EFFECTIVE CONDUCTIVITY OF A DILUTE SUSPENSION AT MODERATE PARTICLE PECLET NUMBERS

The contribution of a shear field to the effective conductivity of a dilute suspension of small particles freely suspended in a viscous fluid is examined. The case of long cylindrical inclusion aligned parallel to the vorticity of a simple shear flow is calculated for particle Peclet numbers of O(1). The solution involves a combination of a domain perturbation and a numerical calculation for the far and the near fields, respectively. The resulting convective contribution to the bulk heat flux is compared with previous asymptotic analysis for Pe → ∞.     

THE LOCAL VOLUME-AVERAGED EQUATIONS OF MOTION FOR A SUSPENSION OF NON-NEUTRALLY BUOYANT SPHERES

The local volume averages of the equations of motion as well as the appropriate boundary conditions are developed for a flowing suspension of non-neutrally buoyant, uniform spheres in an incompressible Newtonian fluid under conditions such that inertial effects can be neglected. These equations do not represent an asymptotic theory with respect to the volume fraction of solids. Higher order terms have been retained everywhere, except where it has been necessary to estimate the velocity distribution within the immediate neighborhood of each sphere by neglecting the effects of the other spheres present. The resulting local volume-averaged equations of motion and boundary conditions involve no free or undetermined parameters.

For the special case of a very dilute suspension of neutrally buoyant spheres, the total local volume average of Cauchy's first law reduces to the form of the Navier-Stokes equation with the effective viscosity computed by Einstein (1906, 1956).

In two succeeding papers, we demonstrate for several flows [in vertical tubes, in a cone-plate viscometer, between rotating concentric cylinders (Couette flow), and between rotating parallel plates] that our general theory describes more concentrated neutrally buoyant suspensions than does its limiting case of very dilute suspensions.     

A CONCISE INTRODUCTION TO SURFACE RHEOLOGY WITH APPLICATION TO DILUTE EMULSIONS OF VISCOUS DROPS

A concise review is provided of fundamentals of interfacial transport and rheology, which includes simple proofs of the surface divergence theorem and the surface Reynolds transport theorem, needed in the derivations. The results are applied to the prototype example of a dilute emulsion of spherical drops suspended in an immiscible continuous fluid, in the circumstance where the interface separating the two phases possesses its own Theological properties (i.e., surface shear and dilatational viscosities). The low-Reynolds-number hydrodynamics of the emulsion droplets in a general linear flow is analyzed using invariant methods, providing the velocity, pressure and stress fields everywhere and allowing the leading order deformation of the drops to be calculated. The average stress in the dilute emulsion is also obtained to first order in the volume fraction of the dispersed phase. The results suggest that simultaneous measurements of the effective viscosity of the emulsion and the deformation of the drops in a linear shear flow can provide an indirect experimental determination of the surface shear and dilatational viscosities.     

Conjugate transport in polymer melt flow through extrusion dies

A numerical study is carried out on the conjugate thermal transport in polymer and food melts flowing through extrusion dies. The simulation is performed to determine the influence of conduction through the die wall and of the thermal boundary conditions on the transport in the fluid and on the conditions at the outlet. An extrusion die with a uniform temperature or heat transfer coefficient specified at the outer surface is considered. It is found that, because of conduction in the solid wall, important physical variables such as centerline velocity, pressure drop, bulk temperature of the fluid and shear experienced by the fluid are strongly affected by the boundary conditions, as well as by the wall thermal conductivity and thickness. Channels of different geometries are used for the study. The flow in a circular straight tube with constant wall thickness is studied first. Flow and thermal transport in different, constricted, channels are studied next. Different wall materials are also considered. Comparisons with some experimental results are presented, indicating good agreement. The fluids considered in this study are highly viscous, polymer melts. Due to high viscous dissipation and temperature-dependent viscosity, the flow and heat transfer are coupled and the problem is quite complicated. The results show that, for some operating conditions, the bulk temperature can be high enough to cause significant heat transfer from the fluid to the wall. The downstream variation in the pressure and temperature are calculated. The thermal boundary conditions are found to have a strong influence on the temperature field and thus on the flow. The general dependence of pressure drop on temperature, flow rate, and geometry is investigated. Several other basic aspects of this problem are also discussed.     

Steady-shear rheological behavior of the suspension of spherical particles in a second-order fluid

In this paper we study the rheological behavior of a dilute suspension of rigid spherical particles in a second-order fluid. We extend the results of viscous fluids to discuss the expression for the bulk stress tensor of a second-order fluid and also obtain an approximate solution to the shear flow problem of this fluid. By combing these results, we write an approximate constitutive equation for the bulk stress tensor for such a suspension and study it in a shear flow. It is found that the new equation predicts no variation in the shear viscosity, but predicts enhancement of the pre-existing non-Newtonian nature of the suspending fluid with regard to the normal stress functions.     

Heat transfer and flow behaviour of aqueous suspensions of titanate nanotubes (nanofluids)

Titanate nanotubes of an aspect ratio of ~ 10 are synthesized, characterised and dispersed in water to form stable nanofluids containing 0.5, 1.0 and 2.5 wt.% of the nanotubes. Experiments are then carried out to investigate the effective thermal conductivity, rheological behaviour and forced convective heat transfer of the nanofluids. The results show a small thermal conductivity enhancement of ~ 3% at 25 °C and ~ 5% at 40 °C for the 2.5 wt.% nanofluid. The nanofluids are found to be non-Newtonian with obvious shear thinning behaviour with the shear viscosity decreasing with increasing shear rate at low shear rates. The shear viscosity approaches constant at a shear rate higher than ~ 100-1000 s^− 1 depending nanoparticle concentration. The high shear viscosity is found to be much higher than that predicted by the conventional viscosity models for dilute suspensions. Despite the small thermal conduction enhancement, an excellent enhancement is observed on the convective heat transfer coefficient, which is much higher than that of the thermal conductivity enhancement. In comparison with nanofluids containing spherical titania nanoparticles under similar conditions, the enhancement of both thermal conductivity and convective heat transfer coefficient of the titanate nanotube nanofluids is considerably higher indicating the important role of particle shape in the heat transfer enhancement. Possible mechanisms are also proposed for the observed enhancement of the convective heat transfer coefficient.     

THE EFFECTS OF VARIABLE FLUID PROPERTIES ON MHD MAXWELL FLUIDS OVER A STRETCHING SURFACE IN THE PRESENCE OF HEAT GENERATION/ABSORPTION

An analysis is performed to investigate the effects of variable viscosity and thermal conductivity on the two-dimensional steady flow of an electrically conducting, incompressible, upper-convected Maxwell fluid in the presence of a transverse magnetic field and heat generation or absorption. The governing system of partial differential equations is transformed into a system of coupled nonlinear ordinary differential equations, and is solved numerically. Velocity and temperature fields have been computed and shown graphically for various values of the physical parameters. The local skin-friction coefficient and the local Nusselt number have been tabulated. It is found that fluid velocity decreases with an increase in the viscosity parameter and the Deborah number. It is also observed that increasing the magnetic parameter leads to a fall in the velocity and a rise in the temperature. Furthermore, it is shown that the temperature increases due to increasing the values of the thermal conductivity parameter and the heat generation parameter, while it decreases with an increase of both the absolute value of the heat absorption parameter and the Prandtl number.     

SPHERICAL FURNACE CALORIMETER FOR DIRECT MEASUREMENT OF SPECIFIC HEAT AND THERMAL CONDUCTIVITY*

A spherical calorimeter was constructed for measuring true specific heat and thermal conductivity. It was formed of two concentric spherical platinum shells, and a spherical sample was fitted into the inner shell. Electric heat was supplied at the center of the sample, and the calorimeter was housed in a spherical electric furnace. Thermal conductivity was measured by determining the inner and outer sample temperatures at steady heat flow using the equation of heat conduction in a sphere; specific heat was measured by noting the temperature rise of the sample with a known heat input while maintaining the calorimeter shells near the adiabatic condition; and a correction for heat leakage was made by using the conductivity determination to calculate this factor. Specific heat and thermal conductivity measurements were made on quartz sand, chrome refractory cement, four types of insulating firebrick, and 85% magnesia insulation over a total temperature range of 100° to 2200°F. The estimated accuracy of specific heat measurement of 3 to 5% is consistent with engineering requirements. No estimate of accuracy can be given as yet for thermal conductivity results.     

Thermal conductivity improvement of phase change materials/graphite foam composites

Effective thermal conductivity of composites of graphite foam infiltrated with phase change materials (PCM) was investigated numerically and experimentally. Graphite foam, as a highly-conductive, highly-porous structure, is an excellent candidate for infiltrating PCM into its pores and forming thermal energy storage composites with improved effective thermal conductivity. For numerical simulation, the graphite structure was modeled as a three-dimensional body-centered cube arrangement of uniform spherical pores, saturated with PCM thus forming a cubic representative elementary volume (REV). Thermal analysis of the developed REV was conducted for unidirectional heat transfer and the total heat flux was determined, which leads to the effective thermal conductivity evaluation. For experimental verification, a sample of graphite foam was infiltrated with PCM. The effective thermal conductivity was evaluated using the direct method of measuring temperature within the sample under fixed heat flux in unidirectional heat transfer. The results indicate a noticeable improvement in the effective thermal conductivity of composites compared to the PCM. Our numerical and experimental results are in agreement and are also consistent with reported experimental results on graphite foam. Moreover, the role of natural convection within the pores is found to be negligible.     

边界条件对石英纤维增强陶瓷基复合材料局部结构温度场的影响分析

随着航天技术的发展,局部复杂结构的温度场预测显得尤为重要。本文针对非烧蚀条件下局部结构温度场预测,分别采用将热流密度通过一维有限元差分计算方法转换成表面温度的定温度边界和直接采用定热流边界的计算方法得出的计算结果进行了对比和分析。得出了对于局部结构中石英纤维增强陶瓷基复合材料,采用定热流边界和定温度边界的计算方法同样合适;对于局部结构中热导率较大的表面材料,采用定热流边界的计算结果更趋合理。     

HEAT TRANSFER IN THE THERMAL ENTRANCE REGION OF AN INTERNALLY HEATED FLOW

The passage of an electrical current through a liquid causes the evolution of heat and when the electrical conductivity depends on the temperature, the rate of evolution varies from point to point in the fluid. Within the thermal entrance region of a duct flow, competition between the rate of evolution and the rate of conduction to bounding surfaces, coupled with differences in residence time between points in planes perpendicular to the flow direction causes local maxima in the temperature field in such planes. The evolution of such temperature fields is studied here using Galerkin's method to approximate solutions of the appropriate differential equation. Temperature fields of this sort influence the electrophoretic migration of small particles in the process known as continuous flow electrophoresis.     

Heat transfer of gas flow through a packed bed

This paper reports an experimental study of both the transient and steady-state heat transfer behaviour of a gas flowing through a packed bed under the constant wall temperature conditions. Effective thermal conductivities and convective heat transfer coefficient are derived based on the steady-state measurements and the two-dimensional axial dispersion plug flow (2DADPF) model. The results reveal a large temperature drop at the wall region and the temperature drop depends on the axial distance from the inlet. The 2DADPF model predicts the axial temperature distribution fairly well, but the prediction is poor for the radial temperature distribution. Length-dependent behaviour of the effective heat transfer parameters and non-uniform flow behaviour are proposed to be responsible. A comparison with previously published correlations and data in the literature shows that the relationships proposed by Bunnell et al. and Demirel et al. agree well with the measured effective radial thermal conductivity, whereas the wall-fluid heat transfer coefficient is better represented by the Li-Finlayson correlation.     

HEAT TRANSFER IN THE THERMAL ENTRANCE REGION OF AN INTERNALLY HEATED FLOW

The passage of an electrical current through a liquid causes the evolution of heat and when the electrical conductivity depends on the temperature, the rate of evolution varies from point to point in the fluid. Within the thermal entrance region of a duct flow, competition between the rate of evolution and the rate of conduction to bounding surfaces, coupled with differences in residence time between points in planes perpendicular to the flow direction causes local maxima in the temperature field in such planes. The evolution of such temperature fields is studied here using Galerkin's method to approximate solutions of the appropriate differential equation. Temperature fields of this sort influence the electrophoretic migration of small particles in the process known as continuous flow electrophoresis.     

Thermal insulation characteristics of roll forming alumina ball material

Rolling ceramic thermal insulation balls have advantages of low cost, large output and easy control of particle size, so it is likely to become the main raw material for 3D printing in the future, but there is little research on its thermal insulation. In this study, we used three kinds of rolling aluminum oxide balls as raw materials to obtain single-granularity-level and multi-granularity-level bulk materials. And the effects of temperature, particle size, and thermal fatigue times on the thermal conductivity of the samples were analyzed. Additionally, the experimental results were verified by FloEFD heat conduction simulation software using finite analysis method to analyze their heat conduction characteristics. With the increase of temperature from 400 °C to 1500 °C, the thermal conductivity of single-granularity-level and multi-granularity-level bulk materials increased linearly. The thermal conductivity of single-granularity-level bulk materials have no direct relationship with the particle size, and the thermal conductivity of multi-granularity-level materials with small particle size difference was a bit lower than that of materials with large particle size difference, and a bit higher than that of materials with single-granularity-level. The simulation results showed that the main reason for the above phenomenon was that the point contact between particles played a dominating role in the heat transfer process. When the contact area increased, the thermal conductivity increased obviously, and the thermal conductivity with the increasing of temperature decreased in a quadratic curve. The improved model considering the shrinkage could improve accuracy of simulation results. Heat flux at the surface contact area was 10.19 times higher than that of the point contact and 15.10 times higher than that of the solid-gas contact at 400 °C. Therefore, reducing the surface contact area and increasing the porosity could significantly reduce the thermal conductivity of the materials.     

THE EFFECT OF VARIABLE THERMAL CONDUCTIVITY ON MICRO-POLAR FLUID FLOW BY CHEBYSHEV COLLOCATION METHOD

In this article, the authors analyzed the effect of thermal conductivity on unsteady magnetohydrodynamic (MHD) free convection in a micro-polar fluid past a semi-infinite vertical porous plate. The fluid thermal conductivity is assumed to vary as a linear function of temperature. By using the Chebyshev collocation method in the spatial direction and the Crank-Nicolson method in the time direction, the boundary layer equations are transformed into a linear algebraic system. There are several material parameters whose affect on the flow have been studied, for instance, thermal conductivity, radiation, magnetic, micro-polar, suction (or injection) parameters, and Prandtl number. Boundary layer and Boussineq approximations have been introduced together to describe the flow field. The domain of the problem is discretized according to the Chebyshev collocation scheme. The numerical results show that, the values of velocity, angular velocity and temperature profiles approach to the steady state when the time reach to infinity. However, the friction factor has been found to increase as micro-polar and thermal conductivity parameters increase. But it decreases as magnetic parameter increases. Meanwhile, Nusselt number increases as thermal conductivity parameter increases, and vice versa with the micro-polar parameter. Moreover, the local couple stress has been found to decrease as micro-polar and thermal conductivity parameters increase. On the other hand, it increases as magnetic parameter increases.     

混合蒸气冷凝过程中均匀温度面上液滴自发移动现象及特性

在某些混合蒸气的冷凝过程中，传热面温度梯度导致冷凝液浓度及表面张力不平衡，从而驱动冷凝液滴产生自发移动现象。此现象产生的前提为传热面具有整体温度分布，即传热面从一侧表面的相对低温状态，随着表面位置变化逐渐过渡到另一侧的相对高温状态，而本论文在水-酒精混合蒸气的冷凝过程中，观测到在均匀温度传热面上也会发生冷凝液滴自发移动现象。通过对具有和不具有初速度的冷凝液滴在均匀传热面上的不同移动特性进行比较分析，确认了具有明显初速度的冷凝液滴在均匀温度领域产生自发移动现象，而无初速度液滴则产生无序运动（非自发移动）。从而验证了在均匀温度传热面，冷凝液滴自发移动的驱动力为液滴移动同时其周围形成的局部温度分布和局部表面张力不平衡的推测。     

INTERACTION OF THERMAL RADIATION IN THE LAMINAR PIPE FLOW OF OPTICALLY THIN GASES

The influence of thermal radiation on laminar forced convection of a gray gas in a pipe flow is studied semi-analytically. The gas is considered as an absorbing-emitting medium and the thin gas model approximation is used to describe the radiative heat flux in the energy equation. Invoking the method of lines (MOL), the nonlinear boundary value problem is reduced to an initial value problem which is eventually solved by a standard Runge-Kutta integration scheme. Numerical results are presented graphically for a selected group of thermal parameters encompassing the thin gas behavior. Additionally, it is found that limiting cases namely: laminar plug flow and laminar parabolic flow, both in the absence of radiation define an envelope for the curves of bulk temperature and total Nusselt number describing the combined thermal process for a thin gas in laminar motion. In general, the comparisons reveal that these asymptotic solutions are valid when the entrance-to-wall temperature ratio is less than 2.     

IGNITION DELAY OF DROPLET CLOUDS: RESULTS FROM GROUP COMBUSTION THEORY

The ignition and evaporation of spherical cloud of droplets in a hot quiescent atmosphere is examined numerically using transient group combustion analysis. Ignition delay times are calculated as a function of cloud radius, ambient temperature, drop size and droplet number density. The ignition temperature for a cloud of drops was found to be less than that obtained from a single drop. The results indicated an interaction between chemical and physical effects resulting in the possibility of an optimal interdrop spacing for ignition of a fuel with a high boiling point. The model results indicate that for interdrop spacing to radius ratio of less than 5, the ignition and evaporation of a cloud of drops is confined to a thin layer at the surface of the cloud. For drops spaced farther apart thermal penetration from the hot ambient is possible resulting in vaporization within the cloud.     

Effect of spoiler columns on heat transfer performance of aluminum nitride-based microchannel heat sink

Microchannel heat sinks (MCHSs) are among the most effective solutions for high-power heating elements; aluminium nitride (AlN) is widely used in various heat sinks owing to its high thermal conductivity. The study aims to investigate the effect of the spoiler column shape, number of rows, and position of the inlet/outlet on the temperature and pressure drop of AlN-based microchannel heat sink using a thermal fluid structure coupling simulation. The results showed that the circular spoiler column had the best dredging effect on the eddy current, which greatly improved the local Nusselt number and heat transfer efficiency. The maximum temperature of the heat sink with circular spoiler columns was 6.53 K lower than that without the spoiler column. The average flow velocity and heat transfer efficiency increased with an increase in the number of spoiler columns and the convective heat transfer area. However, the flow resistance and pressure drop between the inlet and outlet raised. When the inlet and outlet were arranged at the centreline, the flow velocity distribution in the heat sink is more uniform, and the maximum temperature was 160.78 K lower than that on the upper side. Heat transfer experiments were carried out by using three kinds of AlN-based microchannel heat sinks, which was machined by the pickling-assisted laser method. The heat transfer experiments showed that the error between simulation results and test data was less than 0.1%.     

DROP DISPERSION IN SUSPENSION POLYMERIZATION

Four models, two based on laminar shear and two based on turbulent flow, are proposed to describe drop dispersion in non-coalescing systems. The models predict the largest surviving drop size _dmax as a function of geometry, speed and physical property variables.

Laboratory data including suspension polymerization runs support the boundary layer laminar shear model for drops larger than approximately 200 microns. Smaller drops support a turbulence model.

The boundary layer shear model was confirmed in scale-up suspension polymerization runs aimed at producing 1000 micron maximum bead sizes. Five approximately geometrically similar polymerizers were used, varying in size from 7.5 to 15000 liters.