Two‐flux method for transient thermal analysis in a layer of polymer fiber

Transient radiative and conductive heat transfer in a translucent medium with isotropic optical properties is investigated. The radiative two‐flux equation is coupled with the transient energy equation and both equations are solved simultaneously. Transient solutions are obtained for a plane layer with refractive index equal to or larger than one, and with external convection and radiation at each boundary. Illustrative results obtained with the two‐flux method show the effects of changing parameters such as optical thicknesses, refractive index, conduction–radiation parameter, and scattering on the transient temperature distribution within the layer. Results are given at different instances during the transient, and the distribution for the largest time is at or very close to steady state. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 2277–2283, 2006     

Transient combined radiative and conductive heat transfer in plastics

By the addition of metal and oxide particles to plastics, thermal transport properties, heat capacity, and density of polymers can be varied systematically. Radiation effects in a particle filled with various fillers become more important and transient temperature responses including radiation can be significantly different from those by conduction alone. Transient combined conduction–radiation heat transfer is analyzed in a non‐gray layer of plastics, submitted to several thermal and radiative boundary conditions. The numerical method is an implicit finite difference procedure with nonuniform space and time increments. Coupling problems for the prescribed temperatures, prescribed radiative–conductive heat exchange laws, and mixed kind thermal boundary conditions are worked out for opaque as well as vitreous interfaces with specular reflections. Solutions are given to demonstrate the effect of different parameters, such as radiation–conduction parameter, radiation–convection parameter, and emissivity of the surfaces on temperature distribution and heat flux profiles across the layer. J. VINYL. ADDIT. TECHNOL., 11:28–37, 2005. © 2005 Society of Plastics Engineers     

THERMAL CONVECTIVE INSTABILITY IN TRANSLUCENT POROUS MEDIA WITH RADIATIVE HEAT TRANSFER

The onset of thermal convection in a translucent porous layer is considered. Attention is focused on the effect of radiative heat transfer on the critical Rayleigh-Darcy number and the convection cell shape. If we consider the contribution of radiative heat transfer, the basic temperature profile is non-linear and the thermal convective instability is influenced by the ratio of conduction to radiation heat flux, the temperatures at the boundary surfaces, and radiative parameters such as wall emissivity, scattering albedo and extinction coefficient as well as the usual Rayleigh-Darcy number. Effects of these parameters on the onset of convective instability are investigated with the help of linear stability theory employing the Darcy's law and the radiative transport equation simplified by the P₁ approximation. The increased effective thermal conductivity due lo the radiation inhibits the onset of convection and causes increased critical Rayleigh-Darcy number and decreased convection cell size. The results of the present work may be exploited to find out the optimal diameter of aerogel pellets and the air pressure in the double pane window filled with the translucent silica aerogel granules to suppress natural convection.     

Transient Coupled Radiation and Conduction Heat Transfer in a Scattering Layer of ARLEN

ARLEN is a heat-resistant, modified polyamide with a high melting point and a rigidity level comparable to super engineering plastics. It possesses strong dimensional stability and is widely used in engineering and high-temperature applications. At elevated temperatures, radiative transfer becomes important, and transient temperature responses, including radiation, can be significantly different from those by conduction alone. This work considers transient radiative and conductive heat transfer in a plane, absorbing, emitting and isotropically scattering layer of ARLEN. The solution includes the radiative two-flux equation, which is coupled with the transient energy equation, and both equations are solved simultaneously. The two-flux method is used as a simplification for obtaining the radiative heat source term in the energy equation. The external boundaries of the layer are exposed to a radiative environment and can be convectively heated or cooled.     

TRANSIENT MIXED CONVECTION ALONG A VERTICAL PLATE EMBEDDED IN POROUS MEDIA WITH INTERNAL HEAT GENERATION AND OSCILLATING TEMPERATURE

The effects of oscillating plate temperature on transient mixed convection heat transfer from a porous vertical surface embedded in a saturated porous medium with internal heat generation or absorption are studied. The governing equations are transformed into dimenionless form by a set of variables and solved using the Galerkine finite element method. As the energy generation increases, the temperature near the wall will be higher than the wall temperature, thus increasing buoyancy forces inside the boundary layer and consequently increasing the velocity. The increase of energy absorption term for either space or temperature dependence will decrease the velocity inside the boundary layer and increase heat transfer rates. Different temperature and velocity profiles are drawn for different dimensionless groups. Numerical values for Nusselt numbers as well as local skin friction coefficient are also tabulated.     

TRANSIENT MIXED CONVECTION ALONG A VERTICAL PLATE EMBEDDED IN POROUS MEDIA WITH INTERNAL HEAT GENERATION AND OSCILLATING TEMPERATURE

The effects of oscillating plate temperature on transient mixed convection heat transfer from a porous vertical surface embedded in a saturated porous medium with internal heat generation or absorption are studied. The governing equations are transformed into dimenionless form by a set of variables and solved using the Galerkine finite element method. As the energy generation increases, the temperature near the wall will be higher than the wall temperature, thus increasing buoyancy forces inside the boundary layer and consequently increasing the velocity. The increase of energy absorption term for either space or temperature dependence will decrease the velocity inside the boundary layer and increase heat transfer rates. Different temperature and velocity profiles are drawn for different dimensionless groups. Numerical values for Nusselt numbers as well as local skin friction coefficient are also tabulated.     

微细铜丝在水中自然对流换热

采用实验与数值模拟相结合的方法分别研究了封闭空间内水平放置的直径为39.9、65.8、119.1 μm的微细铜丝（微丝）在水中的对流换热,分析了微丝表面自然对流换热特性及机理。实验通过焦耳加热的方法测量了不同直径微丝在水中自然对流的传热系数及Nusselt数。同时建立三维不可压数学模型对微丝在水中的自然对流进行数值模拟,并将计算结果与实验值进行了对比。研究表明,数值模拟结果与实验值基本吻合,微丝在水中自然对流的传热系数随直径减小而显著增大,Nu则明显减小,且Nu随热通量增加的变化率也随直径减小而明显降低;微丝表面边界层厚度随直径减小而变薄,但边界层厚度与微丝直径的比值则逐渐增大;另外,对比微丝与常规尺度圆管表面自然对流的流场、温度场以及边界层分布,发现相同温差下微丝表面自然对流换热的边界层与常规尺度下沿壁面由底部向上发展的形状不同,而是沿微细丝表面呈椭圆形包裹于其上,因此削弱了表面对流换热强度,导致温度场呈现出较明显的导热特征。     

A Composite Heat Transfer Model For Pool Boiling on a Horizontal Tube at Moderate Pressure

The present work is aimed at building a comprehensive heat transfer model for pool boiling on horizontal tubes combining sliding bubble mechanism with natural convection, microlayer evaporation and transient conduction during boundary layer reformation, to predict the boiling heat flux for a given wall superheat. The model has been compared to experimental results from literature for R134a and also to independent experiments conducted by the authors for water. Even with a number of simplified assumptions a reasonably good agreement has been observed between model and experiments in the low and medium heat flux region and moderate pressure.     

ANALYSIS OF SIMULTANEOUS RADIATIVE AND CONDUCTIVE HEAT TRANSFER IN FLUIDIZED BEDS

In the bubbling regime of operation for fluidized beds, the major mechanism for heat transfer is transient conduction to periodic packets of densely packed particles at the heat transfer surface. The well known Mickley and Fairbanks model, with various subsequently proposed modifications, adequately describes this transient conduction mechanism. However, no adequate theory exists for heat transfer in high-temperature fluidized beds where radiative contribution becomes significant.

Analysis of the radiative contribution is complicated by the nonlinear interaction of radiation with conduction/convection. This paper describes a differential formulation of the combined radiative/ conductive heat transfer process. The discrete flux method used by Churchill et al. for radiative transport in heterogeneous media is applied here to the problem of transient heat transfer to packets in fluidized beds. Packets are modeled as radiatively participating media with absorption, scattering, and emission of radiation. Simultaneous solution of the governing differential equations for temperature and forward and backward radiation fluxes permits calculation of instantaneous heat flux at the heat-transfer surface. Radiative transfer during bubble contact is added as a time-weighted contribution.

Using experimental data on radiative cross sections (from packed media experiments) and experimental data on packet residence times (from fluidized bed experiments), the combined conductive/radiative heat transfer to packets was obtained for examples of fluidized beds at different fluidizing velocities and wall temperatures. The analytical results indicate that the relative importance of radiation is affected by particle size, average packet residence time, and the radiative attenuation cross sections. For operating conditions representative of fluidized bed combustion, the model estimates a 10 to 20 percent contribution by radiation to the total heat transfer. Comparison to limited experimental data from the literature shows reasonable agreement.     

ANALYSIS OF SIMULTANEOUS RADIATIVE AND CONDUCTIVE HEAT TRANSFER IN FLUIDIZED BEDS

In the bubbling regime of operation for fluidized beds, the major mechanism for heat transfer is transient conduction to periodic packets of densely packed particles at the heat transfer surface. The well known Mickley and Fairbanks model, with various subsequently proposed modifications, adequately describes this transient conduction mechanism. However, no adequate theory exists for heat transfer in high-temperature fluidized beds where radiative contribution becomes significant.

Analysis of the radiative contribution is complicated by the nonlinear interaction of radiation with conduction/convection. This paper describes a differential formulation of the combined radiative/ conductive heat transfer process. The discrete flux method used by Churchill et al. for radiative transport in heterogeneous media is applied here to the problem of transient heat transfer to packets in fluidized beds. Packets are modeled as radiatively participating media with absorption, scattering, and emission of radiation. Simultaneous solution of the governing differential equations for temperature and forward and backward radiation fluxes permits calculation of instantaneous heat flux at the heat-transfer surface. Radiative transfer during bubble contact is added as a time-weighted contribution.

Using experimental data on radiative cross sections (from packed media experiments) and experimental data on packet residence times (from fluidized bed experiments), the combined conductive/radiative heat transfer to packets was obtained for examples of fluidized beds at different fluidizing velocities and wall temperatures. The analytical results indicate that the relative importance of radiation is affected by particle size, average packet residence time, and the radiative attenuation cross sections. For operating conditions representative of fluidized bed combustion, the model estimates a 10 to 20 percent contribution by radiation to the total heat transfer. Comparison to limited experimental data from the literature shows reasonable agreement.     

A Theoretical Model for the Nongray Radiation Drying of Polyvinylalcohol/Water Solutions

A theoretical analysis of heat transfer and moisture variation was performed while a PVA solution was exposed to high-intensity nongray irradiation and/or air flow convection. Effective absorption coefficients were incorporated in the radiative transfer analysis. The influence of various radiation and convection parameters on the transfer of heat and moisture variation in the coated layers on an optically thick substrate was investigated. The effects of radiation and convection parameters on the transfer process were presented in terms of the rate of water content removal, heat transfer, and moisture distribution. Results were compared to those of drying when using convective heat. It is evident that the use of thermal radiation combined with convective heat will help in improving the drying rate. Numerical results show that both the radiative energy absorbed by the solution and the substrate and the distribution of water mass fraction in the solution are closely related to the rate of water removal from the solution during the process.     

A Theoretical Model for the Nongray Radiation Drying of Polyvinylalcohol/Water Solutions

Abstract

A theoretical analysis of heat transfer and moisture variation was performed while a PVA solution was exposed to high-intensity nongray irradiation and/or air flow convection. Effective absorption coefficients were incorporated in the radiative transfer analysis. The influence of various radiation and convection parameters on the transfer of heat and moisture variation in the coated layers on an optically thick substrate was investigated. The effects of radiation and convection parameters on the transfer process were presented in terms of the rate of water content removal, heat transfer, and moisture distribution. Results were compared to those of drying when using convective heat. It is evident that the use of thermal radiation combined with convective heat will help in improving the drying rate. Numerical results show that both the radiative energy absorbed by the solution and the substrate and the distribution of water mass fraction in the solution are closely related to the rate of water removal from the solution during the process.     

Free convection heat transfer over a horizontal plate at low prandtl number

Boundary layer equations for free convection heat transfer along a semi-infinite horizontal plate are derived by giving more importance to the energy equation. The equations are obtained for low Prandtl number and two separate polynomials are used to approximate the temperature and velocity profiles in these regions. The rate of heat transfer is compared with the available analytical and numerical results based on conventional boundary layer equations.     

NETWORK NUMERICAL SIMULATION OF HYDROMAGNETIC MARANGONI MIXED CONVECTION BOUNDARY LAYERS

The study of a steady coupled dissipative layer, known as the Mangaroni mixed convection boundary layer, in the presence of a magnetic field is presented. The mixed convection boundary layer is generated when in addition to Marangoni (thermocapillary) effects there are also buoyancy effects due to gravity and external pressure gradient effects. In the model considered the Marangoni coupling condition has been included in the boundary conditions at the interface. Similarity transformations are utilized to transform the governing partial differential conservation equations into nondimensional ordinary differential equations in a single independent space variable (η) and solved using the network simulation method (NSM) using an electronic circuit simulator, Pspice. NSM is founded on the classical thermoelectric analogy between thermal and electrical variables. A set of finite-differential equations, one for each control volume, was obtained by spatial discretization of the transformed equations. The solutions obtained are compared with earlier computations using other numerical techniques, showing excellent agreement. The influence of the Marangoni mixed parameter and Hartmann number on the velocity and temperature functions are studied in detail. The effectiveness of utilizing magnetic fields to control heat transfer in Marangoni convection boundary layers is identified. An increase in Hartmann hydromagnetic number (M) is found to strongly decelerate the flow but increase temperatures. An increase in Marangoni mixed convection parameter (λ) for the scenario opposing Marangoni flow (Γ > 0) considerably accelerates the flow but decreases temperatures in the boundary layer. Conversely, an increase in Marangoni mixed convection parameter (λ) for the case favorable to the Marangoni flow (Γ < 0) decelerates the flow but enhances temperatures in the boundary layer. Applications of the model include semiconductor crystal hydromagnetic heat transfer control.     

TRANSIENT LASER HEATING OF SINGLE SOLID MICROSPHERES

The problem of electromagnetic heating of a small sphere is solved for transient and steady state conditions, taking into account the highly nonuniform energy absorption determined from Mie theory. The effects of conduction, convection and radiation boundary conditions are explored to determine the conditions under which radiant energy transfer becomes the dominant mechanism of heat loss and to predict laser intensities required to heat a particle to a specified mean temperature.     

Boundary layer flows with Dufour and Soret effects: I: Forced and natural convection

Similarity solutions of laminar boundary layer flows in forced and natural convection are examined aiming at the evaluation of the coupled effects of heat and mass transport. Momentum, energy and mass balance equations are simultaneously solved under the assumption of the validity of constitutive equations for the heat and mass fluxes of dilute solutes obeying linear forms in accordance with the thermodynamics of irreversible processes. Forced and natural convection cases depend on different similarity variables, with different exponents for the axial variable and different significant physical properties compose the pertinent dimensionless groups. In the first part of this paper thermal diffusion and diffusion thermo effects are studied for the boundary layer flows about a vertical flat plate in forced and in natural convection, separately. The second part deals with the intermediate cases of non-similar of mixed convection, where it is determined by a one-parameter family of transformations (0???1), which reduce to both extreme cases. The mixed convection will be presented in a forthcoming continuation. A modification of the method of solution based on Adomian's polynomials for the resulting boundary value problem is employed.     

A numerical study on unsteady natural convection of air with variable viscosity over an isothermal vertical cylinder

The present study deals with the boundary layer flow and heat transfer of unsteady laminar free convection flow past a semi-infinite isothermal vertical cylinder immersed in air. The fluid viscosity is assumed to vary with the temperature. An implicit finite-difference method has been employed to solve the governing non-dimensional boundary layer equations. A parametric study is performed to illustrate the influence of variable viscosity on the velocity and temperature profiles. The numerical results reveal that the viscosity has significant influences on the transient velocity and temperature profiles, average skin-friction coefficient and the average heat transfer rate. The results indicate that as the viscosity parameter increases, the temperature and the skin-friction coefficient increase, while the velocity near the wall and the Nusselt number decrease.     

MOMENTUM INTEGRAL METHOD FOR FORCED CONVECTION IN THERMAL NONEQUILIBRIUM POWER-LAW FLUID-SATURATED POROUS MEDIA

Forced convection heat transfer for power-law fluid flow in porous media was studied analytically. The analytical solutions were obtained based on the Brinkman-extended Darcy model for fluid flow and the two-equation model for forced convection heat transfer. As a closed-form exact velocity profile is unobtainable for the general power-law index, an approximate velocity profile based on the parabolic model is proposed by subscribing to the momentum boundary layer integral method. Heat transfer analysis is based on the two-equation model by considering local thermal nonequilibrium between fluid and solid phases and constant heat flux boundary conditions. The velocity and temperature distributions obtained based on the parabolic model were verified to be reasonably accurate and improvement is justified compared to the linear model. The expression for the overall Nusselt number was derived based on the proposed parabolic model. The effects of the governing parameters of engineering importance such as Darcy number, power-law index, nondimensional interfacial heat transfer coefficient, and effective thermal conductivity ratio on the convective heat transfer characteristics of non-Newtonian fluids in porous media are analyzed and discussed.     

RADIATIVE DRYING MODEL OF POROUS MATERIALS

A transient one dimensional first principles model is developed for the drying of a porous material (paper) that includes both heat and mass transfer. All three modes of heat transfer are considered; conduction, convection and radiation. The conduction is assumed to be in one dimension, through the porous material. The convection is assumed to exist only at the surface as a boundary condition. The radiation is assumed to be a volumetric phenomenon, so that the material internally absorbs, emits, and scatters energy. The absorption and scattering coefficients are spectrally dependent. Furthermore, the material is considered to have a non-unity refractive index with diffuse surfaces. In the mass transfer it is assumed that water exists in three phases: bound, free and vapor. The results provide profiles within the material for each moisture phase, temperature, and pressure and the effect of radiation on these distributions.     

COMPUTER SIMULATION OF HEAT TRANSFER DURING DRYING AND PREHEATING OF WET IRON ORE IN A ROTARY KILN

In the present study, an improved numerical heat transfer model has been developed for a rotary kiln used for drying and preheating of wet iron ore. The present model includes radiation exchange among hot gas, refractory wall and the solid surface, transient conduction in the refractory wall, and mass and energy balances of the hot gas and the solids. The contribution of gas convection has also been taken into account in terms of a fraction of the radiative heat transfer to the inner refractory wall and the solid surface. The computer results show that the present model can predict the length of the kiln as well as axial solid and gas temperature distributions with reasonably good accuracy. A detailed parametric study reveals that a good design of a rotary kiln requires medium gas flow rate, small angle of inclination and low rotational speed of the kiln.