Mixed convection flow of non‐Newtonian fluid from a slotted vertical surface with uniform surface heat flux

In the present paper, the combined convection flow of an Ostwald–de Waele type power‐law non‐Newtonian fluid past a vertical slotted surface has been investigated numerically. The boundary condition of uniform surface heat flux is considered. The equations governing the flow and the heat transfer are reduced to local non‐similarity form. The transformed boundary layer equations are solved numerically using implicit finite difference method. Solutions for the heat transfer rate obtained for the rigid surface compare well with those documented in the published literature. From the present analysis, it is observed that, an increase in χ leads to increase in skin friction as well as reduction in heat transfer at the surface. As the power‐law index n increases, the friction factor as well as heat transfer increase.     

MIXED CONVECTION BOUNDARY LAYER FLOW OF A MICROPOLAR FLUID ON A HORIZONTAL PLATE

An analysis is performed to study the heat transfer characteristics of laminar mixed convection boundary layer flow of a micropolar fluid past a semi-infinite horizontal fiat plate with variable surface heat flux. A nonsimilar mixed convection parameter £ and a pseudosimilarity variable v are introduced to cast the governing boundary layer equations into a system of dimensionless equations, which are solved numerically using the finite difference method. A single mixed convection parameter is used to cover the entire regime of mixed convection from the pure forced convection limit to the pure free convection limit. The effect of material parameters, the power-law variation of surface heat flux, nonsimilar mixed convection parameter and Prandtl number are considered. The micropolar fluids are observed to display drag reduction and reduced surface heat transfer rate when compared to Newtonian fluids. The effect of the buoyancy force results in the enhancements of friction factor, heat transfer rate and wall couple stress.     

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.     

边界层方程求解传热传质复合自然对流的偏差分析

引　言动量、能量及质量的边界层方程是Naveir Stokes完整方程的简化形式 ,自上世纪初提出以来 ,应用极广 .传热传质复合自然对流是自然界和工业过程中常见的现象 ,由于存在热与物质扩散两种浮力相对大小及方向的差异以及Prandtl数和Schmit数的影响 ,使该问题颇为复杂 .Bottema     

NATURAL CONVECTION HEAT TRANSFER IN A POROUS LAYER WITH MULTIPLE PARTITIONS

Laminar natural convection heat transfer in inclined porous layers with multiple diathermal partitions is studied analytically and numerically. On the basis of the Darcy-Oberbeck-Boussinesq equations, the problem is solved analytically in the limit of a thin layer with constant flux boundary conditions. The relationship between overall heat transfer and the number of partitions N, their relative positions Nu and the angle of inclination φ of the system is determined

The critical Darcy-Rayleigh number R_c for the onset of convection in a bottom-heated horizontal system is predicted. The results are compared with limiting cases of the problem and are found to be in agreement. The influence of a thermal barrier which is sandwiched between two porous layers is also discussed. A numerical study of the same phenomenon, obtained by solving the complete system of governing equations, is conducted. A good agreement is found between the analytical predictions and the numerical simulation.     

Quasi-steady state natural convection in a tilted porous layer

Quasi-steady state laminar natural convection in an inclined porous layer is studied analytically and numerically. On the basis of the Darcy-Oberbeck-Boussinesq equations, the problem is solved analytically in the limit of a thin porous layer heated on one side by a constant heat flux while the other boundaries are maintained adiabatic. For quasi-steady state, the flow and temperature fields and overall heat transfer rates are obtained in terms of the controlling parameters and the onset of convection in a bottom-heated horizontal system is predicted. It is also demonstrated for the case of a bottom-heated layer that for sufficiently small inclinations, multiple unicellular quasi-steady states exist, some of which are unstable. A numerical study of the same phenomenon, obtained by solving the complete system of governing equations, is conducted. Good agreement is found between the analytical predictions and the numerical simulation.     

Unidirectional transport of heat and salt in free convection of water with variable physical properties along a vertical plate with uniform temperature and salinity

The steady laminar boundary layer flow of saline water along an isothermal vertical plate is studied in this paper. The results are obtained with the numerical solution of the boundary layer equations taking into account the variation of all water thermophysical properties with temperature and salinity. The combination of different temperatures and salinities at the boundary conditions results in a large number of upward, downward or bidirectional flows. The present study concerns the wall heat transfer, wall salinity transfer, wall shear stress and velocity and temperature profiles across the boundary layer for unidirectional upward or downward flow.     

FORCED CONVECTION BOUNDARY LAYER FLOW AT A FORWARD STAGNATION POINT WITH NEWTONIAN HEATING

The steady forced convection boundary layer flow near the forward stagnation point of an infinite plane wall generated by Newtonian heating in which the heat transfer from the surface is proportional to the local surface temperature is investigated in this study. The governing partial differential equations are first transformed into a system of ordinary differential equations before they are solved numerically by a finite-difference scheme, namely the Keller box method. Numerical solutions are obtained for a large range of values of the Prandtl number.     

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。     

NATURAL CONVECTION FLOW OF SECOND-GRADE FLUID ALONG A VERTICAL HEATED SURFACE WITH POWER-LAW TEMPERATURE

In this study we investigated the effects of free convection flow of a viscoelastic second-grade fluid along a vertical flat surface with power-law temperature distribution. The boundary layer equations for the momentum and the energy transport have been reduced to local similarity equations using appropriate transformations. Solutions of the reduced equations are obtained employing the local non-similarity method as well as the implicit finite difference method against ξ (the local Deborah number) in the range [0, 10] for fluids having Prandtl numbers of 10, 50, and 100. The regular perturbation solutions are also been obtained for smaller values of ξ together with the Padé approximation. Results thus obtained are discussed in terms of the local skin friction and local rate of heat transfer for different values of the physical parameters, like n and Pr. Effect of the Deborah number, De, on the velocity and temperature profiles has also been shown graphically. It is observed that both the local skin friction and heat transfer coefficients decrease with increase in the value of De for given values of n and Pr.     

COMBINED FORCED AND FREE CONVECTION IN BOUNDARY LAYER FLOW OF NON-NEWTONIAN FLUID ON A HORIZONTAL PLATE

An analysis is presented to study the effects of buoyancy-induced streamwise pressure gradients on laminar forced convection heat transfer to non-Newtonian fluids from a horizontal plate. Numerical solution of the transformed boundary layer equations has been carried out for different values of the flow behavior index and the buoyancy parameter by means of the local nonsimilarity method. A discussion is provided for the effect of the buoyancy force on the friction factor, the dimensionless heat transfer rate and the details of the velocity as well as temperature fields.     

COMBINED CONDUCTION-MIXED CONVECTION-SURFACE RADIATION FROM A UNIFORMLY HEATED VERTICAL PLATE

The present article reports the results of a numerical study on combined conduction-mixed convection-surface radiation from a vertical plate with uniform internal heat generation. The study considers the governing fluid flow and heat transfer equations without boundary layer approximations. Air is taken to be the cooling medium. Stream function-vorticity formulation, coupled with finite volume method, is used to solve the problem. A computer code has been written for the purpose, and results are validated with available experimental and analytical results for asymptotic limiting cases. In addition to making comprehensive parametric studies, useful correlations for evaluating the nondimensional maximum and average temperatures of the plate and mean friction coefficient are deduced based on a large set of data generated from the code.     

气固两相流中颗粒运动强化器壁对流传热的机理

提出了颗粒碰撞壁面过程中颗粒打破边界层和颗粒与壁面导热的强化传热模型,以分析气固两相流中颗粒强化对流传热的机理,通过模型计算研究了风速、颗粒浓度和粒径等因素对颗粒在壁面的停留特性、颗粒在边界层的扰动及对导热和边界层破坏两种强化机制传热比重的影响．以气固两相流横掠圆管的传热过程为例进行计算,计算与实验结果一致,并获得了具有实用价值的关联计算式．     

最小?损优化方法在椭圆换热管内的应用

在流体对流换热分析的基础上得到局部?损率的表达式,以局部?损率为优化目标,满足能量与质量守恒条件,在流动功耗为定值条件下,根据拉格朗日泛函极值原理得到?损为极值时的控制方程组,发展了最小?损优化方法。将该方法应用到椭圆换热单管中,得到优化后的速度场与温度场。优化结果表明,优化流动结构为纵向旋流,具有较好的传热及流动性能,相比未优化椭圆管综合换热性能（Nu/Nu_s）/（f/f_s）可达3.21,同时得到了纵向涡在流场中的分布情况,这对椭圆管内强化换热发展具有指导意义。     

Forced convection subcooled boiling of binary mixtures

A mode based on an additive mechanism of heat transfer is proposed for forced convection subcooled boiling of binary mixtures. The contributing modes of heat transfer are: (i) the heat transferred as latent heat by the rising bubbles, (ii) the heat transferred as the heat contained in the superheated thermal layer that is removed from the surface in the wake of the rising bubbles and (iii) the single phase forced convection heat transfer from the heating surface not influenced by the bubbles. Experimental data from the literature on binary systems show good agreement with the model, validating the postulated mechanism.     

振动圆管外对流换热特性的场协同机理

数值模拟了振动圆管外的对流换热,通过数据后处理分析了振动圆管外对流换热特性与场协同性能间的联系,从场协同原理的大值原则与匹配性原则上对振动圆体外表面传热的规律特性作了解释。振动圆管外的场协同角余弦值在面相位0°与180°处最大,在90°与270°处最小,并且随着时相位靠近平衡位置,其面上各点的场协同角余弦值逐渐变大。场协同匹配性能的分布规律与场协同角余弦值的分布基本相同。振动圆管外的对流传热系数分布规律与场协同余弦值及场协同匹配系数的分布规律一致,表明可以使用场协同原理阐述振动圆管外的对流换热规律。     

RADIATION EFFECT ON FREE CONVECTION LAMINAR FLOW FROM AN ISOTHERMAL SPHERE

Natural convection laminar flow from an isothermal sphere immersed in a viscous incompressible optically dense fluid in the presence of radiation effects has been investigated. The governing boundary layer equations are transformed into a non dimensional form and the resulting nonlinear systems of partial differential equations are reduced to local non-similarity boundary layer equations, which are solved numerically by two distinct, efficient methods, namely, (i) implicit finite difference method together with the Keller box scheme and (ii) local non-similarity method. Numerical results of the velocity and temperature profiles of the fluid are presented. The results of the shearing stress and the heat transfer rate in terms of skin-friction coefficient and Nusselt number respectively are also presented for a wide range of the radiation-conduction parameter or Planck number R _d (=0.0, 1.0, 2.0, 3.0), the surface heating parameter θ _w (=1.1, 1.2, 1.4), and Prandtl number Pr (=7.0, 10.0, 15.0, 20.0).     

垂直梯度磁场作用下水平薄层磁性液体自然对流传热

１前言磁性液体是吸附着表面活性剂的固体磁性颗粒（如Ｆｅ３Ｏ４）分散于基液（如水）中而形成的稳态胶体溶液。它能在重力、磁力及离心力等外力场的作用下不凝聚、不沉淀,是一种集流动性。强磁性于一体的新型材料。磁性液体在化工、机械、电子、动力及航天航空等领域有...     

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.