Transient heat transfer in longitudinal fins of various profiles with temperature-dependent thermal conductivity and heat transfer coefficient

Transient heat transfer through a longitudinal fin of various profiles is studied. The thermal conductivity and heat transfer coefficients are assumed to be temperature dependent. The resulting partial differential equation is highly nonlinear. Classical Lie point symmetry methods are employed and some reductions are performed. Since the governing boundary value problem is not invariant under any Lie point symmetry, we solve the original partial differential equation numerically. The effects of realistic fin parameters such as the thermogeometric fin parameter and the exponent of the heat transfer coefficient on the temperature distribution are studied.     

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.     

The effect of temperature-dependent thermal conductivity in heat transfer simulations of frozen biomaterials

The thermal conductivity value of pure water ice is inversely proportional to the temperature and decreases about 5-fold as the temperature increases from the liquid nitrogen boiling temperature (77 K to the freezing point of pure water. The temperature dependency of the thermal conductivity is typically overlooked in bioheat transfer simulations. A closed-form solution of the one-dimensional temperature distribution in frozen water and blood is presented in this study, based on a new thermal conductivity model. Results indicate that temperatures are overestimated up to 38K, and heat fluxes through the frozen region boundaries are underestimated by a factor of 2, when the temperature dependency of the thermal conductivity is neglected.     

Homotopy perturbation method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity

In this Letter, the homotopy perturbation method (HPM) has been used to evaluate the efficiency of straight fins with temperature-dependent thermal conductivity and to determine the temperature distribution within the fin. The fin efficiency of the straight fins with temperature-dependent thermal conductivity has been obtained as a function of thermo-geometric fin parameter and the thermal conductivity parameter describing the variation of the thermal conductivity. The results reveal that homotopy perturbation method is very effective and simple. The resulting correlation equations can assist thermal design engineers for designing of straight fins with temperature-dependent thermal conductivity.     

Effect of temperature-dependent surface heat transfer coefficient on the maximum surface stress in ceramics during quenching

We study the difference in the maximum stress on a cylinder surface σ_max using the measured surface heat transfer coefficient h_m instead of its average value h_a during quenching. In the quenching temperatures of 200, 300, 400, 500, 600 and 800°C, the maximum surface stress σ_mmax calculated by h_m is always smaller than σ_amax calculated by h_a, except in the case of 800°C; while the time to reach σ_max calculated by h_m (f_mmax) is always earlier than that by h_a (f_amax). It is inconsistent with the traditional view that σ_max increases with increasing Biot number and the time to reach σ_max decreases with increasing Biot number. Other temperature-dependent properties also have a small effect on the trend of their mutual ratios with quenching temperatures. Such a difference between the two maximum surface stresses is caused by the dramatic variation of h_m with temperature, which needs to be considered in engineering analysis.     

Exact analytical solution of a nonlinear equation arising in heat transfer

This Letter shows that the nonlinear equation arising in heat transfer recently investigated in papers [D.D. Ganji, Phys. Lett. A 355 (2006) 337; S. Abbasbandy, Phys. Lett. A 360 (2006) 109; Hafez Tari, D.D. Ganji, H. Babazadeh, Phys. Lett. A 363 (2007) 213] and [M.S.H. Chowdhury, I. Hashim, Phys. Lett. A 372 (2008) 1240] is exactly solvable, analyses the equation fully and, furthermore, gives analytic exact solution in implicit form for each value of parameters of equation.     

真空热流法测定不良导体的导热系数

以恒定导热原理为基础,选用由温度表和温差电偶组成的温度测量装置,在真空环境下测量试样上下压杆对称位置的温度、有效传热面积和试样的厚度,通过计算机计算试样的导热系数.与传统的稳态法比较,采用真空热流法测定导热系数,材料内部的温度分布很快达到稳定,可以减小测量过程中试样及上加热盘和下散热盘侧面散热产生的影响.     

On the theory of nonlinear thermal conductivity

A nonlinear differential equation of thermal conductivity is derived phenomenologically from the general principles of construction of functional Q invariant to the inversion operation I(r →–r), and the temperature evolution dynamics is analyzed in the nonstationary case. The proposed method makes it possible to reveal some general regularities in the physical behavior of such systems for describing irreversible phenomena in self-organization processes. It is noted that an analogous situation may take place, for example, in strongly inhomogeneous structures with stochastic internal heat fluxes.     

翅片长度对纵向翅片扁管换热器换热性能的影响

纵向翅片扁管换热器是一种新型换热器。气体沿扁管轴向方向流动,与管内介质的流动路径平行,可强化传热,减少气侧阻力,不易积灰结垢,维护方便。利用数值模拟方法,以纵向翅片扁管换热器为研究对象,分析翅片长度对换热性能的影响,对换热器的翅片长度进行优化。研究表明,不同进口风速对应不同的有效纵向翅片长度。随着进口风速的增大,翅片的有效长度越大。     

A note on analytical solutions of nonlinear fractional 2D heat equation with non-local integral terms

In this paper, we consider the (2+1) nonlinear fractional heat equation with non-local integral terms and investigate two different cases of such non-local integral terms. The first has to do with the time-dependent non-local integral term and the second is the space-dependent non-local integral term. Apart from the nonlinear nature of these formulations, the complexity due to the presence of the non-local integral terms impelled us to use a relatively new analytical technique called q-homotopy analysis method to obtain analytical solutions to both cases in the form of convergent series with easily computable components. Our numerical analysis enables us to show the effects of non-local terms and the fractional-order derivative on the solutions obtained by this method.     

翅片结构参数对纵向翅片扁管换热器换热性能的影响

以纵向翅片扁管换热器为研究对象,分析翅片长度、翅片高度及翅片间距对换热性能的影响,并对换热器的翅片结构参数进行优化,得出进口风速为2m/s时理想的翅片结构参数为:翅片长度为400mm、翅片高度为25mm、翅片间距为2.7mm.     

Exact solutions of variable coefficient nonlinear diffusion-reaction equations with a nonlinear convective term

Attempts have been made to look for the exact solutions of certain types of nonlinear diffusion-reaction equations which involve not only the quadratic and quartic nonlinearities but also a time-dependent nonlinear convective flux term. In particular, the solitary wave solutions are found. Such equations arise in a variety of contexts in physical and biological problems.     

Similarity solutions for boundary layer flow and heat transfer of a FENE-P fluid with thermal radiation

This Letter presents a numerical study of the flow and heat transfer of an incompressible FENE-P fluid over a non-isothermal surface. The governing partial differential equations are converted into ordinary differential equations by a similarity transformation. The effects of the thermal radiation are considered in the energy equation, and the variations of dimensionless surface temperature and dimensionless surface temperature gradient, as well as the heat transfer characteristics with various physical parameters are graphed and tabulated. Two cases are studied, namely, (i) the sheet with prescribed surface temperature (PST case) and (ii) the sheet with prescribed heat flux (PHF case). Moreover, the mechanical characteristics of the corresponding flow are also presented.     

A thermal conductivity model for nanofluids including effect of the temperature-dependent interfacial layer

The interfacial layer of nanoparticles has been recently shown to have an effect on the thermal conductivity of nanofluids. There is, however, still no thermal conductivity model that includes the effects of temperature and nanoparticle size variations on the thickness and consequently on the thermal conductivity of the interfacial layer. In the present work, the stationary model developed by Leong et al. (J Nanopart Res 8:245–254, 2006) is initially modified to include the thermal dispersion effect due to the Brownian motion of nanoparticles. This model is called the ‘Leong et al.’s dynamic model’. However, the Leong et al.’s dynamic model over-predicts the thermal conductivity of nanofluids in the case of the flowing fluid. This suggests that the enhancement in the thermal conductivity of the flowing nanofluids due to the increase in temperature does not come from the thermal dispersion effect. It is more likely that the enhancement in heat transfer of the flowing nanofluids comes from the temperature-dependent interfacial layer effect. Therefore, the Leong et al.’s stationary model is again modified to include the effect of temperature variation on the thermal conductivity of the interfacial layer for different sizes of nanoparticles. This present model is then evaluated and compared with the other thermal conductivity models for the turbulent convective heat transfer in nanofluids along a uniformly heated tube. The results show that the present model is more general than the other models in the sense that it can predict both the temperature and the volume fraction dependence of the thermal conductivity of nanofluids for both non-flowing and flowing fluids. Also, it is found to be more accurate than the other models due to the inclusion of the effect of the temperature-dependent interfacial layer. In conclusion, the present model can accurately predict the changes in thermal conductivity of nanofluids due to the changes in volume fraction and temperature for various nanoparticle sizes.     

微通道换热器复合翅片的传热特性研究

研究了管径对微通道换热器传热性能的影响,并在百叶窗翅片的基础上开发了两种复合翅片。计算结果表明:在同一迎面风速下,1mm管径的百叶窗翅片Nu数分别比1.5mm和1.8mm管径的大4.8%~10.5%和24.6%~25.8%。JF值增加11%~15%和26%~28%,说明管径为1mm时微通道换热器的综合性能更好。与百叶窗翅片相比,百叶窗-三角翼复合翅片的换热系数减小1.9%~5.4%,但压降降低7.8%~12.7%,表明复合翅片是一种高效低阻翅片。     

计算机辅助测量不良导体的导热系数

介绍了计算机数据采集及处理技术在不良导体导热系数测量实验中的应用及取得的结果．