Assessment of thermal performance of the functionally graded materials in annular fins

Heat transfer enhancement in the annular fins with uniform profile is investigated in the present study. Conventional fin materials are replaced with the functionally graded materials in order to increase the rate of heat transfer and corresponding fin efficiency. Here, the fin material properties, such as conductivity, are assumed to be graded along the annular fin radius, R, as a linear function. The governing equation of the annular fin is computed with an approximate analytical method using the mean value theorem. It is revealed that the in-homogeneity index, β, of the fin material plays an important role on the thermal characteristics of the annular fins. Alternatively, heat dissipation between the fin surface and surrounding fluid in the annular fins increases with increasing the inhomogeneity indices, β. Finally, it is stated that application of the functionally graded material in the annular fins enhances the fin efficiency in comparison to the annular fins with homogeneous material. It is hoped that the results obtained from this study arouse interest among thermal designers and heat exchanger industries.     

Annular convective-radiative fins with a step change in thickness,and temperature-dependent thermal conductivity and heat transfer coefficient

This article investigates the thermal performance of convective-radiative annular fins with a step reduction in local cross section (SRC). The thermal conductivity of the fin’s material is assumed to be a linear function of temperature, and heat transfer coefficient is assumed to be a power-law function of surface temperature. Moreover, nonzero convection and radiation sink temperatures are included in the mathematical model of the energy equation. The well-known differential transformation method (DTM) is used to derive the analytical solution. An exact analytical solution for a special case is derived to prove the validity of the obtained results from the DTM. The model provided here is a more realistic representation of SRC annular fins in actual engineering practices. Effects of many parameters such as conduction-convection parameters, conduction-radiation parameter and sink temperature, and also some parameters which deal with step fins such as thickness parameter and dimensionless parameter describing the position of junction in the fin on the temperature distribution of both thin and thick sections of the fin are investigated. It is believed that the obtained results will facilitate the design and performance evaluation of SRC annular fins.     

First integrals and analytical solutions of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient

Fin materials can be observed in a variety of engineering applications. They are used to ease the dissipation of heat from a heated wall to the surrounding environment. In this work, we consider a nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient. The equation(s) under study are highly nonlinear. Both the thermal conductivity and the heat transfer coefficient are given as arbitrary functions of temperature. Firstly, we consider the Lie group analysis for different cases of thermal conductivity and the heat transfer coefficients. These classifications are obtained from the Lie group analysis. Then, the first integrals of the nonlinear straight fin problem are constructed by three methods, namely, Noether’s classical method, partial Noether approach and Ibragimov’s nonlocal conservation method. Some exact analytical solutions are also constructed. The obtained result is also compared with the result obtained by other methods.     

Conservation laws and associated Lie point symmetries admitted by the transient heat conduction problem for heat transfer in straight fins

Some new conservation laws for the transient heat conduction problem for heat transfer in a straight fin are constructed. The thermal conductivity is given by a power law in one case and by a linear function of temperature in the other. Conservation laws are derived using the direct method when thermal conductivity is given by the power law and the multiplier method when thermal conductivity is given as a linear function of temperature. The heat transfer coefficient is assumed to be given by the power law function of temperature. Furthermore, we determine the Lie point symmetries associated with the conserved vectors for the model with power law thermal conductivity.     

Effect of magnetic and boundary parameters on flow characteristics analysis of micropolar ferrofluid through the shrinking sheet with effective thermal conductivity

Ferrofluids have many applications in mechanical and electrical engineering. In this paper, characteristics of ferrofluid over a shrinking sheet with effective thermal conductivity model are studied by the homotopy perturbation method (HPM) and Akbari-Ganji's method (AGM). Also, the Finite Element Method (FEM) has been applied for numerical solution. The governing equations formulated by the Tiwari-Das model. It is supposed that base fluid and nanoparticles are water and Fe₃O₄respectively. Effect of related parameters of micro-rotation velocity and dimensionless velocity have taken for suction and injection of mass transfer parameter. Results show that the magnetic and boundary parameters, in contrast to the micro-rotation parameter, have the same impact on velocity. Moreover, a comparison has been made between the results of this study with other researchers shows the impressive accuracy and efficiency of these methods.     

矩形肋片热沉(火积)耗散率最小与最大热阻最小构形优化的比较研究

针对矩形肋片热沉, 分别以最大热阻最小化和基于(火积)耗散定义的当量热阻最小化为优化目标, 采用二维传热模型并结合有限元数值仿真对其进行构形优化, 比较了两种目标下的热沉最优构形, 并分析了全局参数(综合了对流换热系数、肋片占据的总面积及其热导率的函数)和材料占比对两种目标(最大热阻、当量热阻)及其对应最优构形的影响. 结果表明: 热沉外形固定时, 两种目标下均不存在最优的肋片厚度; 热沉外形自由变化时, 两种目标下的最优构形存在一定的差异. 此外, 全局参数对两种目标下的最优构形均没有影响, 而材料占比对两种目标下的最优构形均有较大影响. 提高全局参数和材料占比均可以减小最大热阻最小值和当量热阻最小值, 但对两种目标的减小程度不同. 总体上, 调节热沉结构参数使当量热阻最小, 可以同时获得很好的局部极限性能; 而调节热沉结构参数使最大热阻最小, 获得的整体平均散热性能却较差. 因此, 对本文热沉模型进行优化时, 以当量热阻最小化为优化目标更合理.     

基于梯度翅片换热器的热电发电系统性能研究

本文建立了热电发电系统(TEG)多物理场数值模型,并充分考虑换热器流体影响,综合研究了具有不同热侧换热器翅片结构的TEG系统性能。在雷诺数为1000~10000范围内,分析了流体沿程温度分布特征、泵功及热电发电模块的能量转换特性.所研究的三种翅片结构包括:全流道等高度直翅片(Fin-1)、下游强化梯度翅片(Fin-2)以及上游强化梯度翅片(Fin-3).研究表明,通道长高比及热电材料覆盖率一定,热电发电功率及转换效率随流量呈二次曲线变化关系,存在最匹配流量使得系统发电性能最佳。等高度直翅片对流量的变化敏感,随流量增大,则压损增大,导致系统净输出功率及发电效率无收益.而梯度翅片可以在更大范围内产生正收益;下游强化梯度翅片具有最佳的流体沿程温度均匀性,但沿程局部热阻却最大.综合考虑沿程局部热阻分布及泵功消耗,上游强化梯度翅片TEG系统净转换效率最高,因此局部热阻分布及泵功综合因素应为TEG内的换热器合理设计的关键。     

Analysis for flow of Jeffrey fluid with nanoparticles

An analysis of the boundary layer flow and heat transfer in a Jeffrey fluid containing nanoparticles is presented in this paper. Here, fluid motion is due to a stretchable cylinder. The thermal conductivity of the fluid is taken to be temperature-dependent. The partial differential equations of velocity, temperature, and concentration fields are transformed to a dimensionless system of ordinary differential equations. Nonlinear governing analysis is computed for the homotopy solutions. The behaviors of Brownian motion and thermophoresis diffusion of nanoparticles have been examined graphically. Numerical values of the local Nusselt number are computed and analyzed.     

Experimental Study of Wavy Fin Aluminum Plate Fin Heat Exchanger

An experimental study of the air-side thermal hydraulic performance of the aluminum wavy fin in heat exchanger was performed. A series of tests were conducted for 16 wavy fin samples with different geometry parameters. The experimental correlation equations of the wavy fin about the heat transfer and pressure drop are set up using the multiple regression method. The parametric study on the performance of the wavy fins is carried out using the Taguchi method. The study results show that the ratio of the wavy fin amplitude and wavy length is the most important factor that affects the overall thermal hydraulic performance.     

Investigation of Ti6Al4V and AA7075 alloy embedded nanofluid flow over longitudinal porous fin in the presence of internal heat generation and convective condition

The thermal attributes of porous fin due to radiation and natural convection have been carried out in the presence of nanofluid flow. The geometry of the fin taken for the analysis is rectangular profiled longitudinal fin. The temperature-dependent internal heat generation condition is also considered along with Darcy's model. The two types of nanofluid containing titanium alloy(Ti6Al4V) and aluminium alloy(AA7075) immersed in water is considered for the investigation.The modelled nonlinear ordinary differential equation is numerically solved by the Runge–Kutta–Fehlberg technique. The impact of geometric parameter on the heat transfer analysis of the fin due to the flow of both nanofluids is plotted and consequences are physically interpreted. It is observed that the presence of the water-based titanium alloy better enhances the fin heat transfer rate.     

Analytical solutions to heat transfer equations by homotopy-perturbation method revisited

In this Letter, the problem of determining the temperature distribution of a straight rectangular fin with power-law temperature-dependent surface heat flux is revisited. The solution of the corresponding nonlinear boundary-value problem (BVP) based on the homotopy-perturbation method (HPM) presented earlier is corrected and extended.     

多孔圆肋传热传质分析

多孔肋片传热传质过程在自然界中广泛存在,本文对水在多孔圆肋中流动产生的传热传质现象进行了研究,建立了相应的物理数学模型,通过数值计算获得肋片内水的温度和流量分布,以及水沿肋长方向蒸发率的变化。讨论了外界空气温度对多孔肋片中水的流量和蒸发率的影响,并对孔隙率、长径比等因素对肋片传热传质效率的作用进行了分析．     

Study of vapor condensation on curvilinear fins under influence of capillary forces and gravity

The problem on film vapor condensation on curvilinear fins is solved numerically with regard to surface tension and gravity. Steam condensation on a fin of optimized and semicircular form was calculated for various inclinations of the fin relative to the direction of gravity vector and the levels of groove flooding. The calculations showed that the average heat transfer coefficient for a semicircular fin slightly decreases with changing the fin position relative to the direction of gravity vector, at that, the “zero” flow point from which the condensate flows in different directions shifts. For an optimized fin, there is no such shift, and the heat transfer coefficient does not practically change. The top of an optimized fin with a large curvature serves as a kind of "barrier" for the flow. The heat transfer coefficients on optimized fins are significantly higher than those on semicircular fins. The amount of the level of groove flooding significantly affects the condensation efficiency as a whole; however, it does not affect the process of condensation on the convex part of fins.     

Visualization of transient natural convection heat transfer from a vertical rectangular fin

Experiments on thermal visualization of transient natural convection from short vertical rectangular fins were conducted using the technique of laser holographic interferometry. A sequence of infinite-fringe interferograms recorded for the heating regime of an aluminum fin demonstrates the effect of fin base heating on local convection coefficients and reveals alternating and oscillatory buoyancydriven flows similar to those over the top surface of heated horizontal plates. The effect of fin base heating results in greater uniformity of the local heat transfer coefficient along the fin. It also significantly reduces the steady-state heat transfer coefficients of short vertical fins compared to their transient values. Hence, the use of steady-state solutions for the design of short vertical fins operating in transient conditions may not introduce as much error as was previously thought.     

考虑界面接触热阻的一维复合结构的热整流机理

建立了考虑变截面、变热导率及界面接触热阻效应的组合热整流结构的温度场及热整流系数的理论模型和有限元解.数值算例证明了本文模型及算法的可靠性,进而通过参数影响研究确定了若干几何及材料参数对结构热整流系数的影响规律,揭示界面接触热阻对热整流效果的影响机理.研究结果表明长度比、截面半径变化率、热导率、边界条件温差和界面接触热阻等因素必须通过优化设计才能得到最大的热整流系数,同时界面接触热阻的引入也为调控热整流系数提供了一条新的途径.     

NATURAL CONVECTION FROM A VERTICAL RECTANGULAR FIN

An experimental investigation of steady-state natural convection from vertical rectangular mild steel and aluminum fins was conducted using laser holographic interferometry. Infinite-fringe interferograms demonstrate the effect of fin base heating. Depending on the fin material and base temperature, the local heat transfer coefficients vary along the fin with maximum values at positions about 22-48% of the fin height measured from the base. Temperature measurements along the fin show good agreement with the classical one-dimensional corwective and adiabalic tip solutions. Hence, in the thermal design of vertical aluminum fins of low Biot numbers, the classical one-dimensional fin solutions may be used together with an average heat transfer coefficient obtained from established correlations for natural convection from an isothermal flat plate.     

The effect of rubber dampers on engine’s NVH and thermal performance

Fins as extended surfaces are attached to the internal combustion engine surfaces for enhancing the heat transfer. However, these fins vibrate at various frequencies, which produce undesirable radiated noise. To mitigate this effect, automobile industry inserts rubber dampers between these fins. These rubber dampers reduce the fins’ amplitude of vibration and thus reduce the radiated noise from the fin surfaces. Investigations on the effect of rubber dampers on the engine’s NVH (Noise–Vibration–Harshness) and thermal performance using numerical (FEM and CFD) and experimental measurement have been presented in this paper. Experiments were conducted in the semi-anechoic chamber on an engine with and without rubber dampers to measure the radiated noise from the fins. It was found that rubber dampers assist in reducing engine high frequency noise signals at higher engine speeds. Modal and harmonic response analysis was carried out on various designs for NVH characteristics improvement. Prototypes of the final design was made and tested for the NVH performance. Computational fluid dynamics (CFD) simulations were performed on engine with and without rubber dampers to investigate the thermal performance. It was found that rubber dampers increase engine temperature by about 10%. Effect of rubbers dampers on the cost and environmental impact has also been discussed. This paper provides a systematic procedure to investigate the effect of rubber dampers and a method to eliminate these dampers from the engines with the same NVH and better thermal performances.     

Experimental investigation of heat transfer from different pin fin in a rectangular channel

In this study, the effect of both hexagonal pin fins (HPFs) and cylindrical pin fins (CPFs) into the rectangular channel on heat transfer augmentation, Nusselt number and friction factor were experimentally investigated. In planning of the experiments, different Reynolds number, pin fin array, pin fin geometry and the ratio of the distance between pin fin spacing (s) to the pin fin hydraulic diameter (s/D_h) were chosen as the design parameters. Air was used as the fluid. The Reynolds number, based on the channel hydraulic diameter of the rectangular channel, was varied from 3188 to 19531. In the experiments, the heating plate was made of stainless steel foil. The foil was electrically heated by means of a high current DC power supply to provide a constantly heated flux surface. The heat transfer results were obtained using the infrared thermal imaging technique. The heat transfer results of the hexagonal pin fins (HPFs) and cylindrical pin fins (CPFs) are compared with those of a smooth plate. Best heat transfer performance was obtained with the hexagonal pin fins. The maximum thermal performance factor ((?), was obtained as Re = 3188, staggered array, s/D_h = 0, ? = 2.28.     

Modeling of vapor condensation in a longitudinally finned minichannel

Heat transfer with vapor condensation inside a longitudinally finned tube is numerically studied. The proposed model considers vapor condensation on two initial flow areas, namely, annular and rivulet. The model allows prediction of pressure difference along the tube length, vapor velocity profiles in the central channel and an interfin groove, and also a velocity profile in the condensate rivulet at the bottom of the interfin channel, local heat transfer coefficients at different fin points, and average heat transfer coefficients over tube section and length. The calculations showed that in the case of vapor condensation in longitudinally finned tubes of a small diameter it is of fundamental importance to divide the flow tube section into a central channel and interfin channels. The governing vapor velocities in these channels may differ by more than an order of magnitude. The reduced vapor velocity, used in engineering calculations, does not reflect the character of dynamic vapor impact on a condensate film on the most part of the heat transfer surface. For tubes with relatively large fins the proposed model describes vapor condensation almost completely,meanwhile, the mass vapor quality by the time of filling of the grooves reaches 0.01–0.05. The highest heat transfer intensification was obtained for “sharp fins” with a high value of the fin head curvature. Comparison of results of calculation by the model with results of the known experiments on water vapor condensation yields a good qualitative and quantitative agreement for low vapor velocities at the channel inlet (under 30 m/s). The wall thermal conductivity coefficient value affects significantly the condensation efficiency.     

气泡在内置交错矩形肋管道中自由上升的FTM直接数值模拟

采用直接数值模拟的FTM（Front-Tracking Method）方法研究在重力作用下单气泡在竖直内置矩形肋管内的自由上升.选择矩形肋的肋高、肋距与方管宽度的比值作为管道几何特征值,用莫顿数作为流体特征参数,分析不同肋高、肋距及莫顿数情况下的气泡自由上升,研究不同几何特征及流体参数对气泡运动轨迹的影响.研究表明：在矩形肋片的影响下气泡上升时形状不对称,存在水平方向位移,表现为"蛇形"上升.这种现象与管道几何结构及气泡周围流体性质有关,肋高越大,现象越明显;气泡周围流体的粘度越小,水平方向位移越大.