Heat Transfer Analysis of a Microspherical Particle in the Slip Flow Regime by Considering Variable Properties

In order to investigate how far the temperature-dependent fluid properties and characteristic length influence the drag coefficient and the heat flux, a three-dimensional simulation study for a slip flow around an unconfined microspherical particle has been performed. Gas properties such as density, viscosity, conductivity, and mean free path were assumed to vary with temperature. Slip velocity and temperature jump at the gas particle interface were both treated numerically by imposition of the slip boundary conditions. The effects of variable gas properties and Knudsen number on momentum and heat transfer were also taken into account. It was concluded that for microflows with high heat transfer rates, the constant fluid properties approximation is very crude. In addition, the slip velocity and temperature jump affect the heat transfer in opposite ways: a large slip on the wall increases the convection along the surface, whereas a large temperature jump decreases the heat transfer by reducing the temperature gradient at the wall. Therefore, neglecting temperature jump will result in the overestimation of the heat transfer coefficient.     

Turbulent free convection flowÉcoulement turbulent de convection naturelleTurbulente freie konvektionsströmungCвoбoднoкoнвeкTивный тupбuлeнтный пoтoк

The results of an experimental investigation of a turbulent free convection boundary layer are presented for a fluid with a low Prandtl number (mercury). The boundary layer was formed along the isothermally heated vertical wall of a cell.The measured mean temperature profiles and turbulent temperature distributions, indicated the existence of a fully developed boundary layer.In the recorded temperature spectra the high frequencies region, associated with dissipation, was found to exhibit an ?^?3 dependence (? is the frequency of the temperature fluctuations). The presence and development of a “convection subrange” was also identified, dependent upon the Rayleigh number and the location of the point of measurement with respect to the wall.     

An analytical solution for thermocapillary-driven convection of superimposed fluids at zero Reynolds and Marangoni numbers

This study aims to investigate thermocapillary-driven convection in two superimposed fluids in zero gravity. The fluids occupy the space between the walls of a horizontal microchannel which is heated from below by imposing the top wall to a uniform temperature and the bottom wall to a sinusoidal temperature that is higher (on the average) than the temperature of the top wall. The goal is to mimic thermocapillary convection as a result of the variation of the heights of the fluids along the microchannel and to explore the parameters that affect the fluid flow and interface deformation. This is achieved by solving the equations of conservation of mass and momentum and the balance of thermal energy and negligible analytically in both fluids, in the limit of creeping flow regime and negligible convection of heat. It is shown that the induced flow is characterized by periodic convection cells whose period is the same as the period of the imposed temperature field and extend from the interface to the walls in the vertical direction. The flow strength depends on the relative thicknesses of the fluid layers and the ratio of material properties. The maximum flow strength is achieved at a relative thickness that is set by the competition between the thermal and hydrodynamic effects. An estimate of the interface deformation is provided and it is shown that the sense of interface deformation is set by the relative thickness of the fluid layers and the viscosity ratio.     

Penetrative flow due to an isothermal vertical wall in a stable two-layer environment generated by a room fire

An experimental investigation has been carried out on the penetrative natural convection flow and thermal transport resulting from an isothermal vertical surface immersed in a stably stratified, twolayer, ambient medium, in which an essentially isothermal heated layer overlies a relatively cooler isothermal layer of the same fluid. Measurements of the thermal field are carried out for several surface temperatures and the corresponding isotherms obtained. The surface temperature is taken as lower than the upper layer temperature so that a downward natural convection flow is generated adjacent to the surface in the upper zone and the penetration of this flow into the lower region is investigated. Velocity and temperature profiles are measured to determine the mass flow rates across the interface between the two regions. The local heat transfer rates are also measured at various locations on the isothermal plate. For the surface temperature lying between the upper and lower layer temperatures, an upward flow is generated in the lower region and a downward flow in the upper region. The two flows collide near the interface, giving rise to transport across the interface.     

Uni-directional heat flux through the horizontal fluid layer with sinusoidal wall temperature at the top or bottom boundaries

Infinite horizontal fluid layer is considered between the top and bottom walls. Either top or bottom wall temperature is sinusoidally oscillated in terms of the constant average temperature in an opposing horizontal wall. This is the system with no temperature difference between the top and bottom walls in time-averaged sense, as studied by Kalabin et al. for a square channel. The fluid is Newtonian and Boussinesq approximation is made. The fluid layer of height 1 versus the horizontal width 1 or 4 is adopted and numerical computations are carried out for Pr = 1. The time-averaged Nusselt numbers computed both at top and bottom walls give the upward time-averaged heat flux without depending on the temperature oscillation either at the upper or lower walls. This is because the time-dependent convection plumes occur at the almost largest temperature of the bottom wall in comparison to the top wall. The time-averaged heat flux is always positive, i.e., upward, even if the time-averaged temperature difference is zero between the top and bottom walls.     

Experimental studies on transient features of natural convection in particles suspensions

Particle Tracking Velocimetry (PTV), in conjunction with the refractive index matching technique and laser induced fluorescent (LIF) tracer particles, was used to overcome the visualization problem in a particle suspension. A square test section was filled with the particle suspension and impulsively heated from the bottom wall while the two facing vertical walls were kept at a constant temperature. The two-dimensional velocity fields, particle distributions in a plane and the wall temperature fields were visualized simultaneously using three cameras. The results showed peculiar flow patterns such as the formation and vanishing of two-layer convection cells which were distinct from those in a clear, particle-free fluid. Sedimentation driven convection is thought to be the fundamental mechanism for the formation of these two layer convection cells. The overlying particle-free-layer convection was started by the release of the heated clear fluid at the interface between the particle-free layer and the suspension.     

物性参数对环形空间流动和传热影响的模拟研究

利用有限容积法,建立了环形空间内单相流体竖直向上流动过程中流动和传热的稳态模型。模型将环形空间内管设置为具有固定生热速率的发热体;流体与内管壁之间设置流动和传热边界层,以更精确的描述壁面位置流体与固体之间动量和热量的耦合传递过程。通过与常物性模型的对比,流体密度、导热系数和黏度随温度变化的变物性模型,在传热能力上具有一定的减少,流体与固体传热面之间的界面剪切力稍有下降。通过比较常物性模型和变物性模型的Re和Ri,结果表明,随着流体强制循环速度的加大,流体物性变化对流动和传热过程的影响逐渐减小。     

MHD effect on the critical temperature differences of oscillatory thermocapillary convection in two-layer fluid system

The effect of different directional magnetic fields on critical temperature differences of oscillatory thermocapillary convection in a rectangular cavity with differentially heated side walls filled with two viscous, immiscible, incompressible fluids is simulated in the absence of gravity. In this two-layer fluid system, the upper layer fluid is the electrically non-conducting encapsulant boron oxide (B₂O₃), while the lower one is the electrically conducting molten indium phosphide (InP). The interface between the two fluids is assumed to be flat and non-deformable. The computational results show that all the magnetic fields along the x, y and z directions can delay the transition from steady convection to oscillatory convection, and critical temperature differences increase with an increasing Hartmann number. Furthermore, the effect of a magnetic field along the z direction is strongest, followed by that along the y direction, and that along the x direction is the weakest for the same intensity of the magnetic field.     

Natural convection heat transfer in a circular enclosure

Natural convection heat transfer in a circular enclosure, one half of which was heated and the other half of which was cooled, was investigated experimentally, focusing on the effect of the inclination angle. The experiments were carried out with water. Flow and temperature field were visualized by using the aluminum and liquid-crystal suspension method. The results show that with downward heating the heat transfer coefficient increased as the inclination angle of the boundary between the heating wall and the cooling wall approached the vertical. But with upward heating, the heat transfer coefficient showed minimal change, exhibiting a small peak value when the inclination angle was γ ˜ –45°. The heat transfer coefficient of a flat circular enclosure was estimated from the circular enclosure's heat transfer coefficient. These results can be explained by the obtained flow and temperature fields. © 1999 Scripta Technica, Heat Trans Asian Res, 28(2): 152–163, 1999     

Conduction-combined forced and natural convection in lid-driven enclosures divided by a vertical solid partition

Numerical simulations of the conduction-combined forced and natural convection (mixed convection) heat transfer and fluid flow have been performed for 2-D lid-driven square enclosure divided by a partition with a finite thickness and finite conductivity. Left vertical wall of enclosure has two different orientations in positive or negative vertical coordinate. Buoyancy forces are taken into account in the system. Horizontal walls are adiabatic while two vertical walls are maintained isothermal temperature but the temperature of the left moving wall is higher than that of the right stationary wall. Thus, heat transfer regime between moving lid and partition is mixed convection. Conduction occurs along the partition. And, pure natural convection is formed between the partition and the right vertical wall. This investigation covers a wide range of Richardson number which is changed from 0.1 to 10, thermal conductivity ratio varies from 0.001 to 10. It is observed that higher heat transfer was formed for higher Richardson number for upward moving wall for all values of thermal conductivity ratio. When forced convection becomes effective, the orientation of moving lid becomes insignificant. Heat transfer is a decreasing function of increasing thermal conductivity ratio for all cases and Richardson numbers.     

Laminar free-convection in glycerol with variable physical properties adjacent to a vertical plate with uniform heat flux

The steady laminar boundary layer flow of glycerol along a vertical stationary plate with uniform heat flux is studied in this paper. The density, thermal conductivity and heat capacity of this liquid are linear functions of temperature but dynamic viscosity is a strong, almost exponential, function of temperature. The results are obtained with the numerical solution of the boundary layer equations. Both upward flow (plate heating) and downward flow (plate cooling) is considered. The variation of μ with temperature has significant influence on wall heat transfer and much stronger influence on wall shear stress. It was also found that the similarity exponent, which is equal to 0.20 for the classical problem with constant properties, is lower than 0.20 in the upward flow and higher than 0.20 in the downward flow.     

An investigation into the heat transfer characteristics of spiral wall with internal rib in a supercritical sliding-pressure operation once-through boiler

Within the pressure range of 9–28 MPa, mass velocity range of 600–1 200 kg/(m²·s), and heat flux range of 200–500 kW/m², experiments were performed to investigate the heat transfer to water in the inclned upward internally ribbed tube with an inclined angle of 19.5 degrees, a maximum outer diameter of 38.1 mm, and a thickness of 7.5 mm. Based on the experiments, it was found that heat transfer enhancement of the internally ribbed tube could postpone departure from nucleate boiling at the sub-critical pressure. However, the heat transfer enhancement decreased near the critical pressure. At supercritical pressure, the temperature difference between the wall and the fluid increased near the pseudo-critical temperature, but the increase of wall temperature was less than that of departure from nucleate boiling at sub-critical pressure. When pressure is closer to the critical pressure, the temperature difference between the wall and the fluid increased greatly near the pseudo-critical temperature. Heat transfer to supercritical water in the inclined upward internally ribbed tube was enhanced or deteriorated near the pseudo-critical temperature with the variety of ratio between the mass velocity and the heat flux. Because the rotational flow of the internal groove reduced the effect of natural convection, the internal wall temperature of internally ribbed tube uniformly distributed along the circumference. The maximum internal wall temperature difference of the tube along the circumference was only 10 degrees when the fluid enthalpy exceeded 2 000 J/g. Considering the effect of acute variety of the fluid property on heat transfer, the coreelation of heat transfer coefficient on the top of the internally ribbed tube was provided. Translated from Proceedings of CSEE, 2005, 25(16): 90–95 [译自: 中国电机工程学报]     

Upward Heat Flux Through the Horizontal Fluid Layer of Water with Sinusoidal Wall Temperature at the Top or Bottom Boundary

Either top or bottom wall temperature of an infinite horizontal fluid layer at Pr = 6 is sinusoidally oscillated with constant average temperature on the opposing horizontal wall. This is a system with no temperature difference between the top and bottom walls in a time-averaged sense, as studied by Kalabin et al. for a square channel. The fluid is water, and the Boussinesq approximation is made. The computational region of height 1 and horizontal width 1 is adopted and numerical computation is carried out. The results show that the fluctuating Nusselt numbers computed at both the top and bottom walls give positive time-averaged values for two different frequencies computed. Time-dependent convection plumes occur when the bottom wall temperature becomes higher than the top wall temperature. The time-averaged heat flux is always positive, i.e., upward, even if the time-averaged temperature difference is zero between the top and bottom walls. This holds even if the oscillating temperature is on either the top or bottom wall. Two periods of temperature oscillation give one period of oscillation in flow and Nu, at least for the parameters studied.     

MHD effect on the critical temperature differences of oscillatory thermocapillary convection in two-layer fluid system

The effect of different directional magnetic fields on critical temperature differences of oscillatory thermocapillary convection in a rectangular cavity with differentially heated side walls filled with two viscous, immiscible, incompressible fluids is simulated in the absence of gravity. In this two-layer fluid system, the upper layer fluid is the electrically non-conducting encapsulant boron oxide (B₂O₃), while the lower one is the electrically conducting molten indium phosphide (InP). The interface between the two fluids is assumed to be flat and non-deformable. The computational results show that all the magnetic fields along the x, y and z directions can delay the transition from steady convection to oscillatory convection, and critical temperature differences increase with an increasing Hartmann number. Furthermore, the effect of a magnetic field along the z direction is strongest, followed by that along the y direction, and that along the x direction is the weakest for the same intensity of the magnetic field.     

Downward heat transfer in heat-generating boiling pools

A model for heat transfer from the horizontal base of a volume heated boiling pool is proposed. Because of the density difference caused by volume boiling between the bulk fluid and the fluid near the base, the lighter two-phase fluid causes movement of the bulk fluid in the upward direction and causes a negative pressure gradient along the base plate of the pool. This negative pressure drives returning subcooled singlephase liquid in the boundary layer along the base plate. The analysis for the laminar case provides the definition of equivalent Grashof number for the combined (or opposing) two-phase and temperature driven natural convection along the base plate. The turbulent boundary layer is analyzed by assuming a two-layer model in which the inner layer is characterized by viscous and conduction terms and the outer layer by mean convection terms. The similarity analysis of the governing equations yields universal profiles for temperature and velocity and the scaling laws for the inner and outer layers. An asymptotic matching of the temperature profile in the overlap region leads to a heat transfer law that correlates the available experimental data on a volume heated boiling pool satisfactorily.     

Conjugate film condensation and natural convection along the interface between a porous and an open space

This paper reports a theoretical investigation focusing on the interaction between film condensation and natural convection along a vertical wall separating a fluid reservoir from a fluid-saturated porous reservoir. The two reservoirs are maintained at different temperatures. The study consists of two parts: in the first part the condensation phenomenon takes place in the fluid reservoir and the natural convection phenomenon in the porous layer. In the second part, the opposite situation is considered. The main heat transfer and flow characteristics in the two counterflowing layers, namely, the condensation film and the natural convection boundary layer are documented for a wide range of the problem parameters. These parameters appear after boundary layer scaling of the governing equations. Important engineering results regarding the overall heat flux from the condensation side to the natural convection side are summarized in the course of the study. Finally, the effect of the thermal resistance of the wall constituting the interface separating the two reservoirs, on the overall heat flux from the condensation side to the natural convection side is determined.     

Heat transfer enhancement with the use of nanofluids in radial flow cooling systems considering temperature-dependent properties

Heat transfer enhancement capabilities of coolants with suspended metallic nanoparticles inside typical radial flow cooling systems are numerically investigated in this paper. The laminar forced convection flow of these nanofluids between two coaxial and parallel disks with central axial injection has been considered using temperature dependent nanofluid properties. Results clearly indicate that considerable heat transfer benefits are possible with the use of these fluid/solid particle mixtures. For example, a Water/Al₂O₃ nanofluid with a volume fraction of nanoparticles as low as 4% can produce a 25% increase in the average wall heat transfer coefficient when compared to the base fluid alone (i.e., water). Furthermore, results show that considerable differences are found when using constant property nanofluids (temperature independent) versus nanofluids with temperature dependent properties. The use of temperature-dependent properties make for greater heat transfer predictions with corresponding decreases in wall shear stresses when compared to predictions using constant properties. With an increase in wall heat flux, it was found that the average heat transfer coefficient increases whilst the wall shear stress decreases for cases using temperature-dependent nanofluid properties.     

Mixed convection with variable viscosity in an inclined channel with prescribed wall temperatures

The fully developed laminar mixed convection of a Newtonian fluid with temperature-dependent viscosity in an inclined plane channel with prescribed wall temperatures is studied analytically. First, an analytical solution which holds for any dependence of viscosity on temperature is found. Then, a model to describe this dependence is presented and applied to the general solution, and some examples are discussed. The results show that the changes of viscosity with temperature may yield relevant effects on the dimensionless velocity distribution and on the friction factors even in the case of forced convection. On the contrary, the effect of a variable viscosity on the dimensionless pressure drop is important only when it is coupled with that of buoyancy forces. In fact, in some cases, the difference between the pressure and the hydrostatic pressure increases along the flow direction.     

Wall functions for numerical simulation of turbulent natural convection along vertical plates

This paper presents new wall functions of velocity and temperature for natural convection along vertical plates based on dimensional analysis and experimental data. Because only fluid properties and local parameters are included, the proposed wall functions are suitable for numerical simulation and are expected to be also valid in non-isothermal flows in cavities. Moreover, a certain analogy of length, velocity, and temperature scales between natural and forced convection has been found.     

Mixed convection from a vertical plate to non-Newtonian fluids with uniform surface heat flux

This paper proposed a mixed-convection parameter ζ to analyze the steady laminar mixed convection heat transfer between non-Newtonian fluids and a vertical plate with constant wall heat flux. The obtained finite-difference solutions are uniformly valid over the entire range of mixed convection from the pure forced convection limit (ζ = 0) to pure free convection limit (ζ = 1). Typical velocity and temperature profiles in the boundary layer are presented. Furthermore, the variations of the local heat transfer rates as well as wall frictions along the plate are shown explicitly.