Thermal effect on the deformation of a flexible beam with large kinematical driven overall motions

The research investigates the transient longitudinal and transverse deformation of a planar flexible beam with large overall motions in a temperature field. With the increase of temperature, longitudinal deformation is caused by the thermal expansion in axial direction. Due to the coupling of longitudinal and transverse deformation, the transverse deformation is induced, which is significant in cases where temperature increases rapidly in a very short period. Furthermore, the transverse temperature gradient, which is caused by the temperature variation in the transverse direction, may lead to transverse deformation. Considering the thermal strain, equations of motion of a flexible beam with arbitrary large overall motion are derived based on virtual work principle. The high order terms of the strain tensor are taken into account, such that the geometric nonlinear deformation terms are included in the dynamic equations. Simulation results of a rotating beam are shown to reveal the thermal effect and nonlinear effect on the dynamic performance of the beam.     

Gravity-driven motion of a deformable drop or bubble near an inclined plane at low Reynolds number

The creeping motion of a three-dimensional deformable drop or bubble in the vicinity of an inclined wall is investigated by dynamical simulations using a boundary-integral method. We examine the transient and steady velocities, shapes, and positions of a freely-suspended, non-wetting drop moving due to gravity as a function of the drop-to-medium viscosity ratio, λ, the wall inclination angle from horizontal, θ, and Bond number, B, the latter which gives the relative magnitude of the buoyancy to capillary forces. For fixed λ and θ, drops and bubbles show increasingly pronounced deformation in steady motion with increasing Bond number, and a continued elongation and the possible onset of breakup are observed for sufficiently large Bond numbers. Unexpectedly, viscous drops maintain smaller separations and deform more than bubbles in steady motion at fixed Bond number over a large range of inclination angles. The steady velocities of drops (made dimensionless by the settling velocity of an isolated spherical drop) increase with increasing Bond number for intermediate-to-large inclination angles (i.e. 45° ? θ ? 75°). However, the steady drop velocity is not always an increasing function of Bond number for viscous drops at smaller inclination angles.     

An electrothermal analogy between the problems of thermo- and electrocapillary drifts of liquid drops

An analogy is considered between the problem of the steady thermocapillary drift for small Peclet numbers and the problem of the steady electrocapillary drift for a viscous liquid drop in another unbounded viscous liquid when the temperature gradient is constant or the electric potential is constant at infinity.     

Effect of convection on the stability of a liquid with a nonuniformly distributed heavy admixture

The effect of the transverse temperature gradient on the stability of steady motion of a viscous incompressible liquid in a plane vertical layer bounded by two infinite solid surfaces is studied. The motion of the liquid is caused by sedimentation of heavy solid spherical particles distributed nonuniformly across the layer and by the horizontal temperature gradient. Spectra of decrements of small normal perturbations are calculated for different particle sizes and different degrees of nonuniformity of the distribution of admixture particles. The stability of a steady flow of the liquid with an admixture decreases with increasing temperature gradient and increasing particle radius and increases with a tendency of the particles to a uniform distribution. Chelyabinsk State University, Chelyabinsk 454021. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 180–187, September–October, 2000.     

Modeling the motion of a vapor bubble in a tube in an ascending flow

The steady rise of a vapor bubble in a liquid moving in a vertical tube is modeled by means of the Navier-Stokes equations. The shape of the vapor bubble (drop) and the structure of the flow are determined by numerically solving the equations inside and outside the drop. The calculations are made on the interval of intermediate values of the dimensionless parameters and describe the transition to piston-type motion. The solutions obtained are compared with the existing experimental and approximate data for creeping flows. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 76–86, July–August, 1994.     

Viscous dissipation of a power law fluid in axial flow between isothermal eccentric cylinders

We study the temperature distribution of a power law fluid in a pressure-driven axial flow between isothermal eccentric cylinders in bipolar cylindrical coordinates. We begin our analysis by writing the equation of energy in bipolar cylindrical coordinates. We then obtain a dimensionless algebraic analytic solution for temperature profiles under a steady, laminar, incompressible and fully developed flow [Eq. (64)]. We find that the dimensionless temperature profile depends upon the radius ratio of the inner to outer cylinders, the eccentricity, the angular position, and the power law exponent n. The temperature is a strong function of the gap between the cylinders. The temperature profiles are flat in the middle of the gap and then, near the wall, suddenly drop to the wall temperature.     

功能梯度变曲率曲梁的几何非线性模型及其数值解

基于弹性曲梁平面问题的精确几何非线性理论,建立了功能梯度变曲率曲梁在机械和热载荷共同作用下的无量纲控制方程和边界条件,其中基本未知量均被表示为变形前的轴线坐标的函数。以椭圆弧曲梁为例,采用打靶法求解非线性常微分方程的两点边值问题,获得了两端固定功能梯度椭圆弧曲梁在横向非均匀升温下的热弯曲变形数值解,分析了材料梯度指数、温度参数、结构几何参数等对曲梁受力及变形的影响。     

Steady MHD Couette flow with temperature-dependent physical properties

The influence of variation in physical variables on the steady magnetohydrodynamic (MHD) Couette flow with heat transfer is studied. An external uniform magnetic field is applied perpendicular to the parallel plates and the fluid is acted upon by a constant pressure gradient. The viscosity and the thermal as well as electric conductivities are assumed to be temperature dependent. The two plates are kept at two constant but different temperatures, and the viscous and Joule dissipations are considered in the energy equation. A numerical solution for the governing nonlinear coupled equations of motion and the energy equation is obtained. The effect of the temperature-dependent viscosity, thermal conductivity, and electrical conductivity on both the velocity and temperature distributions is examined. H.A. Attia - On leave from: Dept. of Eng. Mathematics and physics, El-Fayoum University, El-Fayoum, Egypt     

Evaporation condensation-induced bubble motion after temperature gradient set-up

Thermocapillary (Marangoni) motion of a gas bubble (or a liquid drop) under a temperature gradient can hardly be present in a one-component fluid. Indeed, in such a pure system, the vapor–liquid interface is always isothermal (at saturation temperature). However, evaporation on the hot side and condensation on the cold side can occur and displace the bubble. We have observed such a phenomenon in two different fluids submitted to a temperature gradient under reduced gravity: hydrogen under magnetic compensation of gravity in the HYLDE facility at CEA-Grenoble and water in the DECLIC facility onboard the ISS. The experiments and the subsequent analysis are performed in the vicinity of the vapor–liquid critical point to benefit from critical universality. In order to better understand the phenomena, a 1D numerical simulation has been performed. After the temperature gradient is imposed, two regimes can be evidenced. At early times, the temperatures in the bubble and the surrounding liquid become different thanks to their different compressibility and the “piston effect” mechanism, i.e. the fast adiabatic bulk thermalization induced by the expansion of the thermal boundary layers. The difference in local temperature gradients at the vapor–liquid interface results in an unbalanced evaporation/condensation phenomenon that makes the shape of the bubble vary and provoke its motion. At long times, a steady temperature gradient progressively forms in the liquid (but not in the bubble) and induces steady bubble motion towards the hot end. We evaluate the bubble velocity and compare with existing theories.     

Viscous flow of a suspension of liquid drops in a cylindrical tube

Viscous flow in a circular cylindrical tube containing an infinite line of viscous liquid drops equally spaced along the tube axis is considered under the assumption that a surface tension, sufficiently large, holds the drops in a nearly spherical shape. Three cases are considered: (1) axial translation of the drops, (2) flow of the external fluid past a line of stationary drops, and (3) flow of external fluid and liquid drops under an imposed pressure gradient. Both fluids are taken to be Newtonian and incompressible, and the linearized equations of creeping flow are used.The results show that both drag and pressure drop per sphere increase as the spacing increases at fixed radius and also increase as the radius of the drop increases. The presence of the internal motion reduces the drag and pressure gradients in all cases compared to rigid spheres, particularly for drops approaching the size of the tube.     

考虑几何非线性和热效应的刚-柔耦合动力学

温度增高和温度梯度会引起梁的纵向、横向变形位移,在一定程度上对刚-柔耦合规律产生影响.该文考虑热应变,从平面梁的非线性的应变与位移关系式出发,建立了刚体运动、弹性变形和温度相互耦合的有限元离散的热传导方程和动力学方程.研究热流作用下的中心刚体-简支梁系统的刚-柔耦合动力学性质,揭示了几何非线性项和热应变对弹性变形和刚体运动影响.     

Gravity-induced motion of a uniformly heated solid particle in a gaseous medium

The steady motion of a uniformly heated spherical aerosol particle in a viscous gaseous medium is analyzed in the Stokes approximation under the condition that the mean temperature of the particle surface can be substantially different from the ambient temperature. An analytical expression for the drag force and the velocity of gravity-induced motion of the uniformly heated spherical solid particle is derived with allowance for temperature dependences of the gaseous medium density, viscosity, and thermal conductivity. It is numerically demonstrated that heating of the particle surface has a significant effect on the drag and velocity of gravity-induced motion. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 74–80, January–February, 2008.     

Mathematical model of heat transfer in a fluid with account for its relaxation properties

Using the terms that take account for the temporal and spatial nonlocality (time variation of the heat flux and the temperature gradient) in the formula of Fourier’s law for the heat flux a differential equation for a fluid in motion is derived that contains the second time derivative and themixed derivative with respect to the spatial and temporal variables. Numerical solution of the problem of heat transfer in the laminar fluid flow in a plane channel demonstrates that, in view of the lag in the time variation of the heat flux from zero to a certain maximum value, the boundary condition of the first kind (thermal shock) cannot be instantaneously realized. The process of its stabilization on the wall is characterized by a certain time interval, whose duration is determined by the relaxation properties of the fluid. At large values of the dimensionless coefficients of the heat flux relaxation and the temperature gradient the boundary condition of the first kind can be realized only as the steady state is attainted, as Fo→∞. In this case, the flow does not contain temperature jumps and negative temperature values.     

Finite element analysis of thermo-elastic behavior of piezoelectric structures under finite deformation

It is noted that the behavior of most piezoelectric materials is temperature dependent and such piezo-thermo-elastic coupling phenomenon has become even more pronounced in the case of finite deformation. On the other hand, for the purpose of precise shape and vibration control of piezoelectric smart structures, their deformation under external excitation must be ideally modeled. This demands a thorough study of the coupled piezo-thermo-elastic response under finite deformation. In this study, the governing equations of piezoelectric structures are formulated through the theory of virtual displacement principle and a finite element method is developed. It should be emphasized that in the finite element method the fully coupled piezo-thermo-elastic behavior and the geometric non-linearity are considered. The method developed is then applied to simulate the dynamic and steady response of a clamped plate to heat flux acting on one side of the plate to mimic the behavior of a battery plate of satelite irradiated under the sun. The results obtained are compared against classical solutions, whereby the thermal conductivity is assumed to be independent of deformation. It is found that the full-coupled theory predicts less transient response of the temperature compared to the classic analysis. In the steady state limit, the predicted temperature distribution within the plate for small heat flux is almost the same for both analyses. However, it is noted that increasing the heat flux will increase the deviation between the predictions of the temperature distribution by the full coupled theory and by the classic analysis. It is concluded from the present study that, in order to precisely predict the deformation of smart structures, the piezo-thermo-elastic coupling, geometric non-linearity and the deformation dependent thermal conductivity should be taken into account. Project supported by the National Natural Science Foundation of China (Nos. 10132010 and 50135030) and the Foundation of In-service Doctors of Xi'an Jiaotong University.     

Laminar heat transfer characteristics of internally finned tube with sinusoidal wavy fin

Comparative numerical study of laminar heat transfer characteristics of annular tubes with sinusoidal wavy fins has been conducted both experimentally and numerically with Re = 299–1,475. The uniform heat flux is imposed on the tube outside wall surface. Two tube materials (copper and stainless steel) are considered. It is found that the fluid temperature profile is not linear but convex along the flow direction due to the axial heat conduction in tube wall, and the effects of axial heat conduction on the heat transfer decreases with an increase in Reynolds number or decrease in tube wall thermal conductivity. The axial distributions of local Nusselt number could reach periodically fully developed after 3–5 cycles. The convectional data reduction method based on the traditional method should be improved for tube with high thermal conductivity or low Reynolds numbers, Otherwise, the heat transfer performance of internally finned tube may be underestimated.     

压电智能结构有限变形下热-机耦合的有限元分析

采用有限元方法研究了结构在热载荷作用下变形与热传导之间的耦合特性．分析表明，结构变形较小，非线性效应很弱时，变形对材料的热传导系数影响很小，对结构的温度分布几乎没有影响；当变形增大，非线性效应增强时，变形对材料的热传导特性影响显著，热载荷作用下结构的温度变化和变形与现行不考虑热-机耦合效应所得结果产生明显差异．因此，为实现压电智能结构形状(振动)的精确控制，分析及实施控制时须考虑热-机耦合及变形对热传导系数的影响．     

Locally similar solutions for hydromagnetic and thermal slip flow boundary layers over a flat plate with variable fluid properties and convective surface boundary condition

This paper presents heat transfer process in a two-dimensional steady hydromagnetic convective flow of an electrically conducting fluid over a flat plate with partial slip at the surface of the boundary subjected to the convective surface heat flux at the boundary. The analysis accounts for both temperature-dependent viscosity and temperature dependent thermal conductivity. The local similarity equations are derived and solved numerically using the Nachtsheim-Swigert iteration procedure. Results for the dimensionless velocity, temperature and ambient Prandtl number within the boundary layer are displayed graphically delineating the effect of various parameters characterizing the flow. The results show that momentum boundary layer thickness significantly depends on the surface convection parameter, Hartmann number and on the sign of the variable viscosity parameter. The results also show that plate surface temperature is higher when there is no slip at the plate compared to its presence. For both slip and no-slip cases surface temperature of the plate can be controlled by controlling the strength of the applied magnetic field. In modelling the thermal boundary layer flow with variable viscosity and variable thermal conductivity, the Prandtl number must be treated as a variable irrespective of flow conditions whether there is slip or no-slip at the boundary to obtain realistic results.     

Modeling fluid and heat transport in the reactive, porous bed of downdraft (biomass) gasifier

A fluid flow and heat transfer model has been developed for the reactive, porous bed of the biomass gasifier to simulate pressure drop, temperature profile in the bed and flow rates. The conservation equations, momentum equation and energy equation are used to describe fluid and heat transport in porous gasifier bed. The model accounted for drag at wall, and the effect of radial as well as axial variation in bed porosity to predict pressure drop in bed. Heat transfer has been modeled using effective thermal conductivity approach. Model predictions are validated against the experiments, while effective thermal conductivity values are tested qualitatively using models available in literature. Parametric analysis has been carried out to investigate the effect of various parameters on bed temperature profile and pressure drop through the gasifier. The temperature profile is found to be very sensitive to gas flow rate, and heat generation in oxidation zone, while high bed temperature, gas flow rate and the reduction in feedstock particle size are found to cause a marked increase in pressure drop through the gasifier. The temperatures of the down stream zones are more sensitive to any change in heat generation in the bed as compared to upstream zone. Author recommends that the size of preheating zone may be extended up to pyrolysis zone in order to enhance preheating of input air, while thermal insulation should not be less than 15 cm.     

Numerical simulation for laminar flow and heat transfer of gas in rectanglar micropassages with constant wall heat flux

Theoretical investigations were performed on the developed laminar flow and convective heat transfer characteristics for incompressible gases flow through rectanglar micropassages with constant wall heat flux. Mathematical models were proposed for considering the change in viscosity and thermal conductivity of gas in the wall-adjacent region from the kinetic theory. The dimensionless velocity distribution and corresponding pressure drop, the dimensionless temperature distribution and corresponding heat transfer characteristics were both simulated numerically, and the results were compared to other report simulations [10–12] with brief discussions.     

Analytical considerations of flow/thermal coupling of nanofluids in foam metals with local thermal non-equilibrium (LTNE) phenomena and inhomogeneous nanoparticle distribution

Foam metals with micro pores own excellent thermal performance, however, poor heat conductive ability of most heat-transfer fluids restricts further heat transfer improvement. Combination of foam metal and nanofluid with highly conductive nanoparticles is a promising solution. Convective thermal characteristics of nanofluids in porous foams are theoretically investigated in this work. Effects of Brownian motion and thermophoretic diffusion of nanoparticles in the base fluid on thermal performance are considered. The nanoparticle and the base-fluid are considered to be in thermal equilibrium and the temperature difference between the nanofluid and foam ligaments is especially considered. Compared with the base-fluid flow in a duct, the velocity distribution for the nanofluid flow in a porous foam is more uniform with a decreased dimensionless temperature. The pressure drop of the nanofluid increases with an increase in the concentration of the nanoparticles. By employing foam metals and nanofluid, the cross-sectional temperature becomes closer to the wall temperature. Simultaneously, notable difference between solid and fluid temperatures can be observed, revealing the LTNE effect of the nanofluid on the porous foam. It is found that the Nusselt number first increases and then decreases with an increase in nanoparticle concentration. Furthermore, the Nusselt number decreases with an increase in the foam porosity. It is found that the thermal performance of a nanofluid in a plain tube is different from that in the foam metals.