Inverse estimation of variable thermal parameters in a functionally graded annular fin using dragon fly optimization

This paper presents an inverse study of heat transfer of a conductive, convective and radiative annular fin made of a functionally graded material. Three major parameters such as conductive–convective parameter, conductive–radiative parameter and the parameter describing the variation of thermal conductivity are inversely estimated from a specified temperature field. The forward solution of temperature field is obtained from the closed form solution of nonlinear heat transfer equation using Homotopy perturbation method (HPM). A dragonfly algorithm that simulates the swarming behaviour of dragonflies, as analogous, is employed in finding out the inverse parameters. The temperature values of the forward solution are used as input data for the inverse analysis. The inverse parameters are then estimated iteratively by minimizing the objective function until the guessed temperature field approximately satisfies the preassigned temperature field of the forward solution. The inverse simulation following HPM-based forward solution converges faster than ordinary differential equation-based forward solution. The reconstructed temperature fields obtained from the various combination of inverse parameters give good agreement (～1% error) with the desired temperature field. Thus, the presented inverse model provides an opportunity to the fin designer for selecting the several feasible combinations of thermal parameters suggesting the material design that result in a prescribed temperature field.     

Accurate predictions for optimum design of a T-shaped fin under an actual wet load condition

An effort is made to develop an analytical model for predicting the thermal performance and optimum design parameters of a wet T-shaped fin by considering variable thermal conductivity of the fin material and variable convective heat transfer coefficient. The temperature distribution is obtained by solving the highly non-linear governing equations by employing three different analytical techniques, namely Variational Iteration Method, Adomian Decomposition Method and Differential Transform Method, and validated by that obtained from the Finite Difference Scheme. The optimisation analysis is carried out by employing the Lagrange multiplier technique. A complete multivariable geometric optimisation is executed, where all the geometric parameters are varied simultaneously to establish the optimum condition. Furthermore, the analysis is done for both insulated and convective fin tip conditions and a comparative analysis on the temperature distribution, fin performance and optimum design parameters is presented between these two cases.     

Vapor condensation on nonisothermal curvilinear fins

An analytical expression is obtained for the optimum curvature of a nonisothermal fin featuring stationary condensation of motionless vapor under the conditions of a significant influence of the surface tension on the motion of a condensed liquid. An algorithm is proposed and realized that finds the optimum surface shape for an unknown temperature distribution in the nonisothermal fin. The algorithm is based on a joint solution of the equations of heat conduction and condensed liquid film flow on the fin surface. Allowance for the thermal conductivity of a material in optimization of the fin shape provides for a significant increase in the condensate outflow as compared to the case of the optimum isothermal fin shape and a finite thermal conductivity of the material.     

Thermal Performance of a Functionally Graded Radial Fin

This paper investigates the steady-state thermal performance of a radial fin of rectangular profile made of a functionally graded material. The thermal conductivity of the fin varies continuously in the radial direction following a power law. The boundary conditions of a constant base temperature and an insulated tip are assumed. Analytical solutions for the temperature distribution, heat transfer rate, fin efficiency, and fin effectiveness are found in terms of Airy wave functions, modified Bessel functions, hyperbolic functions, or power functions depending on the exponent of the power law. Numerical results illustrating the effect of the radial dependence of the thermal conductivity on the performance of the fin are presented and discussed. It is found that the heat transfer rate, the fin efficiency, and the fin effectiveness are highest when the thermal conductivity of the fin varies inversely with the square of the radius. These quantities, however, decrease as the exponent of the power law increases. The results of the exact solutions are compared with a solution derived by using a spatially averaged thermal conductivity. Because large errors can occur in some cases, the use of a spatially averaged thermal-conductivity model is not recommended.     

Ultralow thermal conductivity of isotope-doped silicon nanowires

The thermal conductivity of silicon nanowires (SiNWs) is investigated by molecular dynamics (MD) simulation. It is found that the thermal conductivity of SiNWs can be reduced exponentially by isotopic defects at room temperature. The thermal conductivity reaches the minimum, which is about 27% of that of pure 28Si NW, when doped with 50% isotope atoms. The thermal conductivity of isotopic-superlattice structured SiNWs depends clearly on the period of superlattice. At a critical period of 1.09 nm, the thermal conductivity is only 25% of the value of pure Si NW. An anomalous enhancement of thermal conductivity is observed when the superlattice period is smaller than this critical length. The ultralow thermal conductivity of superlattice structured SiNWs is explained with phonon spectrum theory.     

Exact and approximate analytic solutions of the nonlinear convective fin problem with temperature-dependent thermal conductivity

This article shows that the well-known nonlinear boundary value problem of the differential equation for temperature distribution of convective straight fins with temperature-dependent thermal conductivity is exactly solvable in an implicit form. Furthermore, an exact solution in an explicit form is derived. Also, an accurate analytic solution (series solution) is obtained by a new variation of the Adomian decomposition method.     

Identification of materials in a hyperbolic annular fin for a given temperature requirement

This article deals with the prediction of parameters in an annular hyperbolic fin with temperature-dependent thermal conductivity. Three parameters such as thermal conductivity, variable conductivity coefficient and the surface heat transfer coefficient have been predicted for satisfying a prescribed temperature distribution on the surface of fin. This is achieved by a hybrid differential evolution-nonlinear programming optimization method. The effect of random measurement errors is also considered. It is observed from the present inverse analysis that many feasible materials exist satisfying the given temperature distribution, thereby providing engineering flexibility in selecting any material from the available choices. For a given material, this is possible by regulating the surface heat transfer coefficient.     

Absolute measurements of the thermal conductivity of mixtures of alkene-glycols with water

New absolute measurements of the thermal conductivity of ethylene and propylene glycol and their mixtures with water are presented. The measurements were performed in a tantalum-type transient hot-wire instrument at atmospheric pressure, in the temperature range 295–360 K. The overall uncertainty of the reported values is estimated to be less than ±0.5%, an estimate confirmed by measurements of the thermal conductivity of water. The mixtures with water studied have compositions of 25, 50, and 75%, by weight. A recently proposed semiempirical scheme for the prediction of the thermal conductivity of pure liquids is extended to allow the prediction of the thermal conductivity of these mixtures from the pure components, as a function of both composition and temperature.     

Determination of the thermal conductivity of xenon-helium mixtures at high temperatures by the shock-tube method

The thermal conductivity of gases at high temperatures has been measured by the shock-tube method, which is uniquely suited to measure thermal conductivities of gases at high temperatures above 2000 K. A consistent set of thermal-conductivity data over a wide range of temperatures has been obtained from optimum combinations of shock-tube experiments at high temperatures, previously published data at lower temperatures, and a theoretical correlation of the temperature dependence. In the present study, the thermal conductivity of xenon-helium mixtures has been determined at compositions of 10 and 30 mol% xenon over the temperature range from 300 to 4800 K. Even though there is a large difference between the thermal conductivity of pure xenon and that of helium, it is interesting that the dependences of the thermal conductivity of the mixture on temperature and composition are linear. The experimental results are in good agreement with the predicted values based on the corresponding-states principle and the mixing rule. From these experimental results, interpolating the corresponding-states correlation data, we represent the equation of xenon-helium gas mixtures for thermal conductivity in terms of temperature and composition.     

An approximate analytical prediction about thermal performance and optimum design of pin fins subject to condensation of saturated steam flowing under forced convection

An approximate analytical method has been suggested for solving the governing equation for horizontal pin fins subject to condensation while saturated steam flowing over its under laminar forced convection. Adomian decomposition method is used for determination of the temperature distribution, performance and optimum dimensions of pin fins with temperature dependent thermal conductivity under the condensation of steam on the fin surface. From the results, a significant effect on the temperature distribution in the fin and its performances are noticed with the variation in fin-geometric parameters and thermo-physical properties of saturated vapor. Next, a generalized scheme for optimization has been demonstrated in such a way that either heat-transfer duty or fin volume can be taken as a constraint. Finally, the curves for the optimum design have been generated for the variation of different thermo-physical and geometric parameters, which may be helpful to a designer for selecting an appropriate design condition.     

Absolute measurements of the thermal conductivity of mixtures of alcohols with water

New absolute measurements of the thermal conductivity of mixtures of methanol, ethanol, and propanol with water are presented. The measurements were performed in a tantalum-type transient hot-wire instrument at atmospheric pressure, in the temperature range 300–345 K. The overall uncertainty of the reported values is estimated to be less than ±0.5%, an estimate confirmed by measurements of the thermal conductivity of water. The mixtures with water studied have compositions of 25. 50, and 75%, by weight, of methanol and ethanol and 50%, by weight, of propanol. A recently proposed semiempirical scheme for the prediction of the thermal conductivity of pure liquids is extended to allow the prediction of the thermal conductivity of these mixtures from the pure components, as a function of both composition and temperature.     

Conjugate heat transfer in solar collector panels with internal longitudinal corrugated fins-Part II: Local results

A computational study is conducted to determine, for laminar flow in a solar collector panel or a parallel-plate channel with an internal, longitudinal, corrugated fin, the effects of varying the fin angle (or the fin pitch), the fin thickness, the wall-to-fluid thermal conductivity ratio, and the thermal boundary condition on the local surface temperature and heat flux distributions. The corrugated fin and the two walls form individual triangular flow passages in the collector panel or parallel-plate channel. The results of the investigation show that the variation of the local surface temperature is large when the fin is thin and when the wall/fluid thermal conductivity ratio is small. The local surface heat flux is low near the corners of both the upper and lower triangular flow passages. Near the point of fin attachment on the heated wall, heat may be transferred from the fluid to the fin. Heat may also be transferred from the fluid to the unheated wall near the point of fin attachment. When the thermal conductivity ratio is small, the temperature field in the flow cross section is predominantly stratified. In the limit as the thermal conductivity ratio approaches infinity, the temperature field is that of the thermally fully developed laminar flow in a triangular duct with a streamwise uniform heat flux and peripheral uniform surface temperature boundary condition.     

Steady-state heat transfer through a wall with longitudinal rectangular fins and variable thermal conductivity

A method is examined of solving steady-state problems of heat transfer through a surface with longitudinal rectangular fins in the case when the thermal conductivity depends on temperature.Notation T temperature - T₀ temperature of coolant - T₁ temperature at base of fin - T_N some characteristic temperature - (T) thermal conductivity of fin material - heat transfer coefficient; F-cross-sectional area of fin - fin perimeter - h fin height - L fin length - fin thickness - Q heat flux - O_i change of temperature in i-th section - T_i mean temperature at i-th section     

Modeling and simulations of nanofluids using classical molecular dynamics: Particle size and temperature effects on thermal conductivity

We use molecular dynamics simulations to investigate the thermal conductivity of argon-based nanofluid with copper nanoparticles through the Green-Kubo formalism. To describe the interaction between argon-argon atoms, we used the well-known Lennard-Jones (L-J) potential, while the copper–copper interactions are modeled using the embedded atom method (EAM) potential that takes the metallic bonding into account. The thermal conductivity of the pure argon liquid obtained in the present simulation agreed with available experimental results. In the case of nanofluid, our simulation predicted thermal conductivity values larger than those found by the existing analytical models, but in a good accordance with experimental results. This implies that our simulation is more adequate, to describe the thermal conductivity of nanofluids than the previous analytical models. The efficiency of nanofluids is improved and the thermal conductivity enhancement is appeared when the particle size and temperature increase.     

Thermal performance and optimization of hyperbolic annular fins under dehumidifying operating conditions – analytical and numerical solutions

The thermal performance of hyperbolic profile annular fins subjected to dehumidifying operating conditions is studied. An analytical solution for completely wet fin is derived using an approximate linear temperature–humidity relationship. A numerical solution using actual psychrometric relationship for completely and partially wet operating conditions is then obtained to account for the actual temperature–humidity ratio psychrometric relationship under both partially and fully wet operating conditions. An excellent agreement is observed between analytical and numerical solutions for completely wet fin. The fin optimization is presented based on the analytical solution of completely wet fin. Finally, a finite element formulation is used for studying the two-dimensional effects of orthotropic thermal conductivity on the thermal performance of fin under partially and fully wet operating conditions.     

Absolute measurement of the thermal conductivity of alcohol + n-hexane mixtures

New absolute measurements, by the transient hot-wire technique, of the thermal conductivity of binary mixtures of n-hexane with methanol, ethanol, and hexanol are presented. The temperature range examined was 295–345 K and the pressure atmospheric. The concentrations studied were 75% by weight of methanol and 25, 50, and 75% by weight of ethanol and hexanol. The overall uncertainty in the reported thermal conductivity data is estimated to be ±0.5%, an estimate confirmed by the measurement of the thermal conductivity of water. A recently extended semiempirical scheme for the prediction of the thermal conductivity of mixtures from the pure components is used to correlate and predict the thermal conductivity of these mixtures, as a function of both composition and temperature.     

Thermal analysis of a constructal T-shaped porous fin with radiation effects

This paper presents an analytical technique based on the decomposition method to determine the temperature distribution and thermal performance parameters of a constructal T-shape porous fin. The effect of radiation on natural convective heat transfer is considered in the analysis. The governing energy equations of the stem and flange part of this T-shaped porous fin for the aforementioned conditions are highly nonlinear. The adopted decomposition solution gives an explicit expression of temperature distribution in the fin as a function of a coordinate expressed by infinite power series from which fin performance parameters and heat transfer rates can easily be calculated without the need of linearization. The effects of different geometric and thermophysical parameters on the dimensionless temperature distribution and fin performances are studied. Finally, the increase in heat transfer is noticed by selecting porous medium condition in the fin.     

Umklapp region thermal conductivity of body-centered-cubic3He

The thermal conductivity of body-centered-cubic³He has been measured in isotopically pure samples. In agreement with previous measurements in impure samples, the thermal conductivity in the bcc phase of³He does not obey the simple Umklapp temperature dependence which is found in the higher density hexagonal-close-packed phase. The calculated phonon mean free paths also do not obey a simple Umklapp temperature dependence, providing evidence that the high-temperature specific heat anomaly in bcc³He is not directly responsible for the anomaly in the thermal conductivity.Work supported by grants from the National Science Foundation and the Army Research Office (Durham).     

功能梯度材料亚表面缺陷的热波多重散射问题

基于热传导波动模型,采用波函数展开法,研究了半无限功能梯度材料亚表面球形缺陷的热波多重散射.给出了热波散射的一般解.温度波由调制光束在材料表面激发,球形缺陷表面的边界条件为绝热,非均匀参数为指数函数变化.分析了结构几何参数和物理参数对温度分布的影响,并给出了温度变化的数值结果.本研究可为功能梯度材料的分析研究、物理反问题和红外热波成像等提供理论基础和参考数据.