Boiling on a straight pin fin with variable thermal conductivity

This work theoretically investigated the thermal performance and stability characteristics of a straight pin fin subject to boiling considering a temperature-dependent thermal conductivity of fin, k=k _sat(1+b(T−T _sat)). Steady-state temperature distribution and the associated fin base heat flow were for the first time analytically found, whose stability characteristics were evaluated by linear stability analysis. A positive temperature coefficient b will raise both the fin's temperature and base heat flow. The corresponding stability for stable fin boiling was enhanced. A negative b results in an opposite trend. The use of a mean thermal conductivity in fin boiling calculations is discussed. Received on 3 November 1997     

Transient multiboiling in a pin fin with temperature dependent thermal conductivity

Transient heat conduction in fins undergoing different kinds of convective processes (film, transition, nucleated boiling and natural convection) as in multiboiling processes take place, is a strongly non-linear problem because of the abrupt changes in the heat transfer coefficient that occur at certain temperatures. Transient equations for the thermal fields and fluxes are solved simultaneously, giving the time constant of the process; the stationary solution is compared with the numerical or experimental values of other authors. Temperature dependencies of the heat transfer coefficient and the thermal conductivity is assumed due to the large interval of temperatures occurring. Network Simulation Method is used for the numerical solution, which gives simultaneously thermal field of temperatures and heat fluxes.     

材料热传导系数随温度变化函数的反演方法

材料热传导系数的反演是一类典型的热传导逆问题。针对材料热传导系数随温度变化的情况,本文将材料的热传导系数值按温度区间分段离散,建立了通过材料边界点的温度测量来反演各温度区间热传导系数值的遗传算法和伴随方程法。通过典型算例分析和考虑测量噪声、系统噪声的反演计算结果分析表明：所建立的两种反演算法都是可行有效的,受测量随机噪...     

Steady-state thermal waves in the free-stream flow of an ideal gas with a temperature-dependent thermal conductivity

The structure of the stationary transition layer in a cold ideal gas impinging on a heated permeable surface (lattice) is investigated. Hysteresis occurs in establishing the structure of the stationary transition layer.     

Radiation effect on optimum design analysis of a constructal T-shaped fin with variable thermal conductivity

A constructal T-shaped fin with temperature dependent thermal conductivity of fin the material exposed to both convective and radiative environments is analyzed by Adomian decomposition method. This method provides a closed form of analytical solution for analyzing the temperature distribution, performance and optimum design. A comparative study has been executed among the present and published works. Unlike the published work, dependent parameters on the performance and optimization analysis are highlighted.     

Measurement of temperature-dependent thermal conductivity and viscosity of TiO2-water nanofluids

Nanofluid is an innovative heat transfer fluid with superior potential for enhancing the heat transfer performance of conventional fluids. Many attempts have been made to investigate its thermal conductivity and viscosity, which are important thermophysical properties. No definitive agreements have emerged, however, about these properties. This article reports the thermal conductivity and dynamic viscosity of nanofluids experimentally. TiO₂ nanoparticles dispersed in water with volume concentration of 0.2–2 vol.% are used in the present study. A transient hot-wire apparatus is used for measuring the thermal conductivity of nanofluids whereas the Bohlin rotational rheometer (Malvern Instrument) is used to measure the viscosity of nanofluids. The data are collected for temperatures ranging from 15 °C to 35 °C. The results show that the measured viscosity and thermal conductivity of nanofluids increased as the particle concentrations increased and are higher than the values of the base liquids. Furthermore, thermal conductivity of nanofluids increased with increasing nanofluid temperatures and, conversely, the viscosity of nanofluids decreased with increasing temperature of nanofluids. Moreover, the measured thermal conductivity and viscosity of nanofluids are quite different from the predicted values from the existing correlations and the data reported by other researchers. Finally, new thermophysical correlations are proposed for predicting the thermal conductivity and viscosity of nanofluids.     

The non-isothermal elastic dumbbell: A model for the thermal conductivity of a polymer solution

In a flowing polymeric liquid, molecular orientation will give rise to anisotropic conduction of heat. In this paper, a theory is presented relating the thermal conductivity tensor to the deformation history of the fluid. The basis of this theory is formed by the Hookean dumbbell. It is shown that the anisotropy of the thermal conductivity is proportional to the polymer contribution to the extra-stress tensor. This stress-thermal law makes it relatively simple to incorporate anisotropic heat conduction into the numerical simulation of a flowing polymeric liquid.     

Thermal analysis of annular fins with temperature-dependent thermal properties

The thermal analysis of the annular rectangular profile fins with variable thermal properties is investigated by using the homotopy analysis method （HAM）. The thermal conductivity and heat transfer coefficient are assumed to vary with a linear and power-law function of temperature, respectively. The effects of the thermal-geometric fin parameter and the thermal conductivity parameter variations on the temperature distribution and fin efficiency are investigated for different heat transfer modes. Results from the HAM are compared with numerical results of the finite difference method （FDM）. It can be seen that the variation of dimensionless parameters has a significant effect on the temperature distribution and fin efficiency.     

Effective thermal conductivity of a medium with ellipsoidal particles

The principal components of the effective thermal conductivity tensor, characterizing stationary heat macrotransfer in a dense medium with dispersed ellipsoidal particles of a different material are calculated by a method suggested in [1]. The case of equally oriented ellipsoids and of isotropically distributed ones are considered as examples.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 107–111, January–February, 1974.The author is grateful to Yu. A. Buevich for his interest.     

Analytical and numerical solution along with PC spreadsheets modeling for a composite fin

Heat transfer through composite fins is investigated by both analytical and numerical methods. In this regard, governing differential equations of the two dimensional fin and one dimensional cladding are studied to examine the effect of Biot number and ratio of thermal conductivities of the fin material to the cladding, on the dimensionless temperature profiles. The results show that one dimensional analysis, traditionally used in fin analysis, is not applicable for composite fins, particularly when the conductivity ratio of the composite fin materials is low. In addition, the use of spreadsheet programs in solving the fin problem is investigated in somewhat more detail with regard to the solution as well as presentation of the graphical results.     

Incompressible laminar 2D steady thermal boundary layers with temperature-dependent kinematic viscosity and thermal diffusivity

We prove that the incompressible 2D steady thermal boundary layer equations with temperature-dependent kinematic viscosity ν and thermal diffusivity α is maximally symmetric provided the Prantl number Pr=ν/α is constant and or ν=K₂(AT+B)^K₁ if we neglect energy dissipation and if we take into account dissipation. This result corroborates assumptions often made in applications. When we disregard dissipation, the symmetry Lie algebra assumes the forms L^r⊕L^∞, where L^∞ is an infinite-dimensional Lie algebra and L^r is an r-dimensional Lie algebra with r∈{3,4,5,6}. If we include dissipation, r∈{2,3}. We notice that dissipation has a symmetry breaking effect.We also show how the symmetries can be employed for the calculation of invariant solutions.     

Polymer contribution to the thermal conductivity and viscosity in a dilute solution (Fraenkel Dumbbell model)

The phase-space kinetic theory for polymeric liquid mixtures is used to obtain an expression for the polymer contribution to the thermal conductivity of a nonflowing, dilute solution of polymers, where the polymer molecules are modeled as Fraenkel dumbbells. This theory takes into account three mechanisms for the energy transport: diffusion of kinetic energy (including the Öttinger-Petrillo term), diffusion of intramolecular energy, and the work done against the intramolecular forces. This paper is an extension of previous developments for the Hookean dumbbell model and the finitely-extensible dumbbell model. A comparison among the dumbbell results suggests that the thermal conductivity increases with chain stiffness. In addition, the zero-shear-rate viscosity and first normal-stress coefficient are also given for the Fraenkel dumbbell model.Dedicated to Prof. John D. Ferry on the occasion of his 85th birthday.     

Propagation of a combustion wave in a medium with nonlinear thermal conductivity

A study is made of the problem of the propagation of a thermal wave sustained by an exothermic reaction in a perfect gas. It is assumed that the exothermic reaction begins as a result of the heating of the matter in the medium by the thermal wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 184–188, July–August, 1979.I thank V. A. Levin for interest in the work.     

Absorption of thermal radiation in a semi-transparent spherical droplet: a simplified model

The boundary-value problem for calculation of differential absorption of thermal radiation is formulated based on the modified DP₀ approximation. The solution of this problem is supplemented by simple analytical approximations for the normalised absorbed radiation power. The latter is used together with the analytical approximation for the efficiency factor of absorption, suggested earlier. The resulting simplified model is applied to the specific problem of absorption of thermal radiation by a diesel fuel droplet. Two types of diesel fuel have been considered. It is pointed out that the radial distribution of absorbed thermal radiation power is non-monotonic. The power absorbed in the droplet core is shown to be rather large and almost homogeneous. Also, the absorbed power is large in the vicinity of the droplet surface, but is minimal in the intermediate region. It is pointed out that the variations of the refractive index of diesel fuel with wavelengths can smooth the predicted radial dependence of the thermal radiation power, absorbed in diesel fuel droplets.     

Numerical study on a vertical plate with variable viscosity and thermal conductivity

Free convection over an isothermal vertical plate immersed in a fluid with variable viscosity and thermal conductivity is studied in this paper. We consider the two-dimensional, laminar and unsteady boundary layer equations. Using the appropriate variables, the basic governing equations are transformed to non-dimensional governing equations. These equations are then solved numerically using a very efficient implicit finite difference scheme known as Crank–Nicolson scheme. The fluid considered in this study is of viscous incompressible fluid of temperature dependent viscosity and thermal conductivity. The effect of varying viscosity and thermal conductivity on velocity, temperature, shear stress and heat transfer rate are discussed. The velocity and temperature profiles are compared with previously published works and are found to be in good agreement.