A Universal Model of Heat Transfer in Systems with Penetration Cooling

Penetration cooling is one of the most intensive methods of regulation of heat transfer, which is explained by the highly developed contact (wetted) surface within a porous matrix and by the significant effect of heat flux reduction upon the injection of coolant into the boundary layer. However, there are serious difficulties in performing theoretical analysis of heat transfer within permeable matrices with filtration of coolant because of the absence of a universally accepted approach to the choice of geometric scale of pore channels and criterion relations for the calculation of the coefficient of internal heat transfer, as well as because of the indeterminacy of the boundary conditions on the internal and external surfaces for the coolant temperature. In this paper, all of these problems are coordinated from a unified standpoint, which enables one to formulate a universal model of heat transfer in permeable envelopes. The results of systematic calculations by the suggested mathematical model are used to reveal and optimize the most important parameters of the system of heat shielding designed for the blades of high-temperature rims of gas turbines.     

Unsteady compressible boundary layer flow on the stagnation line of an infinite swept cylinder

Summary Numerical solutions of flow and heat transfer process on the unsteady flow of a compressible viscous fluid with variable gas properties in the vicinity of the stagnation line of an infinite swept cylinder are presented. Results are given for the case where the unsteady temperature field is produced by (i) a sudden change in the wall temperature (enthalpy) as the impulsive motion is started and (ii) a sudden change in the free-stream velocity. Solutions for the simultaneous development of the thermal and momentum boundary layers are obtained by using quasilinearization technique with an implicit finite difference scheme. Attention is given to the transient phenomenon from the initial flow to the final steady-state distribution. Results are presented for the skin friction and heat transfer coefficients as well as for the velocity and enthalpy profiles. The effects of wall enthalpy parameter, sweep parameter, fluid properties and transpiration cooling on the heat transfer and skin friction are considered.     

Heat transfer through a porous plate at cooling gas supply in an asymptotic suction regime

The analytical solution is carried out for the one- and two-dimensional problem of the thermal state of a porous plate surrounded by the flow of high-temperature and homogenous cooling gases in a permeable cooling system. Cooling gas flow in a laminar regime of asymptotic suction is considered, which provides effective heat shielding with minimum dependence on the parameters of the permeable wall. Heat exchange from the high-temperature gas is accepted for both laminar and turbulent boundary layers.     

Transient mixed convection with internal heat generation and oscillating plate temperature

Summary. Oscillating plate temperature effects on transient mixed convection heat transfer from a porous vertical surface with internal heat generation or depletion are considered. The governing equations are transformed into dimensionless form by a set of variables and then solved using the finite element method. It is found that the velocity inside the boundary layer increases and the temperature decreases as time passes. In addition, it is found that when the energy generation is increased, the temperature near the wall will be higher than the wall temperature, and the velocity inside the boundary layer will increase due to an increase of buoyancy forces. Increasing the energy depletion term decreases the velocity inside the boundary layer and increases the heat transfer rate. Different temperature and velocity profiles are drawn for different dimensionless groups. Numerical values of Nusselt number as well as local skin friction coefficient are tabulated. Comparison with previous works shows complete agreement.     

Free convection heat and mass transfer along a vertical surface in a porous medium

Summary This study deals with free convection heat and mass transfer from a vertical plate embedded in a fluid saturated porous medium with constant wall temperature and concentration. The temperature and concentration variations across the boundary layer produce a buoyancy effect which gives rise to flow field. Integral method of Von-Karman type is applied to obtain the analytical solution of this fundamental problem.     

Investigation of the Effect of Electric Field on the Characteristics of Heat Transfer in a Combustion Chamber with a Porous Cooling Flow Train

The effect of an external electric field on the characteristics of heat and mass transfer is investigated in a combustion chamber whose cooling flow train is filled with a porous material. It is found that, if a constant negative potential of 900 V is applied to the combustion chamber, the heat flux from the combustion products to the firing wall increases (by a factor of 2.7), and in the case of a positive potential this heat flux decreases. The obtained experimental data are explained by the effect of ionic wind which interacts with the boundary layer of the firing wall to cause a variation in its geometric and thermophysical parameters, as well as leads to a change in the flame surface. The observed effect may be used to develop an effective system of cooling the combustors of power plants.     

An entry-flow problem for a non-isothermal catalytic-wall reactor

A reacting gas flows into a metal, thin-walled, tube which has a catalytic coating on its inner surface. A strong, temperature-dependent, exothermic reaction occurs giving a local hos spot. It is assumed that the surface temperature is controlled by heat conduction through the metal wall, heat transfer into the gas being negligible. A standard approximate technique is used to derive an integral equation which relates the mass transfer at the wall in the Blasius boundary layer to the wall temperature. A second integral equation is derived from the heat-conduction problem for the metal wall, and the coupled equations are solved numerically. The maximum temperature rise at the wall is found to be significantly higher than that obtained when a fully developed flow passes over a catalytic coating.     

高温熟料非稳态非热平衡渗流换热模型

回转窑卸入篦冷机的高温水泥熟料为红热半透明的多孔介质,其复杂的气固换热机理给篦冷机的工艺改进带来较大难度。针对这一问题,将高温红热颗粒等效为光学厚介质,推导了一种高温熟料颗粒间传导与辐射综合换热系数,基于渗流力学与传热学理论,建立了考虑高温熟料颗粒间热辐射效应的水泥熟料非稳态非热平衡渗流换热模型。通过对所建模型进行求解,得到了料层内熟料温度与气体温度的分布规律,比较了不同区域冷却速率的差异,获得了辐射传热因素对料层温度分布的影响。     

Generalized relations for the calculation of heat transfer at the entry of gas to a porous layer

The analytical and numerical solutions are performed of the problem on temperature field and heat transfer in the region of entry of cooling gas into a porous layer. Calculation relations are suggested.     

Heat Transfer in a Micropolar Fluid along a Non-linear Stretching Sheet with a Temperature-Dependent Viscosity and Variable Surface Temperature

In this paper, heat transfer characteristics of a two-dimensional steady hydromagnetic natural convection flow of a micropolar fluid passed a non-linear stretching sheet taking into account the effects of a temperature-dependent viscosity and variable wall temperature are studied numerically for local similarity solutions by applying the Nachtsheim-Swigert iteration method. The results corresponding to the dimensionless temperature profiles and the local rate of heat transfer are displayed graphically for important material parameters. The results show that in modeling the thermal boundary layer flow with a temperature-dependent viscosity, consideration of the Prandtl number as a constant within the boundary layer produces unrealistic results and therefore it must be treated as a variable rather than a constant within the boundary layer. The results also show that the local rate of heat transfer strongly depends on the non-linear stretching index and temperature index.     

The effect of turbulent mixing on the dynamics of a liquid layer accelerated by a compressed air flow

The influence of a turbulent mixing (TM), developed at the unstable boundary of a liquid layer accelerated by a hot compressed gas flow, on the efficiency of the subsequent energy transfer from the accelerated liquid layer to a gas layer compressed by the liquid was experimentally studied. It was found that the TM development may significantly decrease the energy takeoff by the accelerated liquid layer, which is explained by cooling of the hot compressed gas as a result of the increased heat transfer from gas to liquid in the TM zone. The experimental data indicate that the gas energy losses can reach several tens percent.     

Boundary layer on a permeable wall with suction of gas

The differential model of turbulence, supplemented with transport equation for turbulent heat flux, is used to perform a numerical investigation of the boundary layer on a permeable wall with suction of gas. It is demonstrated that the protraction of transition from laminar to turbulent mode of flow and the laminarization of the initial turbulent boundary layer occur under conditions of suction of gas. This is evidenced both by the behavior of integral and local characteristics of flow and heat transfer and by the degeneracy of turbulence when the suction of laminar turbulent layer becomes asymptotic. The critical values of the suction parameter are determined.     

Heat‐flux‐specified boundary treatment for gas flow and heat transfer in microchannel using direct simulation Monte Carlo method

Direct simulation Monte Carlo (DSMC) method has been widely used to study gaseous flow and heat transfer in micro‐fluidic devices. For flows associated with microelectromechanical systems (MEMS), the heat‐flux‐specified (HFS) boundary condition broadly exists. However, problems with HFS boundary have not been realized in the simulation of microchannel flows with DSMC method. To overcome this problem, a new technique named as inverse temperature sampling (ITS) is developed. This technique provides an approach to calculate the molecular reflective characteristic temperature from the specified heat flux at the wall boundary. Coupling with DSMC method, the ITS technique can treat the HFS boundary condition in DSMC method for both simple gas and gas mixtures. For validation, heat flux obtained from two‐dimensional Poiseuille flows with wall‐temperature‐specified (WTS) boundary condition is employed as the initial thermal boundary condition of our new method. Sampled wall temperature by the ITS method agrees well with the expected value. Pressure, velocity and temperature distributions under these two thermal boundary conditions (WTS and HFS) are compared. Effects of molecule collision model and gas–surface interaction model are also investigated. Results show that the proposed ITS method could accurately simulate gaseous flow and heat transfer in MEMS. Copyright © 2007 John Wiley & Sons, Ltd.     

多孔泡沫金属中指数规律变热流平板表面的层流对流传热分析

采用Brinkman-Forchheimer-extended Darcy流动模型和局部非热平衡传热模型(双温度模型),对指数规律变热流密度条件下的多孔泡沫金属中平板表面的层流对流传热进行了分析,并得出了平板表面的热边界层的厚度和局部的对流传热系数的表达式。结果发现:平板表面的热边界层的厚度发展沿流动方向逐渐增大,但是增大的趋势由迅速趋向平缓;局部对流传热系数沿流动方向逐渐减小,而后趋于稳定。最后推导出了局部的对流传热Nusselt数的准则方程。     

钢铁工业中的自由边值问题

This paper considers two novel free boundary problems that emerge from modelling processes basic to steel manufacture.The first process concerns the spray cooling of hot steel sheet during the process of continuous casting. Here, an important practical consideration is the non-monotonicity of the measured heat transfer from the steel as a function of the steel temperature. In order to understand this phenomenon, a two-phase flow model is written down for the heating and vapourisation of the water spray. This model relies on a microscale analysis of droplet vapourisation and, in a steady state, it reduces to a coupled system of nonlinear ordinary differential equations for the spray temperature and water content. This system predicts the conditions for the existence or otherwise of a free boundary separating the two-phase region from a dry vapour layer close to the steel plate.The thickness of this vapour layer is determined by the solution of a generalised Stefan problem. The second process concerns the macroscopic modelling of pig iron production in blast furnaces. In the simplest scenario, the blast furnace may be roughly divided into a porous solid region. overlaying a hot high pressure gaseous zone. The gas reacts with the solid in a thin "intermediate region" at the base of the solid region and it is in this intermediate region that the pig iron is produced. A free boundary model is proposed for the location of the intermediate region and its stability is investigated.     

Free Boundary Problems in the Steel Industry

This paper considers two novel free boundary problems that emerge from modelling processes basic to steel manufacture. The first process concerns the spray cooling of hot steel sheet during the process of continuous casting. Here, an important practical consideration is the non-monotonicity of the measured heat transfer from the steel as a function of the steel temperature. In order to understand this phenomenon, a two-phase flow model is written down for the heating and vapourisation of the water spray. This model relies on a microscale analysis of droplet vapourisation and, in a steady state, it reduces to a coupled system of nonlinear ordinary differential equations for the spray temperature and water content. This system predicts the conditions for the existence or otherwise of a free boundary separating the two-phase region from a dry vapour layer close to the steel plate.The thickness of this vapour layer is determined by the solution of a generalised Stefan problem. The second process concerns the macroscopic modelling of pig .iron production in blast furnaces. In the simplest scenario, the blast furnace may be roughly divided into a porous solid region overlaying a hot high pressure gaseous zone. The gas reacts with the solid in a thin “intermediate region“ at the base of the solid region and it is in this intermediate region that the pig iron is produced. A free boundary model is proposed for the location of the intermediate region and its stability is investigated.     

Heat transfer in a viscoelastic boundary layer flow through a porous medium

This paper examines the viscoelastic fluid flow and heat transfer characteristics in a saturated porous medium over an impermeable stretching surface with frictional heating and internal heat generation or absorption. The heat transfer analysis has been carried out for two different heating processes, namely (i) with prescribed surface temperature (PST-case) and (ii) prescribed surface heat flux (PHF-case). The governing equations for the boundary layer flow problem result similar solutions. For the specified five boundary conditions, it is not possible to solve directly the resulting sixth-order nonlinear ordinary differential equation. For the present incompressible boundary layer flow problem with constant physical parameters, the momentum equation is decoupled from the energy equation. Two closed–form solutions for the momentum equation are obtained and identified the realistic solution of the physical problem. Exact solution for the velocity field and the skin-friction are obtained. Also, the solution for the temperature and the heat transfer characteristics are obtained in terms of Kummers function. Asymptotic results for the temperature function for large Prandtl numbers are presented. The work due to deformation in the energy equation, which is essential and escaped from the attention of researchers while formulating the visco-elastic boundary layer flow problems, is considered. Drastic variation in the values of heat transfer coefficient is observed when the work due to deformation is ignored.The authors would like to thank the reviewers for their valuable comments/ suggestions to improve the clarity of the paper.     

Influence of boundary conditions on the cooling effect of crushed-rock embankment in permafrost regions of Qinghai–Tibetan Plateau

The crushed-rock layer is a highly porous medium that has been used to ensure the stability of embankment in permafrost regions. At present, depending on different boundary conditions (impermeable and permeable) of crushed-rock layer in embankment, the crushed-rock embankments are divided into two kinds of structures in the construction of Qinghai–Tibetan railway in China. One is a closed-boundary crushed-rock embankment; the other is an open-boundary crushed-rock embankment. In order to investigate the influence of boundary conditions (impermeable and permeable) on the cooling effect of a crushed-rock embankment, two numerical models of the unsteady two-dimensional hydrokinetic equations for incompressible fluid are presented to analyze the velocity and temperature characteristics of crushed-rock embankment with different embankment heights under impermeable and permeable boundary conditions for a period of 50 years. The results indicate: (1) the boundary conditions (impermeable and permeable) of crushed-rock embankment can have a very large impact on the heat transfer pattern within it in windy permafrost regions of Qinghai–Tibetan Plateau. The cooling effect of the closed crushed-rock embankment mainly relies on natural convection within crushed-rock layer, which is caused by the thermal boundary condition, but the cooling effect of the open crushed-rock embankment is due to the heat transfer enhancement because of internal forced convection induced by the external low temperature air flow (wind); (2) from the temperature distributions of crushed-rock embankments, it can be found that, under the assumption that the air temperature will be warmed up by 2.6 °C in a period of 50 years and in the areas where the mean annual air temperature is − 4.0 °C, when embankment is low, the cooling effects of crushed-rock embankment have no obvious difference under the two boundary conditions, and the cooling effect of closed crushed-rock embankment is only a little better than that of open one; however, when embankment is high, the boundary conditions cause a distinct influence on the temperature distribution of crushed-rock embankment, and the cooling effect under the permeable boundary condition is far better than that under the impermeable boundary condition. However, the asymmetric temperature distribution problem of the high crushed-rock embankment, caused by permeable boundary and external wind, must be considered when it is designed and constructed.     

Unsteady compressible 3-dimensional boundary-layer flow near an asymmetric stagnation point with mass transfer

The heat and mass transfer for unsteady laminar compressible boundary-layer flow, which is asymmetric with respect to a 3-dimensional stagnation point (i.e. for a jet incident at an angle on the body), have been studied. It is assumed that the free-stream velocity, wall temperature, and surface mass transfer vary arbitrarily with time and also that the gas has variable properties. The solution in the neighbourhood of the stagnation point has been obtained by series expansion in the longitudinal distance. The resulting partial differential equations have been solved numerically using an implicit finite-difference scheme. The results show that, in contrast with the symmetric flow, the maximum heat transfer does not occur at the stagnation point. The skin-friction and heat-transfer components due to asymmetric flow are only weakly affected by the mass transfer as compared to those components associated with symmetric flow. The variation of the wall temperature with time has a strong effect on the heat transfer component associated with the symmetric part of the flow. The skin friction and heat transfer are strongly affected by the variation of the density-viscosity product across the boundary layer. The skin friction responds more to the fluctuations of the free stream oscillating velocities than the heat transfer. The results have been compared with the available results and they are found to be in excellent agreement.     

Compressible turbulent boundary layer on a permeable plate with injection of foreign gas

A numerical solution is obtained for equations of motion, diffusion, and energy using a three-parameter model of turbulence for boundary layer with different thermal boundary conditions on a permeable plate with injection of foreign gas. For an ideal gas with constant values of Prandtl and Schmidt numbers, the numerical solution is compared with limiting dependences for dimensionless temperature and enthalpy of gas on the wall. For helium/xenon mixtures with a low value of Prandtl number, the effect of intensity of injection and of the values of Reynolds and Mach numbers on the integral and local characteristics of flow and heat and mass transfer is investigated.