide insight into the complex transport processes associated with mist flows. The simulations indicate that significantly higher heat transfer coefficients are obtained with mist flows as compared to air flows, highlighting the potential for the use of mist flows for enhanced thermal management applications.     

Numerical simulation of steady state heat transfer in a ceramic-coated gas turbine blade

As gas turbine entry temperature (TET) increases, thermal loading on first stage blades increases and, therefore, a variety of cooling techniques and thermal barrier coatings (TBCs) are used. In the present work, steady state blade heat transfer mechanisms were studied via numerical simulations. Convection and radiation to the blade external surface were modeled for a super alloy blade with and without a TBC. The effects of surface emissivity changes, partial TBC coatings and uncertainties in external heat transfer coefficient were also simulated. The results show that at 1500 K TET, radiation heat transfer rate from gas to an uncoated blade is 8.4% of total heat transfer rate which decreases to 3.4% in the presence of a TBC. The TBC blocks radiation, suppresses metal temperatures and reduces heat loss to the coolant. These effects are more pronounced at higher TETs. With selective coating, substantial local temperature suppression occurs. In the presence of radiation and/or TBC, the uncertainties in convection heat transfer coefficient do not have a significant effect on metal temperatures.     

Experimental and Numerical Investigation of Enhancement of Heat and Mass Transfer in Adsorbent Beds

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Thermal performance analysis of a flat slab phase change thermal storage unit with liquid-based heat transfer fluid for cooling applications

This paper presents the results of a thermal performance analysis of a phase change thermal storage unit. The unit consists of several parallel flat slabs of phase change material (PCM) with a liquid heat transfer fluid (HTF) flowing along the passages between the slabs. A validated numerical model developed previously to solve the phase change problem in flat slabs was used. An insight is gained into the melting process by examining the temperatures of the HTF nodes, wall nodes and PCM nodes and the heat transfer rates at four phases during melting. The duration of the melting process is defined based on the level of melting completion. The effects of several parameters on the HTF outlet temperature, heat transfer rate and melting time are evaluated through a parametric study to evaluate the effects of the HTF mass flow rate, HTF inlet temperature, gap between slabs, slab dimensions, PCM initial temperature and thermal conductivity of the container on the thermal performance. The results are used to design a phase change thermal storage unit for a refrigerated truck.     

Mixed convection heat transfer in horizontal rectangular ducts with radiation effects

The study of mixed convection heat transfer in horizontal ducts with radiation effects has been numerically examined in detail. This work is primarily focused on the interaction of the thermal radiation with mixed convection for a gray fluid in rectangular horizontal ducts. The vorticity–velocity method is employed to solve the three-dimensional Navier–Stokes equations and energy equation simultaneously. The integro-differential radiative transfer equation was solved by the discrete ordinates method. The attention of the results is focused on the effects of thermal buoyancy and radiative transfer on the development of temperature, the friction factor and the Nusselt number. Results reveal that radiation effects have a considerable impact on the heat transfer and would reduce the thermal buoyancy effects. Besides, the development of temperature is accelerated by the radiation effects.     

Transient numerical analysis of a multi-layered porous heat exchanger including gas radiation effects

Thermal characteristics of a new type of multi-layered porous heat exchanger (PHE) are identified in the present study. This system works based on the energy conversion between gas enthalpy and thermal radiation. It has a five-layered structure consisting of two high temperature, two heat recovery and one low temperature sections. These sections are separated from each other by four quartz glass windows. In the two high temperature sections, the enthalpy of high temperature gas flow is converted to thermal radiation that is emitted toward the three adjacent layers where the low temperature air flows are effectively heated by the reverse conversion from thermal radiation into gas enthalpy. The gaseous radiation is also considered, such that in each section, a transient theoretical analysis is conducted for a one-dimensional system where convection, conduction and radiation take place simultaneously in both gas and solid phases. The coupled energy equations for the gas flows and porous layers based on the two-flux radiation model are solved numerically to identify the transient heat transfer characteristics of the system. It is shown that this type of porous heat exchanger has a very high efficiency especially when the porous layers have high optical thicknesses.