FINITE ELEMENT ANALYSIS FOR LAMINAR FLOW AND HEAT TRANSFER IN FINITE ROD BUNDLES

This investigation deals with the application of finite element method to solve the thermohydraulic problem of laminar fully developed flow in the interior and wall sub-channels of finite fuel rod bundles. A variational principle has been used for the solution of the momentum and energy equations. Wall shear stress and temperature distributions, ƒRe and Nusselt numbers are obtained for the sub-channels of different configurations. The results are compared with solutions generated by collocation and finite difference methods.     

MASS TRANSFER FROM FLAT PLATES TO POWER-LAW FLUIDS IN LAMINAR FLOW

Mass transfer from vertical flat plates to water and 0.5 to 1.5% aqueous CMC solutions is measured in the Reynolds number range of 10^{- 2}to 6.0 x 10₃. Blasius analysis has been found to be valid only up to a Reynolds number of 100, below which Graetz-Leveque solution is more appropriate.     

CONJUGATE HEAT TRANSFER IN FALLING LAMINAR LIQUID FILMS

An analysis is presented for the heat transfer characteristics of a falling liquid film flow over a fin by the conjugate convection-conduction theory. Numerical results are presented for the dimensionless heat transfer coefficients, local and overall heat fluxes and temperature distribution of the fin by a simultaneous solution of the convective boundary layer equations of the fluid and the energy equation of the fin.     

ANALYTICAL STUDY OF HEAT TRANSFER TO LAMINAR FLOW OF NON-NEWTONIAN FLUIDS IN ANNULUS

An analytical study is made of the problem of laminar flow heat transfer to pseudoplastic fluids in a concentric circular tube annulus. The solution is obtained for simultaneously developing velocity and temperature profiles and constant wall heat flux. Constant property results are presented for different values of flow behavior index, n, and several inner to outer tube radius ratios and Prandtl numbers. Variable property solutions, with strongly temperature-dependent consistency index are obtained. The effect of viscous dissipation on the results of heat transfer is also presented.     

COMPARISON OF METHODS FOR SOLVING NONLINEAR FINITE-ELEMENT EQUATIONS IN HEAT TRANSFER

We have developed two new methods for solving the finite-element heat-transfer equations with highly nonlinear boundary conditions and material properties. When compared with the more commonly employed successive substitution and Newton-Raphson procedures, the new methods speed convergence rates, increase the radius of convergence, or reduce user interaction. The first method accelerates the standard Newton-Raphson technique when the degree of the nonlinearity is known (for example, radiation boundary conditions or a prescribed temperature dependence in the thermal conductivity). The accelerated Newton-Raphson can reduce the computational time by more than 80% when compared with the standard Newton-Raphson technique. The second method employs feedback to regulate the solution algorithm during execution. Comparisons of these methods are given for several practical examples.     

DISPERSED FLOW HEAT TRANSFER IN CIRCULAR BENDS

This paper presents an experimental study of dispersed flow heat transfer in 90-degree circular bends. From extensive measurements, two different heat transfer patterns are identified, i.e. heat transfer without and with rewetting. Their intrinsic mechanisms are analysed, based on the present experimental evidence and our previous theoretical studies. Effects of mass flow rate, wall heat flux, system pressure and curvature ratio on heat transfer are also investigated. An empirical criterion is developed to identify the heat transfer pattern in the bend.     

DISPERSED FLOW HEAT TRANSFER IN CIRCULAR BENDS

This paper presents an experimental study of dispersed flow heat transfer in 90-degree circular bends. From extensive measurements, two different heat transfer patterns are identified, i.e. heat transfer without and with rewetting. Their intrinsic mechanisms are analysed, based on the present experimental evidence and our previous theoretical studies. Effects of mass flow rate, wall heat flux, system pressure and curvature ratio on heat transfer are also investigated. An empirical criterion is developed to identify the heat transfer pattern in the bend.     

CONJUGATE HEAT TRANSFER WITH TURBULENT FLOW IN A CIRCULAR TUBE

A steady heat transfer problem has been analyzed as a conjugate problem with turbulent flow in a circular tube. The three kinds of thermal boundary conditions considered here are specified as constant temperature, constant heat flux and constant heat transfer coefficient at the outer surface of the wall.

From the results of numerical calculation for Prandtl numbers in the range 0.01 ≤ Pr ≤ 10 and for Reynolds numbers in the range 10⁴ ≤ Re ≤ 10⁵, it was confirmed that the dimensionless parameter R_c could have significant effects on the heat transfer and the temperature field in the fluid adjacent to the wall.     

FLOW AND HEAT TRANSFER FOR THREE-DIMENSIONAL FLOW OVER AN EXPONENTIALLY STRETCHING SURFACE

This study analyzes the laminar boundary-layer flow and heat transfer characteristics of a steady, three-dimensional viscous fluid driven by a horizontal surface stretched exponentially in two lateral directions. The simulations in this study assume that the surface temperature is also distributed exponentially and reduce the governing equations to a set of ordinary differential equations using a similarity transformation. This study develops a numerical procedure that combines the Ackroyd method and Runge-Kutta integration scheme to solve the transformed equations. Results show that heat transfer characteristics depend strongly on the stretching ratio, temperature exponent, and Prandtl number.     

横纹槽管束在不同支承结构下的传热及流阻性能试验

<正>横纹槽管是苏联60年代由Mигай和Kaлинин等人开发的双面强化管（图1）。它只有边界层分离流,而无对传热作用不大却使流阻增加较多的螺旋流,故其性能明显优于螺     

GENERALIZED FINITE DIFFERENCE SOLUTION FOR HEAT AND MASS TRANSFER FROM A FINITE CYLINDER DURING QUENCH

A generalized nondimensional solution is presented that describes heat or mass transfer from a finite cylinder during quench. The solution is applicable to three important cases:

Conduction with convection heat transfer at the surface during any single step hot or cold quench.

Conduction with radiation heat transfer at the surface during a single step cold quench with negligible background radiation.

Diffusion with surface desorption of a diatomic gas from a metal specimen during a single step quench in a high vacuum with negligible background pressure.

Application of the generalized solution, which utilizes the numerical method of finite differences with forward stepping, is illustrated by determining a cylinder's transient temperature distribution and surface transfer rate (both instantaneous and cumulative) for an example L/D ratio of 2.0. Selected results are graphed and tabulated for the three cases. The results for the conduction/convection case are verified using the familiar analytical product solution as well as the lumped solution. For the conduction/radiation and diffusion/desorption cases, no analytical solutions are available other than the lumped limit which is in agreement.     

定热通量加热下微三角形槽道中滑移流动的换热特性

微三角形截面通道是现代工程实际应用中常涉及到的流动通道.针对微三角形槽道利用正交函数法求解了滑移流区内带温度跳跃边界条件的能量方程,对不可压缩气体在微三角形槽道内充分发展层流滑移流动的换热特性进行了理论分析,获得了轴向定热通量加热、周向均匀壁面温度条件下微三角形槽道内的温度分布和换热特性的分析解.计算结果表明：正交函数法适用于微三角形槽道内滑移流动换热特性的分析计算;在滑移流区,微三角形槽道内的平均Nusselt数随Knudsen数的增加而减小,其随高宽比变化的分布曲线随Knudsen数的增加而平行下移,Nusselt数比随Knudsen数的变化关系基本不受高宽比的影响.     

HEAT TRANSFER IN A LAMINAR CYLINDRICAL WALL JET WITH UNIFORM SURFACE HEAT FLUX

The steady state flow and heat transfer characteristics of a laminar cylindrical wall jet are obtained for uniform surface heat flux conditions. Local nonsimilarity solutions as well as series solutions are presented for the velocity and thermal fields. Numerical results are given for the wall shear stress, surface temperature variation and temperature field for a Prandtl number of 0.73.     

HEAT TRANSFER AND FLUID FLOW IN A NONISOTHERMAL CONSTRAINED VAPOR BUBBLE

A Constrained Vapor Bubble (CVB) with a relatively large Bond number formed by partially underfilling liquid in an evacuated cavity is capable of high thermal conductance. Il operates on the principle of closed loop phase-change along with capillarity to circulate the working fluid. Analytical investigations were conducted to compare with existing experimental data. A steady-state fluid flow model combined with a two-dimensional heat transfer model was developed and solved to yield key operating parameters ( i.e., temperature and liquid meniscus curvature) of the CVB. The modeling results of the outside wall temperature in the evaporator were found to agree well with the measured experimental data. An area average heat transfer coefficient was used to characterize the heat transfer on the inside wall of the evaporator. The value of this heat transfer coefficient was found to increase with the heat flow rate. The fluid flow model with the heat transfer model in the evaporator to provide the energy balance was used successfully to fit the experimental curvature data. The mass flow rate in the bottom corners of the CVB was found to be higher than that in the top corners due to the gravitational body force.     

HEAT TRANSFER AND FLUID FLOW IN A NONISOTHERMAL CONSTRAINED VAPOR BUBBLE

A Constrained Vapor Bubble (CVB) with a relatively large Bond number formed by partially underfilling liquid in an evacuated cavity is capable of high thermal conductance. Il operates on the principle of closed loop phase-change along with capillarity to circulate the working fluid. Analytical investigations were conducted to compare with existing experimental data. A steady-state fluid flow model combined with a two-dimensional heat transfer model was developed and solved to yield key operating parameters ( i.e., temperature and liquid meniscus curvature) of the CVB. The modeling results of the outside wall temperature in the evaporator were found to agree well with the measured experimental data. An area average heat transfer coefficient was used to characterize the heat transfer on the inside wall of the evaporator. The value of this heat transfer coefficient was found to increase with the heat flow rate. The fluid flow model with the heat transfer model in the evaporator to provide the energy balance was used successfully to fit the experimental curvature data. The mass flow rate in the bottom corners of the CVB was found to be higher than that in the top corners due to the gravitational body force.     

空气横掠波纹管束的流动与传热性能

引　言管壳式换热器是石油化工行业应用十分广泛的换热设备 ,它具有易于制造、耐压高等特点 .但是普通管壳式换热器换热效率低 ,因此开发高效传热元件对管壳式换热器的进一步推广应用具有十分重要的意义 .采用翅片管换热器可以大大强化换热 ,但是阻力也增加很多 ,并且容易积垢 ,影响使用 .近年来开发的波纹管换热器由于加工方便、易于制造而越来越受到人们的重视[1～ 4 ] .但对于流体横掠波纹管束时流动传热性能的研究却少见报道 .本文对如图 1所示的波纹管束组成的换热器进行了实验测定 ,研究了 3种排数的阻力与换热规律 ,为设计换热器提供…     

移动颗粒床中高温气体渗流传热数值计算

针对移动颗粒床中物料层内的高温气体渗流传热现象 ,考虑渗流与传热的相互作用 ,采用局部非热平衡假设建立了多孔介质渗流传热物理数学模型并进行了数值计算 .研究了不同情况下床内填充多孔介质中的流速、气固温度和床层压力损失 .计算结果表明 ,高温热气对移动床颗粒料层的热渗透主要发生在渗流入口端区域 ,增大入口渗流速度以及减小床层物料下移速度将导致物料温度沿床高慢速下降 ,热渗透深度扩大 ,热渗透作用区域内的物料温度水平提高 .在热渗透作用区域 ,孔隙率对流场和压力损失有很大的影响 .研究结果对于移动颗粒床反应器的设计与运行具有一定的参考作用     

MASS TRANSFER THROUGH PERMEABLE WALLS: A NEW INTEGRAL EQUATION APPROACH FOR CYLINDRICAL TUBES WITH LAMINAR FLOW

Mass transfer through cylindrical semipermeable walls is analyzed. The solution is obtained in terms of integral equations. Despite the existence of a non-homogeneous boundary condition on the semipermeable wall, the solution thus obtained is particularly advantageous since the associated eigenvalue problem is independent of the Sherwood number. This parameter takes into account the main conductances at the tube wall.

The approach is applied to the case of mass transfer from the interior of a capillary tube with semipermeable walls to an external fluid. The flow in the tube is laminar, and the external flow is assumed turbulent.

The mathematical methodology employed provides a framework to develop numerical schemes of fast and sure convergence.     

LAMINAR FLOW HEAT TRANSFER WITH INLINE MIXERS INSERTS

Heat transfer coefficients were measured for heat transfer to a Newtonian fluid flowing in laminar flow through a tube with inline mixer inserts. Kenics “Static” mixer and Ross LPD mixer inserts were studied as heat transfer augmentation devices. The mixer inserts were in the inner tube of a concentric tube heat exchanger. Steam was condensed in the annulus of the exchanger. Significant heat transfer enhancement was obtained with both inserts at the expense of even greater pressure drop increases. The use of the Ross mixer insert gave greater augmentation than did the use of the kenics insert. An analysis using the analogy between momentum and heat transfer allowed the prediction of heat transfer coefficients from pressure drop measurements. The predicted coefficients were in good agreement with experimentally measured heat transfer coefficients for laminar flow.     

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).