Transient forced convection in the entrance region of a porous tube

The problem of transient forced convection in the entrance region of a cylindrical porous medium with developing thermal boundary layer is investigated. The hydrodynamic behaviour of the flow is assumed to be steady and fully developed, and both Darcian and non-Darcian effects on the flow are considered. Thermal transients are created by a step change in the temperature of the tube wall. The effect of different fluid and solid-matrix parameters on Nusselt number, thermal entrance length, total heat absorbed and mixing cup temperature are considered.     

SIMULTANEOUSLY DEVELOPING LAMINAR FLOW AND HEAT TRANSFER IN THE ENTRANCE REGION OF A CIRCULAR TUBE WITH CONSTANT WALL TEMPERATURE

The developing flow and heat transfer in the entry region of a heated circular tube is analyzed for the case of constant wall temperature. An integral or boundary-layer solution is presented which has a number of advantages over earlier Karman-Pohlhausen integral analyses. Thus, in the present analysis, the velocity and temperature distributions, the local and mean drag coefficients, and the local and mean Nusselt numbers approach their fully-developed values asymptotically. The new analysis is based on the hydrodynamic inlet-filled region concept originally proposed by Ishizawa (1966) and later adopted by Mohanty and Asthana (1978) to flow through a circular tube. This concept is extended to the combined entry-length problem by introducing a thermal transition region, herein called the thermally-filled region, between the thermal inlet boundary-layer region and the thermally fully-developed region. A thermal shape factor is also introduced which ensures smooth transition of all pertinent thermal quantities from the entrance region to the fully-developed region. Results for the variation of the local and mean Nusselt numbers with axial distance along the tube for Pr = 0.1,0.5,0.7,1,5, and 10 are presented. These results agree well with the numerical solutions of Hombeck (1965), Manohar (1969), and Hwang and Sheu (1974) and also with the correlations of Churchill and Ozoe (1973).     

Analysis of laminar flow forced convection heat transfer with uniform heating in the entrance region of a circular tube

A new integral or boundary-layer solution for laminar flow heat transfer in the combined entrance region of a circular tube is presented for the case of constant wall heat flux. The solution is based on the hydrodynamic inlet-filled region concept originally proposed by Ishizawa (1966) and later adopted by Mohanty and Asthana (1978) to hydrodynamically developing flow through a circular tube. Unlike available boundary-layer solutions, the new analysis provides results which join smoothly and asymptotically to the fully developed values. Results for the Nusselt number were found to agree favorably with available numerical solutions.     

CC板通道入口效应对传热特性和阻力特性的影响

选取低Reynolds数k-ε湍流模型,采用数值模拟的方法计算了不同Reynolds数下入口效应和CC板通道单元体传热特性、阻力特性的关系。数值模拟的结果表明：入口效应的存在使得CC板通道前3个单元体的湍流强度显著变大,在第4个单元体之后入口效应对传热特性的影响可以忽略;随着Reynolds数的增加,由于CC板通道入口处湍流强度增加的程度逐渐变小,入口效应对传热效果的强化能力下降;随着Reynolds数的增加,入口段和充分发展段的摩擦阻力系数均有所下降;此外,由于入口效应的存在,CC板通道入口段的摩擦阻力系数比充分发展段高20%左右。     

倾斜管内热进口段自然强制复合对流传热

用数值分析方法研究了倾斜管内热进口段自然强制同向复合对流传热 ,分析了浮力、倾斜角及轴向导热对流动和传热特性的影响 ,得到了速度、温度、壁面剪切应力、局部及平均Nusselt数的分布和变化 研究结果显示Pe=71时平均Nusselt数的最大值位于 2 5°～ 45°之间 ,Pe=2 5时则在 90°处出现 .     

Forced convection heat transfer to a power-law fluid in arbitrary cross-section ducts

A numerical method is developed to predict the three-dimensional forced convection laminar incompressible flow of a power law fluid in arbitrary cross-section straight ducts. The continuity equation and boundary layer forms of the energy and momentum equations in rectangular coordinates are transformed into new orthogonal coordinates with boundaries coinciding with the coordinate surfaces. The resulting equations are solved using the finite difference technique. The numerical scheme is capable of handling different hydrodynamic and thermal entry boundary conditions but results are only presented for uniform inlet velocity and temperature profiles and isothermal wall. To demonstrate the wider applicability of the method local heat transfer coefficients and pressure drop in square, trapezoidal and regular pentagonal ducts are computed as functions of pertinent thermal and hydrodynamic parameters.     

Low peclet number heat transfer in the thermal entrance region of parallel-plate channels with unequal wall temperatures

The problem of low-Peclet-number thermal entry heat transfer for plane Poiseuille flow in parallel-plate channels with uniform but unequal wall temperatures is approached by the eigenfunction expansion method utilizing the Gram-Schmidt orthonormalization procedure. The formulation considers axial heat conduction and allows upstream heat penetration through the thermal entrance. Numerical results are obtained for the case with entrance condition parameter θ₀ = 1 and Peclet number Pe = 1, 5, 10 and 50. The effect of Peclet number on temperature distributions in both upstream and downstream regions is studied. At Pe = 50, the concept of thermal boundary layer is applicable and the present series solution does not yield physically reasonable temperature distribution locally near the upper plate at the thermal entrance. The difficulty may be attributed to the nature of thermal boundary conditions at the thermal entrance and the transition from elliptic problem to parabolic problem with the increase of Peclet number.     

Low peclet number heat transfer in the thermal entrance region of parallel-plate channels with unequal wall temperatures

The problem of low-Peclet-number thermal entry heat transfer for plane Poiseuille flow in parallel-plate channels with uniform but unequal wall temperatures is approached by the eigenfunction expansion method utilizing the Gram-Schmidt orthonormalization procedure. The formulation considers axial heat conduction and allows upstream heat penetration through the thermal entrance. Numerical results are obtained for the case with entrance condition parameter θ₀ = 1 and Peclet number Pe = 1, 5, 10 and 50. The effect of Peclet number on temperature distributions in both upstream and downstream regions is studied. At Pe = 50, the concept of thermal boundary layer is applicable and the present series solution does not yield physically reasonable temperature distribution locally near the upper plate at the thermal entrance. The difficulty may be attributed to the nature of thermal boundary conditions at the thermal entrance and the transition from elliptic problem to parabolic problem with the increase of Peclet number.     

Laminar forced convection in the thermal entrance region of curved pipes with uniform wall temperature

The thermal entrance region heat transfer problem for fully developed laminar flow in curved pipes with uniform wall temperature is approached by an alternating direction implicit method for the parabolic energy equation for a flow regime with Dean number ranging from 0 to an order of 100. This work represents an extension of the classical Graetz problem in straight tubes to curved pipes. The graphical results for temperature developments in the form of temperature profiles through the horizontal and vertical planes, isothermals and local Nusselt number variations in the thermal entrance region are presented in such a way as to illustrate clearly the interaction between the secondary flow and the developing temperature field for Prandtl numbers of 0.1, 0.7, 10 and 500. For a given Dean number, the effect of Prandtl number is to shorten the thermal entrance length (I/Gz) and the temperature field develops rather rapidly with large Prandtl number. The effect of Dean number is similar to that of Prandtl number with Dean number effect becoming much more appreciable at high Prantdl numbers than at low Prandtl number.     

轴向导热对微通道内传热特性的影响

以去离子水为工质,在当量直径为155.3 μm的三角形硅基微通道中进行了传热特性的实验研究;采用轴向导热与总加热量的比值和轴向导热准则数来分析轴向导热对微通道内传热特性的影响;基于实验结果,对入口段长度进行了计算。根据红外热像仪的测量结果,局部壁面温度沿流动方向上呈非线性规律分布,并计算得出局部Nusselt数沿流动方向上的分布规律。轴向导热与总加热量的比值的变化范围为0.106～0.275,表明轴向导热对微通道内传热特性的影响显著,特别是在Reynolds数较小的情况下。对轴向导热准则数进行了新的修正,在热流密度与入口温度相近的情况下,轴向导热准则数随Reynolds数的增加而减小。     

Two-dimensional Simulation for Hydrogen/Air Combustion in a Monolith Reactor

Recent studies on hydrogen combustion were reviewed briefly. The laminar flow and combustion of premixed hydrogen/air mixture in a cylindrical channel of a monolith reactor with and without catalytic wall was numerically modeled by solving two-dimensional (2-D) Navier Stokes (N S) equations, energy equation, and species equations. Eight gas species and twenty reversible gas reactions were considered. The control volume technique and the SIMPLE algorithm were used to solve the partial differential equations. The streamlines of the flow field, temperature contours, the entrance length, and the concentration fields were computed. It is found that the entrance zone plays an important role on flow and temperature as well as species distribution. Therefore, the flow cannot be assumed either as fully developed or as plug flow. There is a small but strong thermal expansion zone between the wall and the entrance. Both diffusion and convection affect the heat and mass transfer processes in the expansion zone. Thus the equations of momentum, energy and species conservations should be used to describe hydrogen/air combustion in the monolith reactor. The hot-spot location and concentration field of the homogeneous combustion is strongly influenced by the inlet velocity and temperature, and the equivalence ratio. The catalytic combustion of premixed hydrogen/air mixture over platinum catalyst-coated wall in a cylindrical channel was also simulated.     

Transient forced convection in the entrance region of porous concentric annuli

The problem of transient laminar forced convection in the entrance region of a porous concentric annulus with developing thermal boundary layer is solved numerically by the finite difference technique. The hydrodynamic behaviour of the flow is assumed to be steady and fully developed, and both Darcian and non-Darcian effects on the flow are considered.     

Effect of Thermal Asymmetry on Laminar Forced Convection Heat Transfer in a Porous Annular Channel

The effect of thermal asymmetry on laminar forced convection heat transfer in an annular porous channel with a Darcy dissipation of fluid kinetic energy was investigated numerically. The cylindrical surfaces making the channel boundaries were kept at constant but different temperatures. The thermal asymmetry thus imposed on the system results in an asymmetric temperature field and different heat fluxes across the channel boundaries. Depending on the Darcy, Péclet and Reynolds numbers, the thermal asymmetry may lead to a reversal of the heat flux along the channel at least at one of the channel walls. The corresponding Nusselt number becomes zero and subsequently experiences a discontinuity, thereby jumping from infinite negative to infinite positive, or vice versa. This feature is observed in the region of thermal development. In the fully developed heat transfer region, the Nusselt numbers can be positive or negative for the same inlet conditions, depending on the heat source strength. In the case of a plug flow, the analytical expressions for the Nusselt numbers have been obtained.     

Thermophoretic deposition efficiency in a cylindrical tube taking into account developing flow at the entrance region

This study investigates the effect of developing flow in a circular tube on the thermophoretic particle deposition efficiency using the critical trajectory method numerically. When both flow and temperature are fully developed (combined fully developed), present results agree with previous theories for the long tube where the flow temperature approaches that of the wall. When the flow is fully developed and temperature is developing, it is found that only near the thermal entrance region (or temperature jump region) of the tube the deposition efficiency is slightly higher than the combined fully developed case (flow and temperature), while the deposition efficiency remains the same for the long tube. When both flow and temperature are developing (or combined developing), the deposition efficiency is about twice that of the combined fully developed case for the long tube and is much higher near the entrance of the tube. Non-dimensional equations are developed empirically to predict the thermophoretic deposition efficiency in combined developing and combined fully developed cases under laminar flow conditions.     

Heat transfer in turbulent forced convection between parallel-plates

The thermal entry region heat transfer due to turbulent forced convection of a Newtonian fluid inside a parallel-plate duct maintained at constant uniform temperature is solved analytically and the local Nusselt numbers are determined with a high degree of accuracy up to the region very close to the inlet. The calculated local Nusselt numbers are compared with those obtained from a recently proposed empirical correlation.     

Thermal and hydrodynamic characteristics of constructal tree‐shaped minichannel heat sink

A three‐dimensional thermal and hydrodynamic model for constructal tree‐shaped minichannel heat sink is developed. The heat and fluid flow in the constructal heat sink with an inlet hydraulic diameter of 4 mm are numerically analyzed, taking into consideration conjugate heat transfer in the channel walls. The pressure drop, temperature uniformity, and coefficient of performance (COP) of the constructal tree‐shaped heat sink are evaluated and compared with those of the corresponding traditional serpentine flow pattern. The results indicate that the constructal tree‐shaped minichannel heat sinks have considerable advantages over the traditional serpentine flow patterns in both heat transfer and pressure drop. The strong and weak heat flow can be effectively allocated in tree‐shaped flow structures; hence, the inherent advantage of uniform temperature on the heating surface in the constructal tree‐shaped heat sink is demonstrated. And in tree‐shaped flow structures, the local pressure loss due to confluence flow is found to be larger than that due to diffluence flow. In addition, an aluminum constructal tree‐shaped minichannel heat sink is fabricated to conduct the verification experiment. The experimentally measured temperature distribution and pressure drop are in agreement with the numerical simulation, which verifies that the present model is reasonable. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

低质量流率蒸汽真空水平管内凝结传热特性的实验研究

对换热长度为3.4 m、内径为38 mm的真空水平管内的蒸汽凝结流动换热特性进行了实验研究。分析了蒸汽质量流率小于9 kg/(m²·s),蒸汽饱和温度为50、60和70℃,换热温差为3~7℃时对凝结过程的影响。通过对分层流动冷凝换热机理分析,建立了热分区角计算模型。实验结果表明,热分区角随着质量流率的增加而增加,随着传热温差的增大而增大;饱和温度对管内凝结的局部传热系数和热分区角影响较小。通过以热分区角为分区界限,建立了局部传热系数经验关联式,在预测实验工况下,对于管顶部膜状冷凝区,预测精度在±25%以内;对于管底部冷凝液对流换热区,预测精度在+25%~-35%。     

板式换热器波纹通道的流动与传热机理

采用Realizable k-ε湍流模型,针对一种人字形板间波纹通道的流动与传热机理进行了数值模拟研究。考察了不同Reynolds数湍流状态下波纹通道中沿壁面的平均以及局部表面特征数（Nu和f）的变化规律,揭示了流动与传热参数在波纹通道不同横向剖面的分布规律。结果表明在Re<7860时,凹壁面Nu更大;Re>7860时,凸壁面Nu更大;随着Re的增大凹壁面f大于凸壁面。凹壁面的Nu在近入口和近出口处存在两个峰值,并且在近出口处存在极大值;而凸壁面在近入口处存在一个极大值,在近出口处存在极小值。凹壁面的f在近出口处出现陡升现象,而凸壁面则在近入口处出现陡升。随着Re增大,剖线v和TKE增大,而T减小。另外,v、T和TKE在近凹壁面区域皆突然增大。     

固定床传热中的参数估值传热参数中的床高效应

本文试验测定了固定床的传热数据,计算和分析表明,床高效应反映了加热段进口热边界层对传热参数的影响,不能通过在传热 模型中引入轴向导热项或采用抛物线型进口边界条件获得补偿;轴向导热项对拟合传热参数以及模拟床层内的温度场均无意义,因此拟均相模型应该采用ＰＦ模型的形式。要想到可靠的传热参数,必须通过不同床高下的传热 数据来获得传热参数的渐近值。