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.     

Nonlinear thermovibrational convection regimes in a horizontal, exothermic fluid layer

Finite-amplitude convection in a plane, horizontal, exothermic fluid layer in the presence of a static gravitational field and longitudinal high-frequency oscillations is investigated. Nonlinear regimes established after the loss of stability are studied. A numerical finite difference procedure is used. The flow configurations are determined, along with the nonlinear hydrodynamic and heat-transfer characteristics. Maps of the regimes are plotted for the superposition of thermovibrational and thermogravitational excitation mechanisms. It is shown that the intensification of heat transfer by fully developed convection lowers the fluid temperature and raises the threshold of thermal explosion. Deceased. Ural Branch of the Russian Academy of Sciences, Perm. Translated from Fizika Goreniya i Vzryva, Vol. 31, No. 6, pp. 89–98, November–December, 1995.     

Oscillatory convection in a horizontal porous layer saturated with a viscoelastic fluid

When a horizontal porous layer saturated with a viscoelastic liquid is heated from below, the onset conditions of thermal convection are found to be functions of Darcy-Rayleigh number, wave number, and viscoelastic properties. In this study, the linear stability was studied analytically in order to investigate the viscoelastic effects of saturated liquids on the onset conditions in connection with oscillatory instabilities at the threshold of stationary convection. It is suggested that the resulting oscillatory instabilities occur at lower values of Darcy-Rayleigh number than the critical value for the stationary convection. From the occurrence of oscillatory instabilities of viscoelastic liquid, it is expected that the periodic motion should be replaced by stationary modes in a horizontal porous layer.     

Laminar natural convection heat transfer from a slender vertical cone to a power-law fluid

A theoretical analysis of laminar natural convection heat transfer from a slender vertical cone to a power-law fluid has been done by the approximate integral method. Assuming unequal thermal and momentum boundary layer thicknesses, and using the appropriate boundary and compatibility conditions, a “similar” solution of the boundary layer equations has been obtained for high Prandtl numbers. Due to lack of experimental data for power-law fluids, a comparison of the predictions of the present analysis has been done with the experimental data available for Newtonian fluids and good agreement has been found.     

Buoyancy-driven convection in a horizontal fluid layer under uniform volumetric heat sources

Buoyancy effect in an internally heated horizontal fluid layer is considered under the linear stability analysis. The horizontal fluid layer is confined between a rigid adiabatic lower boundary and a rigid isothermal upper boundary. The onset of thermal convection is analyzed by using the propagation theory which transforms partial disturbance equations into ordinary ones similarly under the principle of exchanges of stabilities. The eigenvalue problem is solved by the method of rapidly converging power series. In addition, the connection of stability condition to the fully developed heat transport is investigated. Results show that the critical time to mark cellular convection has increased with a decrease in the Prandtl number. Based on the present stability criteria, a new correlation of the Nusselt number is produced as a function of both the Rayleigh number and the Prandtl number. It is shown that the present correlation on thermal convection compares reasonably with existing experimental data of water.     

Nonisothermal flow of a generalized power-law fluid in converging sections for rubber extrusion

A method for predicting pressure drop and temperature distribution in convergent sections is proposed. The generalized power-law rheological equation of state is used. Only the shear component of the converging flow is considered in order to estimate its contribution to total flow in such sections. A finite-difference scheme was used to simulate the flow. The method was applied to an ethylenepropylene terpolymer compound using different angles of approach for which the pressure drop and the extrudate temperature had been measured experimentally. Comparison with theoretically predicted data showed excellent agreement for small angles, while for large angles the inclusion of extensional effects was found to be necessary. The contribution of viscous dissipation effects was found to be negligible for the converging sections tested.     

壁面粗糙度对通道流动特性的影响

从管道壁面附近的流动结构着手,指出摩阻偏差系数不仅取决于相对粗糙度,还取决于粗糙元疏密度、流动再附长度等具体几何、水力特征,粗糙度对流阻的影响能否忽略不能单纯以相对粗糙度是否小于5%为标准。采用流道收缩效应的处理方法,理论地分析这些特征对偏差系数的影响,揭示出偏差系数随粗糙元密度与Re的增加而增加,粗糙元分布很疏或者Re很小时粗糙度的影响可以忽略的规律。     

Natural convection in a heat generating fluid bounded by two horizontal concentric cylinders

Convective flow and heat transfer of a Boussinesq fluid contained between two horizontal concentric cylinders is investigated under the effects of two driving mechanisms – an externally-imposed temperature gradient across the annulus, and a uniform internal heat generation. Numerical results for flow field and temperature distribution are obtained in terms of four dimensionless parameters, namely the radius ratio, R, the Prandtl number, Pr, the Rayleigh number, Ra*, and the ratio, S, between the characteristic temperature induced by internal heating and the applied temperature difference between the boundaries. Depending on the value of S, the flow pattern is made up of either one or two vortices in each half cavity, and heat is transferred into or out of the cavity through the hot wall. In particular, for a certain value of the applied temperature difference, the hot wall apparently acts as a thermally-insulated boundary, the internal heat is completely lost through the cold wall, and the fluid undergoes a transition from a bicellular to a unicellular flow regime.     

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.     

Dynamics of self-organizing single-line particle trains in the channel flow of a power-law fluid

The formation of self-organizing single-line particle train in a channel flow of a power-law fluid is studied using the lattice Boltzmann method with power-law index 0.6 ≤ n ≤ 1.2,particle volume concentration 0.8% ≤Φ≤ 6.4%,Reynolds number 10 ≤ Re ≤ 100,and blockage ratio 0.2 ≤ k ≤ 0.4. The numerical method is validated by comparing the present results with the previous ones.The effect n,Φ,Re and k on the interparticle spacing and parallelism of particle train is discussed.The results showed that the randomly distributed particles would migrate towards the vicinity of the equilibrium position and form the ordered particle train in the power-law fluid.The equilibrium position of particles is closer to the channel centerline in the shear-thickening fluid than that in the Newtonian fluid and shear-thinning fluid.The particles are not perfectly parallel in the equilibrium position,hence IH is used to describe the inclination of the line linking the equilibrium position of each particle.When self-organizing single-line particle train is formed,the particle train has a better parallelism and hence benefit for particle focusing in the shearthickening fluid at high Φ,low Re and small k.Meanwhile,the interparticle spacing is the largest and hence benefit for particle separation in the shear-thinning fluid at low Φ,low Re and small k.     

Combined forced and free convection flow past a horizontal flat plate

The problem of simultaneous forced and free convection flow of a Newtonian fluid past a hot or cold horizontal flat plate is investigated by means of numerical solutions of the full equations of motion and thermal energy subject only to the Boussinesq approximation. These solutions span the parameter ranges 10 ≤ Re ≤ 100, 0.1 ≤ Pr ≤ 10, and –2.215 ≤ Gr/Re^5/2 ≤ 2.215 where Re, Pr, and Gr are based on the ambient free stream fluid properties and the overall plate length l. When Gr > 0, the boundary flow near the plate surface is accelerated relative to the corresponding forced convection flow, with a resulting increase in both the local skin friction and heat transfer coefficients. When Gr < 0, the boundary flow is decelerated, the local skin friction and heat transfer are decreased, and the flow actually separates for Gr/Re^5/2 < –0.8 when Pr = 0.7. In the latter circumstance, an increasing degree of upstream influence is observed as Gr/Re^5/2 is further decreased.     

撞击流反应器内幂律流体流动特性的数值模拟

采用数值模拟方法对撞击流反应器内幂律流体的流动特性进行研究,分析了不同喷嘴间距和入口流速下清水和不同质量分数幂律流体的径向射流扩展率、径向速度衰减率、剪切应力、表观黏度等分布规律,研究表明：幂律流体中径向射流的径向速度分布规律与清水径向射流相似。随喷嘴间距的增大,扩展率增大,径向速度衰减率减小,平均剪切应力呈先增大后减小的变化规律,其中L=3D时平均剪切应力值最大,更利于流体混合。入口流速越大,扩展率越小,径向速度衰减率越大,平均剪切应力也随之增大。幂律流体的平均剪切应力大于清水,且随质量分数的增大,其扩展率增大,为清水扩展率的1.3~3.3倍,而幂律流体的径向速度衰减率从-1.268~-1.125降低到-1.144~-1.082,逐渐小于清水。幂律流体径向射流区域的剪切应力呈“M”形分布,表观黏度则呈“W”形分布,流体的流变性质对撞击流反应器内流体的流动规律影响显著。     

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.     

Lattice Boltzmann simulation of power-law fluid flow in the mixing section of a single-screw extruder

The single-screw extruder is commonly used in polymer processing where the performance of the mixing section is significant in determining the quality of the final product. It is therefore of great interest to simulate the flow field in a single-screw extruder. In this paper simulations of non-Newtonian fluids in a single-screw extruder are performed using the lattice Boltzmann model.     

Free convection boundary-layer flow over horizontal plates and discs

Free convection flows near horizontal surfaces are discussed for those cases in which a similarity solution can be obtained. Particular cases considered are those of asymptotically large and vanishingly small Prandtl numbers. The solution for the relevant velocity, temperature and pressure functions has to be carried-out numerically. For the particular cases when the Prandtl number is either sufficiently large, or sufficiently small, this integration would yield general functions, no longer dependent on the Prandtl number. Numerical data are included.     

Mixed convection mass transfer studies of opposing and aiding flow in a parallel plate electrochemical flow cell

Studies of combined natural and forced convection in a vertical parallel plate electrochemical cell in laminar conditions in cases of opposing and aiding flow are reported. In an ongoing project it was necessary to identify conditions in which natural convection had no significant influence on mass transfer rates at the cell walls so that data could be validly compared with purely laminar flow computational models. For the different electrode lengths investigated, natural convection dominated at low Reynolds number and there was no Reynolds number dependence. At high Reynolds number the data approached the laminar flow solution. At intermediate Reynolds number, however, there existed a distinct region where free and forced convection were significant. At high electrolyte concentrations data did not merge with laminar flow equations until Re=1000 and low electrolyte concentration data for the large plate could not be compared with numerical predictions below Re of 250. An attempt was made to compare the data with those of other workers on combined forced and natural convection heat and mass transfer.     

Mixed convection in a doubly stratified micropolar fluid saturated non‐Darcy porous medium

The effects of thermal and solutal stratification on mixed convection along a vertical plate embedded in a micropolar fluid saturated non‐Darcy porous medium are analysed. The nonlinear governing equations and their associated boundary conditions are initially cast into dimensionless forms by pseudo‐similarity variables. The resulting system of equations is then solved numerically using the Keller‐box method. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. The velocity, microrotation, temperature and concentration profiles are shown for different values of the coupling number, non‐Darcy parameter, mixed convection parameter, thermal and solutal stratification parameters. The numerical values of the skin friction, wall couple stress, heat and mass transfer rates for different values of governing parameters are also tabulated. © 2011 Canadian Society for Chemical Engineering     

Flow of a temperature dependent power-law model fluid between parallel plates: An approximation for flow in a screw extruder

This paper formulates concisely the problem of fully developed flow of a temperature dependent power-law fluid between parallel plates. An exact solution, in the absence of pressure gradients, is developed. The method has been validated by a comparison with an independent numerical solution. This work is applicable to melt transport in shallow partly filled screw channels, drag flow regimes in the metering zone of a screw extruder and, generally, to flows in hydrodynamically thin layers associated with negligible pressure gradients. A numerical example is included dealing with the extrusion of polypropylene. A general discussion is given concerning the utility of the new theory. Effects of pressure gradients are included in the discussion.