A nongray analysis of radiating–convecting rectangular plate-fin arrays

A complete analysis of heat transfer in rectangular fin arrays has been conducted taking into consideration convection and radiation at all surfaces, as well as radiative exchange between the fins and all neighboring surfaces. The analysis assumes diffuse nongray surfaces and uses the spectral optical properties of stainless steel AISI 430. Three different gray models were proposed in order to assess the effect of the gray assumption on the heat-transfer characteristics. Results are presented for the temperature and radiative-flux distributions along the fin, the radiative flux along the base, the contribution of the radiative component to the overall heat transfer, and the effectiveness of the fin array. Significant deviations in some of these results were found between the nongray model and the gray models. In general, convection was found to be the more effective mode of heat transfer in fin arrays and the effectiveness of the array decreases as the contribution of the radiative component increases.     

Transformational-zone method of calculation of complex heat exchange during flow of optically active medium inside tube of diffuse grey surface

The paper presents analytical and experimental investigations of influence of radiative heat transfer on complex heat exchange during flow of optically active gas inside a pipe of diffusegrey properties. It was assumed that the pipe is heated from the outside by a constant heat flux and gas flowing inside is both absorbing and emitting and of small optical density. The influence of length and radiative properties of the pipe surface and of the gas temperature distribution on the wall and in the gas were analysed. The influence of radiative energy transfer on overall heat transfer coefficient was estimated. Mathematical model of radiative convective heat exchange in a system of one-dimensional temperature field, based on zone division method of Hottel and surface transformation, was verified numerically and experimentally. The results of numerical calculations were compared with experimental results obtained during carbone dioxide (CO₂) flow inside electrically heated ceramic tube. The set of nonlinear differential equations was solved by Runge-Kutta method with Hamming modification and with the use of separable-kernel method.     

Analysis of laminar flow forced convection heat transfer in the entrance region of a circular pipe

A numerical solution, for incompressible, steady-state, laminar flow heat transfer in the combined entrance region of a circular tube is presented for the case of constant wall heat flux and constant wall temperature. The development of velocity profile is obtained from Sparrow's entrance region solution. This velocity distribution is used in solving the energy equation numerically to obtain temperature profiles. Variation of the heat transfer coefficient for these two different boundary conditions for the early stages of boundary layer formation on the pipe wall is obtained. Local Nusselt numbers are calculated and the results are compared with those given byUlrichson andSchmitz. The effect of the thermal boundary conditions is studied by comparing the uniform wall heat flux results with uniform wall temperature.     

Numerical analysis of transient laminar forced convection of nanofluids in circular ducts

In this study, forced convection heat transfer characteristics of nanofluids are investigated by numerical analysis of incompressible transient laminar flow in a circular duct under step change in wall temperature and wall heat flux. The thermal responses of the system are obtained by solving energy equation under both transient and steady-state conditions for hydro-dynamically fully-developed flow. In the analyses, temperature dependent thermo-physical properties are also considered. In the numerical analysis, Al₂O₃/water nanofluid is assumed as a homogenous single-phase fluid. For the effective thermal conductivity of nanofluids, Hamilton–Crosser model is used together with a model for Brownian motion in the analysis which takes the effects of temperature and the particle diameter into account. Temperature distributions across the tube for a step jump of wall temperature and also wall heat flux are obtained for various times during the transient calculations at a given location for a constant value of Peclet number and a particle diameter. Variations of thermal conductivity in turn, heat transfer enhancement is obtained at various times as a function of nanoparticle volume fractions, at a given nanoparticle diameter and Peclet number. The results are given under transient and steady-state conditions; steady-state conditions are obtained at larger times and enhancements are found by comparison to the base fluid heat transfer coefficient under the same conditions.     

Numerical analysis of interaction between non-gray radiation and forced convection flow over a recess using the full-spectrum k-distribution method

In the present work, the interaction between non-gray radiation and forced convection in a laminar radiating gas flow over a recess including two backward and forward facing steps in a duct is investigated numerically. Distributions of absorption coefficients across the spectrum (50 cm^?1 < η < 20,000 cm^?1) are obtained from the HITRAN2008 database. The full-spectrum k-distribution method is used to account for non-gray radiation properties, while the gray radiation calculations are carried out using the Planck mean absorption coefficient. To find the divergence of radiative heat flux distribution, the radiative transfer equation is solved by the discrete ordinates method. The effects of radiation–conduction parameter, wall emissivity, scattering coefficient and recess length on heat transfer behaviors of the convection–radiation system are investigated for both gray and non-gray mediums. In addition, the results of gray medium are compared with non-gray results in order to judge if the differences between these two approaches are significant enough to justify the usage of non-gray models. Results show that for air mixture with 10 % CO₂ and 20 % H₂O, use of gray model for the radiative properties may cause significant errors and should be avoided.     

Combined radiative and convective heat transfer in a three-dimensional rectangular channel at different wall temperatures

 This paper deals with a numerical study of combined convective and radiative heat transfer in a three-dimensional rectangular duct with hydrodynamically and thermally developing laminar flow. The gas is assumed to be an incompressible, absorbing, emitting, isotropically scattering, gray medium. Isothermal, gray, diffuse boundary walls at different temperatures are assumed. The finite-volume method (FVM) is adopted to describe both convective and radiative heat transfer. The coupled continuity and momentum equations are solved by means of SIMPLER algorithm. Numerical results for the radiative flux show very good agreement with the available data. The effects of aspect ratio, optical thickness, scattering albedo and wall emissivity on the mean bulk temperature are also investigated. By splitting the heat flux into convective and radiative contributions, the relative importance of these components is assessed for a typical range of values of the parameters. Received on 9 February 1999     

Conjugate heat transfer with radiation from a vertical circular pin in a non-newtonian ambient medium

An analysis is presented for the heat transfer characteristics of a steady, laminar, mixed convective flow of power-law type non-Newtonian fluid over a circular pin by the conjugate convection-conduction theory including radiative effects under optically thick limit approximation. Numerical results are presented for the dimensionless heat transfer coefficients, local and overall heat fluxes and temperature distribution of the pin by a simultaneous solution of the convective boundary layer equations of the fluid and the energy equation of the pin.     

The critical radius of insulation in thermal radiation environment

Critical radius of insulation for a circular tube subjected to radiative and convective heat transfer has been studied analytically. It is assumed that condensation or evaporation takes place inside the circular tube such that the bulk fluid temperature inside the tube remains constant. As the fluid is transported from one end to the other, either an increase or decrease of heat transfer is desired depending on the application. The variation of the rate of heat transfer with respect to the variation of insulation thickness is studied. It is found that an critical insulation thickness may exist such that the heat transfer between the fluid and the radiative environment becomes a maximum. For certain special cases, explicit solutions to the critical insulation thickness are obtained.     

Radiative heat transfer calculations in real gases

A general formulation for radiative heat transfer calculations is presented, based on integrated quantities such as total emissivities and absorptivities. The procedure is intended particularly for combustion chamber applications of varying degree of complexity, the radiative active medium consisting of gases such as H₂O and CO₂ and of soot. First, some preliminary calculations are given for the often treated radiative equilibrium cases of plane parallel plates and infinite concentric cylinders. Then an example of a combustion chamber calculation is studied where the radiative heat transfer calculation is included in a system of partial differential equations describing momentum, heat and mass transfer with combustion.     

Heat transfer to flowing polymer melts

A theoretical and experimental study of heat transfer to polymer melts flowing through ducts is presented. The mathematical model provides for shear heating and expansion cooling effects for various wall boundary conditions.Experimental results, obtained in tube flow, show reproducible temperature and velocity profiles and the data confirm the predictions of the magnitude of the shear heating and expansion cooling effects.It is concluded that the method can be justified for predicting heat transfer in more complex geometries and some preliminary results are presented.     

Magnetic Heat Transfer Enhancements on Fin-Tube Heat Exchangers

通过DNS方法解耦合的三维非稳态流动和固流体能量方程组,本文研究了两平行磁质平板和圆管所组成的肋片式圆管换热器单元与震荡流体间的传热过程.对不同的磁场频率和振幅的三维动态流热场的模拟结果表明增强磁场频率和振幅能很有效地增加周期平均传热强度达到强化传热的目的.     

Numerical investigation of premixed combustion in a porous burner with integrated heat exchanger

In this paper, we perform a numerical analysis of a two-dimensional axisymmetric problem arising in premixed combustion in a porous burner with integrated heat exchanger. The physical domain consists of two zones, porous and heat exchanger zones. Two dimensional Navier–Stokes equations, gas and solid energy equations, and chemical species transport equations are solved and heat release is described by a multistep kinetics mechanism. The solid matrix is modeled as a gray medium, and the finite volume method is used to solve the radiative transfer equation to calculate the local radiation source/sink in the solid phase energy equation. Special attention is given to model heat transfer between the hot gas and the heat exchanger tube. Thus, the corresponding terms are added to the energy equations of the flow and the solid matrix. Gas and solid temperature profiles and species mole fractions on the burner centerline, predicted 2D temperature fields, species concentrations and streamlines are presented. Calculated results for temperature profiles are compared to experimental data. It is shown that there is good agreement between the numerical solutions and the experimental data and it is concluded that the developed numerical program is an excellent tool to investigate combustion in porous burner.     

Laminar convective heat transfer of non-Newtonian nanofluids with constant wall temperature

Nanofluids are obtained by dispersing homogeneously nanoparticles into a base fluid. Nanofluids often exhibit higher heat transfer rate in comparison with the base fluid. In the present study, forced convection heat transfer under laminar flow conditions was investigated experimentally for three types of non-Newtonian nanofluids in a circular tube with constant wall temperature. CMC solution was used as the base fluid and γ-Al₂O₃, TiO₂ and CuO nanoparticles were homogeneously dispersed to create nanodispersions of different concentrations. Nanofluids as well as the base fluid show shear thinning (pseudoplastic) rheological behavior. Results show that the presence of nanoparticles increases the convective heat transfer of the nanodispersions in comparison with the base fluid. The convective heat transfer enhancement is more significant when both the Peclet number and the nanoparticle concentration are increased. The increase in convective heat transfer is higher than the increase caused by the augmentation of the effective thermal conductivity.     

The stokes flow from half-space into semi-infinite circular cylinder

The infinite-series solutions for the creeping motion of a viscous incompressible fluid from half-space into semi-infinite circular cylinder are presented. The results show that inside the cylinder beyond a distance equal to 0.5 times the radius of the tube from the pore opening, the deviation of the velocity profile from Poiseuille flow is less than 1%. The inlet length in this case is comparable to that computed for a finite circular cylinder pore by Dagan et al.^[1]. In the half-space outside the cylinder pore region, the flow is strongly affected by the wall. Beyond one radius of the tube from the orifice, the solutions match almost exactly the flow through an orifice of zero thickness given by Sampson^[2]. The relationship between the pressure drop and the volumetric flow rate is also computed in the present paper for the semi-infinite tube.     

Radiative heat transfer augmentation of natural gas flames in radiant tube burners with porous ceramic inserts

Experiments were conducted using porous ceramic inserts to enhance the radiative heat transfer from natural gas flames in a straight-through radiant tube burner. The performance of the radiant tube burner with partially stabilized zirconia and silicon carbide inserts is compared to a baseline case of no inserts at three levels of combustion air preheat. Spectral intensities, temperatures within the radiant tube burner, tube wall temperatures, and exhaust temperatures were measured to determine the effectiveness of the enhanced heat transfer due to the inserts. Exhaust emission constituents were also measured to determine the effect that the inserts have on exhaust products. NO_x emissions are reduced by up to 30% with the inserts. The silicon carbide inserts have higher spectral intensities and total radiative energy transfer than partially stabilized zirconia inserts. Both inserts have enhanced radiant heat transfer compared to the no-insert configuration, with the radiative enhancement due to inserts as great as five times that of the no-insert configuration. The net result is increased tube wall temperatures and decreased exhaust temperatures with the ceramic inserts.     

Einfluß der thermischen Randbedingung auf den laminaren Wärmeübergang im Kreisrohr bei hydrodynamischer Einlaufströmung

Heat transfer characteristics of hydrodynamically developing laminar flow in a circular duct with different thermal boundary conditions were calculated by solving the equations of continuity, motion and energy in finite difference form. Results are presented for linear, sinusoidal and exponential variations of the prescribed wall heat flux along the duct length. A comparison shows that the influence of the thermal boundary condition on heat transfer increases with increasing development of velocity and temperature profiles. As a side result an improved correlation for heat transfer with constant wall heat flux in hydrodynamically developing flow is presented.     

爆震室壁面条件对脉冲爆震发动机爆震性能的影响

在爆震室内快速形成稳定传播的爆轰波是脉冲爆震发动机的关键．本文利用有限速率化学反应模型,考虑粘性、热对流,基于N-S方程对氢气与空气/氧气为反应混合物的爆震发动机爆震室内流场进行计算．从流场压力、速度、涡量、湍流动能等方面研究爆震室壁面条件对燃烧爆轰性能的影响,分析流场爆轰波压力与流场湍动能的关系,讨论可燃气体燃烧转爆轰的机理．结果表明：爆震室内燃烧爆轰机理受到化学反应能量释放、壁面摩擦效应、壁面与外界热交换的影响．在文中讨论的范围内,相比于半圆形和三角形的爆震室装置,矩形的爆震室增强装置能在更短的时间内得到较高的爆轰波压力和湍动能峰值．壁面粗糙层高度（粗糙度）影响爆震室的燃烧爆轰性质．当壁面粗糙度为0.15mm时,粗糙度对爆轰的激励作用大于抑制作用,能较快形成稳定的爆轰波,且推力为35.5N;随着壁面对流换热系数的增大,爆震室壁面的散热加剧．当壁面对流换热系数大于临界值2.6W/(m2·K)时,爆震室内不能形成稳定的爆震波．     

The radiative Knudsen layer

The analogy between the kinetic theory of gases and photon gas dynamics (see [1], for instance) means that many qualitative results obtained in kinetic theory can be extended to photon gas dynamics. This includes the behavior of a radiating optically thick gas near solid surfaces. It is known that in an optically thick gas the radiative heat conduction approximation is inapplicable at distances of the order of the mean free path of the radiation from the surface of a body [1, 2]. The behavior of a photon gas near a surface can be predicted on the basis of the complete radiative transfer equation. In the present paper the problem of such wall layers in an optically thick gas (which have much in common with the well-known Knudsen layers) is solved in the approximation of a gray gas in local thermodynamic equilibrium. For simplicity only the steady-state case is considered. Expressions for the temperature jumps at the surface in a wide range of gas temperatures are obtained.Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 4, pp. 113–121, July–August, 1973.In conclusion the author thanks M. N. Kogan for the topic and guidance during the conduction of this work.     

Combined radiation and natural convection in a rectangular cavity with a transparent wall and containing a non-participating fluid

This paper describes a numerical method for the study of combined natural convection and radiation in a rectangular, two-dimensional cavity containing a non-participating (i.e. transparent) fluid. One wall of the cavity is isothermal, being heated either by solar radiation or independently. The opposite wall is partially transparent, permitting radiation exchanges between the cavity and its surroundings and/or the Sun; that wall also exchanges heat by convection from its external surface to the surroundings. The other two walls are adiabatic: convection and radiation there are balanced, so that there is no heat transfer through those walls. The equations of motion and energy are solved by finite difference methods. Coupled to these equations are the radiative flux boundary conditions which are used to determine the temperature distribution along the non-isothermal walls. A two-band radiation model has been employed. Results are presented for a square cavity with a vertical hot wall at 150 °C, the ambient at 20 °C and 10⁴ ? Ra ? 3 × 10⁵, in the absence of direct insolation. The effects on the flow and heat transfer in the cavity of radiation and external convection have been examined. More extensive results will be presented in subsequent papers.     

Heat transfer and two-phase flow characteristics of refrigerants flowing under varied heat flux in a double-pipe evaporator

A mathematical model based on the annular flow pattern is developed to simulate the evaporation of refrigerants flowing under varied heat flux in a double tube evaporator. The finite difference form of governing equations of this present model is derived from the conservation of mass, energy and momentum. The experimental set-up is designed and constructed to provide the experimental data for verifying the simulation results. The test section is a 2.5 m long counterflow double tube heat exchanger with a refrigerant flowing in the inner tube and heating water flowing in the annulus. The inner tube is made from smooth horizontal copper tubing of 9.53 mm outer diameter and 7.1 mm inner diameter. The agreement of the model with the experimental data is satisfactory. The present model can be used to investigate the axial distributions of the temperature, heat transfer coefficient and pressure drop of various refrigerants. Moreover, the evaporation rate or the other relevant parameters that is difficult to measure in the experiment are predicted and presented here. The results from the present mathematical model show that the saturation pressure and temperature of refrigerant decrease along the tube due to the tube wall friction and the flow acceleration of refrigerant. The liquid heat transfer coefficient increases with the axial length due to reducing the thickness of the liquid refrigerant film. Due to increase of the liquid heat transfer coefficient, increasing wall heat flux is obtained.Finally, the evaporation rate of refrigerant increases with increasing wall heat flux.