HEAT TRANSFER IN ISOTROPIC TURBULENCE

The direct interaction approximation (Kraichnan 1959) was used to calculate thermal eddy diffusivities, intensities or temperature fluctuations, and various correlation functions for heat transfer in an isotropic turbulent flow with a uniform mean temperature gradient. The calculated results compare reasonably well with values from experiments in a heated wind tunnel and may be of value in the analysis of more complex heat transfer processes.     

COMBINED HEAT AND MASS TRANSFER IN FREE CONVECTION ALONG A ROTATING PLATE UNDER UNIFORM HEAT AND UNIFORM MASS FLUXES

The problem of combined heat and mass transfer in laminar free convection along a vertically rotating plate subjected to a uniform heat flux and/or a uniform mass flux is studied analytically. The governing non-dimensional nonlinear coupled partial differential equations are solved by local similarity and local nonsimilarity approach. Numerical results for the local Nusselt number, the local Sherwood number and the local wall shear stress for the convective-diffusion of hydrogen, water vapor and naphthalene into the air are presented in tabular forms. The analysis extends the range both when the concentration buoyancy force assists as well as opposes the thermal buoyancy force.     

COMBINED HEAT AND MASS TRANSFER IN FREE CONVECTION ALONG A ROTATING PLATE UNDER UNIFORM HEAT AND UNIFORM MASS FLUXES

The problem of combined heat and mass transfer in laminar free convection along a vertically rotating plate subjected to a uniform heat flux and/or a uniform mass flux is studied analytically. The governing non-dimensional nonlinear coupled partial differential equations are solved by local similarity and local nonsimilarity approach. Numerical results for the local Nusselt number, the local Sherwood number and the local wall shear stress for the convective-diffusion of hydrogen, water vapor and naphthalene into the air are presented in tabular forms. The analysis extends the range both when the concentration buoyancy force assists as well as opposes the thermal buoyancy force.     

TRANSIENT BEHAVIOR OF NATURAL CONVECTION INSIDE A VERTICAL CYLINDER

The transient behavior for natural convection heat transfer within a vertical cylindrical enclosure was studied using the SIMPLER numerical algorithm. Initially, the temperature of the internal fluid was uniform. The unsteady state heat transfer was initiated by a temperature step change applied to all boundaries. The boundary temperature was then increased at the same rate as the center temperature until pseudosteady state was achieved. (Pseudosteady state is comparable to steady state convection for a fluid with uniform heat generation.) The transient heat transfer coefficient and the intensity of flow, along with the magnitude and the location of the minimum temperature, mean temperature, and maximum stream function are presented. Temperature and stream function contours are used to show the penetration of heat from the boundary and the development of the flow patterns. The local Nusselt number is also provided as supplementary information. A cylinder with HID = 1 was considered, with the Prandtl number of the fluid equal to 7 and a Rayleigh number of 10⁵. A characteristic length defined as 6 x (volume)/(surface area), which was found to produce the best regression results in our previous studies, was used in defining the Nusselt number and the Rayleigh number. The initial heat transfer rate was found to be correlated by

Nu =0.938 (Dimensionless Time) ^-0567

Oscillatory phenomena were found in support of the prediction made by Patterson and Imberger.     

Laminar natural convection characteristics in an enclosure with heated hexagonal block for non-Newtonian power law fluids

This work illustrates the steady state, two dimensional natural convective flow and heat transfer features in square enclosure containing heated hexagonal block maintained either at constant wall temperature(CWT) or uniform heat flux(UHF) thermal conditions. Governing equations(mass, momentum and energy) are solved by using finite volume method(FVM) with 3rd order accurate QUICK discretization scheme and SIMPLE algorithm for range of field pertinent parameters such as, Grashof number(10~3≤ Gr ≤ 10~6), Prandtl number(1 ≤ Pr ≤ 100) and power law index(0.5 ≤ n ≤ 1.5). The analysis of momentum and heat transfer characteristics are delineated by evolution of streamlines, isotherms, variation of average Nusselt number value and Colburn factor for natural convection(j_(nH)). A remarkable change is observed on fluid flow and thermal distribution pattern in cavity for both thermal conditions. Nusselt number shows linear variation with Grashof and Prandtl numbers; while rate of heat transfer by convection decreases for power law index value. Higher heat transfer rate can be achieved by using uniform heat flux condition. A Nusselt number correlation is developed for possible utilization in engineering/scientific design purpose.     

非均匀热流边界条件下螺旋管内流动传热的场协同分析

建立了螺旋管内流动换热的物理数学模型,对均匀和非均匀热流边界条件下螺旋管内湍流传热进行了数值模拟。结果表明：当对螺旋管表面施加相同的加热功率时,均匀热流边界条件下湍流传热系数高于非均匀热流边界条件下的湍流传热系数,且均匀热流边界条件下螺旋管内的场协同角低于非均匀热流边界条件;非均匀热流边界条件时,在相同的De下,曲率较小的螺旋管传热系数大,且曲率较小的螺旋管内场协同角较小;同时,随着管径的增大,螺旋管内的传热系数也随之下降,但螺旋管内的场协同角随之增大。     

Laminar mixed convection in the thermal entrance region of horizontal rectangular channels with uniform heat input axially and uniform wall temperature circumferentially

This paper presents a numerical study on laminar mixed convection in the thermal entrance region of horizontal rectangular channels with uniform heat input axially and uniform wall temperature circumferentially. A relatively novel numerical method of solution is developed to obtain the developing velocity and temperature fields. The values of Prandtl number are 0.7 and 7.2, corresponding to air and water, respectively. The values of Rayleigh number are 0, 10⁴, 3 × 10⁴ and 10⁵. The channel aspect ratios considered are 0.2, 0.5, 1, 2 and 5. Variations in local friction factor ratios and local Nusselt numbers are presented. It is found that the circumferential boundary condition of uniform wall temperature significantly increases the value of local Nusselt number as compared to that found in earlier works under the boundary condition of uniform wall heat flux. But the boundary condition effect on the friction factor is shown to be comparatively minor. The asymptotic solutions at z → are compared to the existing numerical data with good agreement.     

螺旋隔板三维翅片管传热实验研究与数值模拟

文章对冷却水在换热器管程流动并与壳程的热油逆流换热条件下,对螺旋隔板三维翅片管换热器的传热与压降性能进行了实验研究,并与光滑管进行了对比。在相同壳程Reynolds数下,三维翅片管的壳程Nusselt数是光滑管的2.2—2.9倍,而压降是光滑管的2.3倍左右。采用计算流体力学软件F luent 6.0对螺旋隔板三维翅片管和光滑管换热器进行了数值模拟。结果表明,螺旋流条件下光滑管表面速度矢量均匀、稳定,而三维翅片表面的速度矢量因翅片激发流体而产生湍动和不规则的二次流,从而强化了流体的对流传热。对于螺旋隔板三维翅片管换热器,壳程Nusselt数和压降的数值模拟结果与实验计算值吻合良好,最大偏差分别为6.3%和9.8%。     

THE GALERKIN METHOD FOR TWO-PASS CROSSFLOW HEAT EXCHANGER PROBLEM

The Galerkin method is applied to solve the two-pass crossflow heat exchanger problem in the case of neither fluid mixed throughout. Four variants of flow arrangements differing in identical and/or inverted order of coupling the passes in an overall counter-current scheme are considered. The passes are not necessarily equal with respect to the number of heat transfer units. The power of the method presented can be seen in the fact that the exchanger effectiveness can be predicted with less than 0.1% error even in the case of the first order approximation. The convergence toward the exact results by carrying out the computations to higher order terms is demonstrated. Four-significant-figure effectiveness tables based on the first order approximation are given for each type of flow arrangement for N_tu up to 10. The effectiveness deterioration caused by unequal N_tu's per pass (due to different heat transfer coefficients, different fining, different core length, etc.) is presented in the form of charts.     

The effect of fin conductance on laminar heat transfer characteristics of internally finned tubes

An analytical solution for the temperature distribution and Nusselt number during fully developed laminar flow in internally finned tubes is obtained taking into consideration the realistic situation of fins with finite thermal conductivities. Axially uniform heat flux and circumferentially uniform temperature are assumed at the outer surface of the tube. For any tube geometry, it was found that the heat transfer characteristics are influenced by a single parameter K, which is directly related to the angle subtended by the fin, and the thermal conductivities of the fluid and the fin material. Nusselt numbers corresponding to different values of K are presented for a range of tube geometries     

EFFECTS OF HEAT GENERATION-ABSORPTION AND CHEMICAL REACTION ON MAGNETOHYDRODYNAMIC FLOW IN A PERMEABLE MOVING PLATE: NETWORK NUMERICAL STUDY

This study addresses the transient heat and mass transfer problem by laminar flow of a Newtonian, viscous electrically conducting, and heat generating/absorbing fluid on a continuously moving permeable surface. It was carried out with the well-known network simulation method. The effect of the parameters involved in the process were analyzed, so the influence of the parameters is represented graphically for several cases. The dimensionless parameters used in this study are: chemical reaction parameter, Prandtl number, Grashof number, absorption coefficient or heat generation, Schmidt number, and Hartmann number. The results presented are important because of the relevance of the conclusions for the steady and transient cases. In the study, the flow was considered laminar and two-dimensional. In addition, the transverse magnetic field is uniform and viscous dissipation effects, Hall effect, and Joule heating are omitted.     

Optimal design of a heat exchanger undergoing reaction fouling

The design of heat exchangers which resist fouling is examined. It is shown that for asymptotic reaction fouling in a uniform wall temperature exchanger with outlet fluid temperature kept constant, it is possible to obtain an optimum combination of exchanger size and tube-side temperature. This optimum minimises the amount of fouling in the system. An equation which gives a good approximation to the optimum is derived, and its limitations discussed.     

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.     

Measuring Flow Velocity and Uniformity in a Model Batch Digester Using Electrical Resistance Tomography

The literature shows that the extent of delignification in batch digesters varies as a function of chip location in the vessel. This non-uniformity may be exacerbated by a number of factors but is commonly attributed to poor and/or non-uniform liquor flow through the reactor (which causes poor chemical and heat distribution to the chip mass during the cook). Electrical resistance tomography (ERT) was used to evaluate the uniformity of liquor flow in a laboratory model digester under scaled industrial conditions (a 1:15 geometrically scaled vessel, a vessel to particle diameter ratio of 93:1 to minimize wall effects, and close approximation of liquor superficial velocity and pore Reynolds number). Local interstitial flow velocities were measured using pixel-pixel cross correlation techniques. It was possible to create uniform zones in the digester, but a stagnation point was observed in the centre of the vessel at the screen level. This point coincides with the location of highest kappa numbers (lowest degree of cooking) reported in industrial tests.     

Heat transfer to submerged surfaces in coarse-grained pressurized fluidized beds and fixed beds

This contribution reports on the theory underlying a uniform representation of heat transfer to submerged surfaces in fixed bed reactors and of gas convective part of heat transfer in fluidized beds with coarse-grained bulk solids and/or at elevated pressure. Based on an analysis of the pressure drop behaviour of fixed bed percolation at different gas pressures and with different bulk solids, a new dimensionless pressure drop parameter was developed. Fixed bed heat transfer data are very well correlated by this new dimensionless number. As soon as fluid throughput is in excess of minimum fluidization velocity, the pressure drop parameter transforms into the well-known Archimedes number. These two dimensionless numbers are connected by the condition of equilibrium for pressure drop and mass of practices in a fluidized bed. This equilibrium is fulfilled as soon as fluidization commences. Up to now, the Archimedes number has been generally accepted as the significant parameter, determining the gas convective part of heat transfer in fluidized beds; however, without any physical interpretation of this parameter. Introduction of the pressure drop number, which is consistent with the Archimedes number, reduces the heat transfer behaviour to pressure drop characteristics. The usefulness of this concept is proven by the comparison of experimental results and prediction.     

连续螺旋折流板换热器流动与传热性能及熵产分析

采用数值模拟的方法,研究了螺旋角对连续螺旋折流板换热器流动与传热性能的影响,并以熵产数为指标对换热器性能进行了基于热力学第二定律的分析评价。结果表明,相同质量流量时壳程传热系数和压降均随螺旋角的增大而降低,且后者降低的幅度大于前者。连续螺旋折流板换热器壳程横截面上切向速度分布较弓形折流板换热器更加均匀。在靠近中心假管的内层区域,同一径向位置的轴向速度随螺旋角的增大而降低,而在靠近壳体壁面的外层区域则相反。螺旋角越大,不同径向位置的换热管间的换热量分布均匀性越好。壳程质量流量相等时,换热器中传热引起的熵产占总熵产的比重随着螺旋角的增大而增加,熵产数随着螺旋角的增大而降低。     

边界条件对颗粒-流体对流传热的影响

对单个球形颗粒与周围流体的对流传热进行数值模拟,考察了等温边界、等热流量边界和流固耦合边界条件的影响。结果表明,流固耦合边界和等温边界所得时均面积加权努塞尔数与经验公式计算结果基本一致,等热流量边界模拟结果大于其它两种边界条件结果。时间平均局部面积加权努塞尔数的分布表明,当流动稳定且不发生分离时,努塞尔数从前滞点到后滞点逐渐减小;当出现非稳态涡旋时,努塞尔数从前滞点到分离角附近逐渐减小并出现最小值,后逐渐增大直至后滞点。     

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.     

Simulation of packed-bed separation processes using orthogonal collocation

The two-point boundary value problem resulting from the heat and material balance equations of a packed separation column are solved using polynomial approximation techniques. The model equations are based on the two-film theory of mass transfer. The resulting partial differential equations are first reduced to ordinary differential equations and then integrated using semi-implicit Runge-Kutta method of integration. Application of orthogonal collocation simplifies the solution of the two-point boundary value problem. For the examples studied, the algorithm is found to converge rapidly with respect to the number of collocation points used in the polynomial approximation.     

Inverse determination of boundary heat fluxes in a porous enclosure dynamically coupled with thermal transport

The inverse natural convection problem of estimating the heat source profiles in a porous enclosure is proposed in the present work. The physical model for the momentum conservation equation makes use of the Darcy-Brinkman equation, which allows the no-slip boundary condition on a solid wall to be satisfied. An iterative Fletcher-Reeves conjugate gradient method is applied such that the gradient of the cost function is introduced when the appropriate sensitivity and adjoint problems are defined. Particularly, the pressure-based SIMPLE algorithm is adopted to solve the continuum direct, sensitivity and adjoint problems in unification. Effects of thermal Rayleigh number, Darcy number, heat flux profiles, sensor locations and quantity on the accuracy of inverse solutions are investigated with or without the measurement errors. Additionally, the fluid and heat transport structures in the uniform porous layer are analyzed using the streamlines and heatlines, and the heat transfer potential is also explained by the variation of overall Nusselt number. Noise data solutions are regularized by stopping the iterations with the discrepancy principle of Alifanov, before the high frequency components of the random noises are reproduced. The present method solves inverse strong convection problem satisfactorily without any a priori information about the unknown heat flux to be estimated.