Forced convection heat transfer from axisymmetric bodies to non-Newtonian fluids

A theoretical analysis for forced convection heat transfer from axisymmetric bodies immersed in non-Newtonian power-law fluids has been performed. Results for the velocity shape factor, local friction coefficient, and the Nusselt number are presented for different values of Prandtl number and the power-law index. The local friction coefficient results are compared with available experimental data and it is shown that asymptotic expressions suffice to get accurate predictions of heat transfer at low and high Prandtl numbers.     

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.     

Mixed Convection of a Bingham Fluid in Differentially Heated Square Enclosure with Partitions

This paper reports a two-dimensional numerical investigation of mixed convection inside a liddriven square enclosure, completely filled with a non-Newtonian fluid obeying the Bingham model, having two rectangular adiabatic partitions mounted in different dispositions. Due to the problem’ complexity, the latter is solved using finite volume method when the SIMPLER algorithm is adopted for the pressure-velocity coupling. In order to investigate the yield stress effects on flow field and heat transport, we maintain the Richardson number (Gr/Re²) as 0.01, 1 and 10, respectively, which generates a good simulation of forced, mixed and natural convection dominated flow. The Prandtl and Grashof numbers are fixed at 50 and 10⁴, respectively, while the Bingham number covers the range from 0 to 30. The validity of the computing code was ascertained by comparing our results with the numerical ones already available in the literature and that for both cases: Newtonian and non-Newtonian fluid. The phenomenon is analyzed through the streamlines, the isotherms and the Nusselt numbers with special attention to the partitions’ arrangement and its size. It is found that all parameters related to the geometrical dimensions of the partitions play a crucial role on the temperature distribution, flow field and heat transfer enhancement. For all values of the Bingham number, the mean Nusselt number is found as an increasing function of the decrease Richardson number. Thus, the heat transfer improves.     

MOMENTUM INTEGRAL METHOD FOR FORCED CONVECTION IN THERMAL NONEQUILIBRIUM POWER-LAW FLUID-SATURATED POROUS MEDIA

Forced convection heat transfer for power-law fluid flow in porous media was studied analytically. The analytical solutions were obtained based on the Brinkman-extended Darcy model for fluid flow and the two-equation model for forced convection heat transfer. As a closed-form exact velocity profile is unobtainable for the general power-law index, an approximate velocity profile based on the parabolic model is proposed by subscribing to the momentum boundary layer integral method. Heat transfer analysis is based on the two-equation model by considering local thermal nonequilibrium between fluid and solid phases and constant heat flux boundary conditions. The velocity and temperature distributions obtained based on the parabolic model were verified to be reasonably accurate and improvement is justified compared to the linear model. The expression for the overall Nusselt number was derived based on the proposed parabolic model. The effects of the governing parameters of engineering importance such as Darcy number, power-law index, nondimensional interfacial heat transfer coefficient, and effective thermal conductivity ratio on the convective heat transfer characteristics of non-Newtonian fluids in porous media are analyzed and discussed.     

COMBINED LAMINAR FREE AND FORCED CONVECTION FROM A VERTICAL PLATE TO POWER LAW FLUIDS

The boundary layer heat transfer for the steady two-dimensional incompressible combined laminar free and forced convection from a vertically static or moving plate to a power-law non-Newtonian fluid is analyzed by local similarity method. The effects of the flow index, buoyancy parameter, modified Prandtl number and streamwise distance on the heat transfer rate are discussed for the prescribed surface temperature and prescribed wall heat flux cases.     

COMBINED LAMINAR FREE AND FORCED CONVECTION FROM A VERTICAL PLATE TO POWER LAW FLUIDS

The boundary layer heat transfer for the steady two-dimensional incompressible combined laminar free and forced convection from a vertically static or moving plate to a power-law non-Newtonian fluid is analyzed by local similarity method. The effects of the flow index, buoyancy parameter, modified Prandtl number and streamwise distance on the heat transfer rate are discussed for the prescribed surface temperature and prescribed wall heat flux cases.     

半周加热横纹管内熔盐强化传热特性

半周加热太阳能吸热器管给管内对流传热系数带来影响,基于此,建立半周加热横纹管内熔盐对流传热的实验台和数值计算模型,分析横纹管槽宽、槽深对管内熔盐传热性能的影响规律,结果表明：从横纹管绝热侧到加热侧,周向管内壁温度逐渐升高,周向管内局部Nusselt数先减小后缓慢增大至稳定。横纹管凹槽处轴向管内壁温度明显低于平滑段,凹槽处轴向管内局部Nu较大,凹槽后与平滑段交界处管内局部Nu最小。横纹管槽越宽,加热侧轴向管内局部Nu越小,管内平均Nu越小,传热综合性能评价因子PEC越大。横纹管槽越深,轴向管内局部Nu越大,管内平均Nu越大,传热强化倍数Nu/Nu _ST越大。槽宽对横纹管PEC的影响比槽深明显,槽深对横纹管内Nu/Nu _ST影响比槽宽大。通过线性拟合得到半周加热横纹管内熔盐传热Nu的关联式,其计算Nu与模拟值最大偏差在±7%以内。     

LAMINAR BOUNDARY LAYER HEAT TRANSFER TO POWER-LAW FLUIDS

The heat transfer for the steady two-dimensional incompressible laminar boundary layer of power-law non-Newtonian fluids past a semi-infinite static or moving flat plate is studied by local similarity method. Four cases are considered: static plate with prescribed wall temperature and heat flux; and moving plate with prescribed wall temperature and heat flux. The effescts of the flow index, streamwise distance and modified Prandtl number on the temperature distribution and heat transfer rate are discussed in detail.     

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.     

Free convection in power-law fluids from a heated sphere

In this work, the governing field equations describing heat transfer from a heated sphere immersed in quiescent power-law fluids have been solved numerically. In particular, consideration has been given to elucidate the role of Grashof number (Gr), Prandtl number (Pr) and power-law index (n), on the value of the Nusselt number (Nu) for a sphere in the natural convection regime. Further insights are provided by presenting streamline and constant temperature contours. The results presented herein encompass the following ranges of conditions: 10≤Gr≤10⁷; 0.72≤Pr≤100 and 0.4≤n≤1.8 thereby covering both shear-thinning and shear-thickening types of fluid behaviours. Broadly, all else being equal, shear-thinning behaviour can enhance the rate of heat transfer by up to three-fold where as shear-thickening can impede it up to ～30?40% with reference to that in Newtonian fluids. The paper is concluded by presenting detailed comparisons with the scant experimental data and the other approximate treatments of this problem available in the literature.     

耦合表面张力的封闭腔体内管外自然对流传热特性

采用格子-玻尔兹曼方法（LBM）构建了考虑表面张力影响下封闭腔体内加热圆柱外自然对流数学模型。在分别对自然对流与表面张力模型模拟验证的基础上，探究了液固表面张力与重力场下浮升力同时作用下加热圆柱外流体自然对流的传热特性。结果表明，在给定Ra数下（10³≤Ra≤10⁶），随着表面张力的增大（Oh数减小），封闭腔体内管外自然对流扰动会加剧，流型会变复杂，壁面换热效率有明显提高。在Ra数为10⁵，长度比（加热圆柱半径和方腔长度之比）为1/10情况下，加入表面张力σ=0.076302N/mm（Oh=0.122），腔体左侧壁面平均努塞尔数和加热圆柱壁面与未加表面张力相比分别提高了93.5%和60.35%。当表面张力大小和自然对流的浮升力相当时，此时的流场波动更加明显剧烈，在一定范围内增大浮升力反而减弱换热。     

Laminar mixed convection in the entrance region of shrouded arrays of heated rectangular blocks

Laminar mixed convection in the entrance region of shrouded arrays of heated rectangular blocks is approximated numerically for large Prandtl number fluids. The problem considered is related to the convective cooling of electronic components mounted on horizontal circuit boards. Two heating conditions are investigated; in case 1, the uniformly heated components are facing upwards and, in case 2, the heated components are facing downwards. Typical fluid streamlines and isotherms, block wall temperature distributions and local Nusselt numbers are presented. It is found that the secondary flow leads to a significant enhancement in heat transfer for cases where the block faces upwards rather than downwards.     

绝热圆腔内4根冷热微管阵列振动强化传热实验

目前针对微细管管外同时有自然对流和周期横向振动存在情况下的混合对流问题鲜有研究。为了探究这种现象, 进而开发一种新型的换热器, 本文提出了一种由4根冷热微细管组成的微管阵列, 将其平行放置于有中间流体的圆形腔体内, 并对管束施加微小横向振动的混合对流传热机理进行研究。详细描述了实验系统及实验方法, 以及后期对实验数据的处理方法, 得到了传热Nu数随管间自然对流强度Ra数, 强迫振动Re_v数等量纲为1参数的变化曲线;揭示了该结构形式下传热特性随冷热管温差、振动频率、微管振幅等传热规律。结果表明, 横向振动在小温差情况下传热强化效果更为明显。将本文实验数据与Lemlich单管振动实验中的数据进行对比, 表明了振动对4根微管阵列的强化传热效果比单根管更明显。     

Laminar Flow and Heat Transfer Characteristics in Jackets of Triangular Flow Channels

Laminar flow and heat transfer characteristics of jacketed vessel with triangular flow channels were numerically studied under hydrodynamically and thermally fully developed conditions. Constant heat flux at theheated wall was assumed. The numerical program code interms of vorticity, stream function, axial velocity com ponent and energy equations was written based on a finite volume method. Based on the numerical results, the flow and temperature field were given, and the effects of Dean and Prandtl numbers on flow and heat transfer were ex amined, and the correlations of flow resistance and mean Nusselt number were developed for the jacket. The results show that the structure of secondary flow is steady two vortices in the investigated range of dimensionless curvatureratio and Reynolds number. Two peaks of local Nusselt number increase significantly with Prandtl and Dean num ber increasing, but the local Nusselt numbers near two ends and at the center of the heated wall increase only slightly. The center and two ends of heated wall are the poor positions for heat transfer in the jacket. Compared with the outer half coil jacket at the same area of heated wall, curvature radius, Reynolds number and Prandtl number, e jacket of triangular flow chmnel has lower flow resistance and less mean Nusselt number.     

COMPREHENSIVE, THEORETICALLY BASED, CORRELATING EQUATIONS FOR FREE CONVECTION FROM ISOTHERMAL SPHERES

Correlating equations are developed for the local and mean Nusselt number for free convection from an isothermal sphere as a function of the Rayleigh and Prandtl numbers. These expressions are based primarily on theoretical solutions for limiting cases, and hence are presumed to be more reliable than purely empirical correlations. The predictions of the proposed expressions are, however, validated by comparisons with prior experimental data. The expressions for the mean Nusselt number are shown to be applicable for all Ra and Pr. The expressions for the local Nusselt number are limited in applicability to the laminar boundary layer regime. The same equations are applicable to mass transfer and to combined heat and mass transfer in terms of the Sherwood, Schmidt and appropriately modified Rayleigh numbers.     

MHD flow of a micropolar fluid towards a vertical permeable plate with prescribed surface heat flux

The problem of a steady mixed convection stagnation point flow towards a permeable vertical plate with prescribed surface heat flux immersed in an incompressible micropolar fluid is studied numerically. The governing partial differential equations are first transformed into a system of ordinary differential equations using a similarity transformation, before being solved numerically by a finite-difference scheme known as the Keller-box method and the Runge–Kutta–Fehlberg method with shooting technique. The effects of the material parameter, buoyancy parameter, suction/injection parameter and the Prandtl number on the fluid flow and heat transfer characteristics are discussed. It is found that dual solutions exist for both assisting and opposing flows. The skin friction coefficient and the local Nusselt number increase in the presence of suction and magnetic field. Moreover, suction as well as fluids with larger Prandtl number widens the range of the buoyancy parameter for which the solution exists.     

Effects of Viscous Dissipation on Heat Transfer between an Array of Long Circular Cylinders and Power Law Fluids

The free surface model has been combined with the equations of motion and of thermal energy to investigate the role of viscous dissipation on heat transfer between banks of long cylinders and power law (shear‐thinning and shear‐thickening) fluids. The equations of motion cast in the stream function/vorticity formulation have been solved numerically using a second‐order accurate finite difference method to obtain extensive information on the behaviour of local and surface‐averaged Nusselt numbers over a range of Reynolds numbers 1 – 500, for a wide range of power law indices (0.4 ≤ n ≤ 2.0), Brinkman numbers (0 ≤ Br ≤ 5) and Prandtl numbers (Pr = 1, 1000) at two representative solid volume fractions corresponding to the porosities of e = 0.4 and 0.9. Two different thermal boundary conditions are considered at the cylinder surface: constant temperature (CT) and constant heat flux (CHF). The results presented herein provide a fundamental knowledge about the influence of viscous dissipation on the heat transfer characteristics. The results reported herein further show that the effect of Brinkman number on heat transfer is strongly conditioned by the thermal boundary condition, Prandtl number and the power law index.     

Analysis of heat recovery and thermal transport within entrapped fluid based on heatline approach

The wide applications of indirect heating and cooling processes have opened scope for various researchers to explore in-depth analysis and applications of systems involving heat exchange processes. This paper targets the analysis and visualization of heat transfer in entrapped triangular cavities within adjacent square tubes forming a system of practical application especially in pollution control with hot fluid flowing through the stack and entrapped cold fluid confined within the triangular cavities. Also, efficient heat recovery has been examined for the entrapped fluid in the system. The parameters for this study are the Prandtl number (Pr), Rayleigh number (Ra) and Nusselt number (Nu). Complete details of heating patterns in both triangular cavities have been analyzed with heatline approach for visualization of heat flow. At low Rayleigh number, it is found that the heatlines are smooth and perfectly normal to the isotherms indicating the dominance of conduction for both the triangles. But as Ra increases, flow slowly becomes convection dominant. Multiple secondary circulations within the upper triangle are formed for fluids with low Pr, whereas this is absent in higher Pr fluids. Multiple circulation cells for smaller Pr also correspond to multiple cells of heatlines which illustrate less thermal energy transport from hot wall. On the other hand, the dense heatlines at bottom wall display enhanced heat transport for larger Pr. But interestingly for lower triangle there is hardly any variation of patterns with the increase in Prandtl number in the system. Analysis is concluded with the average Nusselt number plots. It is found that fluid with higher Pr may be recommended for upper triangle, but fluid with all ranges of Pr may be used for lower triangle.     

Mixed convection flow of a power-law fluid in horizontal ducts

The laminar mixed convection heat transfer of a non-Newtonian fluid modelled by a power-law constitutive equation is studied. The equations of motion subject to the Boussinesq approximation and an axially uniform heat flux and peripherally uniform wall temperature condition are discretized by finite difference approximation and are solved by the successive relaxation method. Dual solutions with two-cell and four-cell patterns have been observed in certain regions of the parameter space. The secondary flow caused by the buoyancy force has a shear thinning effect for pseudoplastic fluids. The Nusselt number, however, always increases with increasing Grashof number.     

A generalized approach to heat transfer in pipe flow with internal heat generation

In the last few years, there has been a renewed interest in the molten salt reactor (MSR), one of the “Generation IV International Forum” concepts, which adopts a circulating molten salt mixture as both heat generator (fuel) and coolant. The heat transfer of a fluid with internal heat generation depends on the strength of the source whose influence on the heat exchange process is significant enough to demand consideration. At present, few studies have been performed on the subject from either an experimental or a numerical point of view.This study considers fluids with a wide range of Reynolds numbers, flowing through smooth and straight circular tubes within which the flow is hydrodynamically developed but thermally developing (conditions of interest for MSR core channels). The study aims at an assessment of the heat transfer modelling for a large variety of fluids (with Prandtl numbers in the range 0≤Pr≤10⁴), in particular taking into account the influence of the internal heat generation on the temperature distribution, which plays an important role in the case of molten salts for nuclear reactors. To this purpose, the general and unified solution of the heat transfer equation is applied to the turbulent Graetz problem with boundary conditions of the third kind and arbitrary heat source distribution, incorporating recent formulations for turbulent flow and convection.Computed results are shown to be in a good agreement with experimental data concerning heat transfer evaluations for both fully developed and thermally developing flow conditions, over a large range of Prandtl numbers (10^?2<Pr<10⁴). Finally, a preliminary correlation, which includes the Prandtl number range of interest for molten salts, is proposed for the Nusselt number predictions in the case of simultaneous uniform wall heat flux and internal heat generation.