An analytic solution of one-dimensional steady-state Pennes’ bioheat transfer equation in cylindrical coordinates

Based on the Pennes’ bioheat transfer equation, a simplified one-dimensional bioheat transfer model of the cylindrical living tissues in the steady state has been set up for application in limb and whole body heat transfer studies, and by using the Bessel’s equation, its corresponding analytic solution has been derived in this paper. With the obtained analytic solution, the effects of the thermal conductivity, the blood perfusion, the metabolic heat generation, and the coefficient of heat transfer on the temperature distribution in living tissues are analyzed. The results show that the derived analytic solution is useful to easily and accurately study the thermal behavior of the biological system, and can be extended to such applications as parameter measurement, temperature field reconstruction and clinical treatment.     

内通传热流体的圆管外相变材料的无量纲储传热准则的研究

建立了分析内通传热流体的圆管外相变材料储,储热特性的理论模型,并提出分析瞬态相变层厚度分布,传热流体轴向温度分布及圆管相变材料储,传热量的新方法：温度－固液界面移动交替迭代法,通过理论分析和数值计算,得到确定上述参数的无量纲公式,公式与数据点的平均拟合精度分别为０．３％、１．６２％和２．５％。准则公式计算值与相同条件下的文献值吻合,验证了本文模型、方法和结果的正确性。所得的无量纲公式不局限于某一种     

Analytical modelling of heat transfer from a single slab in freezing

The present study deals with the experimental and theoretical analysis of the transient heat transfer from an individual slab body to the medium during freezing. In this respect, a new model was developed to determine the heat transfer coefficient and this heat transfer coefficient was used in the computation of the dimensionless theoretical temperature distribution. On the other hand, experimental work was performed to measure the centre temperatures of the individual slab products (viz. dried figs) during freezing at the median temperature of -22°C. In the comparison of the theoretical and experimental temperature distributions, very good agreement was found.     

An Analytic Solution of One-dimensional Steady-state Pennes'''' Bioheat Transfer Equation in Cylindrical Coordinates

Based on the Pennes' bioheat transfer equation, a simplified one-dimensional bioheat transfer model of the cylindrical living tissues in the steady state has been set up for application in limb and whole body heat transfer studies, and by using the Bessel's equation, its corresponding analytic solution has been derived in this paper. With the obtained analytic solution, the effects of the thermal conductivity, the blood perfusion, the metabolic heat generation, and the coefficient of heat transfer on the temperature distribution in living tissues are analyzed. The results show that the derived analytic solution is useful to easily and accurately study the thermal behavior of the biological system, and can be extended to such applications as parameter measurement, temperature field reconstruction and clinical treatment.     

污垢对管内层流换热性能影响的热力学分析和评价

采用热力学第二定律，分别在恒壁温和恒热流两种典型工况下分析了污垢对管内层流换热性能的影响；引入单位传热量的熵增率对污垢管道的热力学性能进行了评价；讨论了管内流体雷诺数(无污垢时)、量纲为1的入口换热温差、量纲为1的热流密度和污垢层厚度等参数对单位传热量熵增率的影响；并把结果和紊流时的对应工况进行了比较。结果可为工程上换热设备的优化设计提供依据。     

Numerical investigation on porous media heat transfer in a solar tower receiver

In order to investigate the steady heat transfer characteristics of a porous media solar tower receiver developed in China, this paper applies the steady heat and mass transfer models of the porous media to solar receivers, chooses the preferable volume convection heat transfer coefficient model, solves these equations by using the numerical method, and analyzes the typical influences of the porosity, average particle diameter, air inlet velocity, and thickness on the temperature distribution. The following conclusions have been drawn: in the same position or relative position along the downstream, the bigger the average particle diameter is, the higher the solid matrix dimensionless temperature is, the higher the air dimensionless temperature is. The bigger the porosity is, the lower the solid matrix dimensionless temperature is, the bigger the porosity is, the higher the air dimensionless temperature is. The bigger the thickness is, the lower the solid matrix dimensionless temperature is, the higher the air dimensionless temperature is. In a certain depth, the bigger the air inlet velocity is, the higher the solid matrix dimensionless temperature is. After a certain depth, the bigger the air inlet velocity is, the lower the solid matrix dimensionless temperature is, and the bigger the air inlet velocity is, the higher the air dimensionless temperature is. The paper can provide a reference for this type of receiver design and reconstruction.     

板式相变贮能换热器传热模型和热性能分析

建立了板式相变贮能换热器的无量纲传热模型。它对流体入口流量、入口温度随时间变化情况和需考虑入口效应及添加肋片的情况均适用。模型解和文献准稳态解吻合。作为算例,藉此模型从各时刻的流体温度、相变界面随空间的分布情况和相变蓄热比、相变传热效率、传热系数、完全相变截面位置随时间的变化情况六个角度分析了一板式相变贮能换热器的相变传热性能。该模型可为板式相变贮能换热器的结构优化设计和热性能分析提供帮助。     

Heat transfer characteristics of microencapsulated phase change material slurry in laminar flow under constant heat flux

Due to its large apparent specific heat during the phase change period, microencapsulated phase change material slurry (MPCMS) has been suggested as a medium for heat transfer. In this paper, the convective heat transfer characteristics of MPCMS flowing in a circular tube were experimentally and numerically investigated. The enhanced convective heat transfer mechanism of MPCMS, especially in the thermal fully developed range, was analyzed by using the enthalpy model. Three kinds of fluid–pure water, micro-particle slurry and MPCMS were numerically investigated. The results show that in the phase change heat transfer region the Ste number and the Mr number are the most important parameters influencing the Nusselt number fluctuation profile and the dimensionless wall temperature. Re_b, d_p and c also influence the Nusselt number profile and the dimensionless wall temperature, but they are independent of phase change process.     

Laminar heat transfer of gas in a parallel‐plate microchannel with one wall temperature constant and the other adiabatic

Based on “wall‐adjacent layer” effect, the convective heat transfer for developed laminar flow of gas through parallel‐plate microchannel with one wall temperature constant and the other adiabatic was analyzed theoretically. Considering the change in thermal conductivity and viscosity of gas in the region adjacent to the solid wall, mathematical models were built and the dimensionless temperature distribution and the corresponding heat transfer characteristics were simulated numerically. The results indicate that the laminar heat transfer coefficient is less than that of the larger passages, while the dimensionless temperature is greater than that of the larger passages. Compared with the monotonous boundary conditions, the varied heat transfer coefficient amplitude of mixed boundary condition is lower. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(1): 58–64, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10075     

Estimation of temperature distribution in biological tissue by using solutions of bioheat transfer equation

A living body has a system for maintaining its temperature. We have investigated the heat transfer characteristics common to each organ and therapy using heat transfer. The one‐dimensional bioheat transfer equation with bioheat generation was converted into a dimensionless form and solved by Laplace transformation on the assumption that biological tissue is homogeneous. A dimensionless steady‐state solution and transient solution were derived analytically. These solutions can represent the characteristics of the temperature distribution common to each organ. Comparison with numerical solutions has confirmed that these solutions can be applied to estimate the temperature distribution of inhomogeneous biological tissue. It is proved that the size of the region where temperature change occurs, the steady‐state thermal penetration depth, is decided by biological properties. Furthermore, the time needed to reach a steady state, or the time it takes for biological tissue to reach a steady state, is calculated by using these solutions. Additionally, a temperature chart was proposed for each organ or tissue. This chart can serve as a guideline for medical doctors in formulating thermal therapy. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(6): 374– 386, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20210     

Performance study on heat and moisture transfer in soil heat charging

In some cold areas, the system performance of the soil source heat pump system is reduced by the decreasing underground soil temperature, which is caused by the thermal imbalance between the heating demand in winter and the cooling demand in summer. Soil heat charging with solar energy in non-heating seasons is proposed for solving the problem. It has been found from previous studies that the effect of the moisture transfer on the heat transfer within porous media could not be neglected especially under higher temperature difference. Therefore, this paper provides an investigation on the heat and moisture transfer in soil during soil heat charging at high temperature. A numerical model is developed for the study. The simulation results are compared with the testing data from the authors' previous study for the model verification. Based on the verified model, the performance of the heat and moisture transfer in soil during soil heat charging in a longer time and a larger area is investigated in the paper. The results show that the testing data match very well with the simulation results within a relative error of ±9% and the mathematical model is reliable for the performance prediction of heat and moisture transfer in soil heat charging. The soil volumetric water content (VWC) distribution tends to be stable after soil heat charging for 13 days and the heat source has an effective influence on soil VWC distribution within 2.4?m. The effect of the heat source temperature and initial VWC on the soil temperature and VWC distribution and heat power is proved to be obvious. Loam has a better performance in soil heat charging than sand.     

An experimental study of heat transfer in oscillating flow through a channel filled with an aluminum foam

An experimental study has been conducted on the heat transfer of oscillating flow through a channel filled with aluminum foam subjected to a constant wall heat flux. The surface temperature distribution on the wall, velocity of flow through porous channel and pressure drop across the test section were measured. The characteristics of pressure drop, the effects of the dimensionless amplitude of displacement and dimensionless frequency of oscillating flow on heat transfer in porous channel were analyzed. The results revealed that the heat transfer in oscillating flow is significantly enhanced by employing porous media in a plate channel. The cycle-averaged local Nusselt number increases with both the kinetic Reynolds number Re_ω and the dimensionless amplitude of flow displacement A₀. The length-averaged Nusselt number is effectively increased by increasing the kinetic Reynolds number from 178 to 874 for A₀ = 3.1-4.1. Based on the experimental data, a correlation equation of the length-averaged Nusselt number with the dimensionless parameters of Re_ω and A₀ is obtained for a porous channel with L/D_h = 3.     

幂律流体饱和多孔介质通道中的粘性耗散效应

针对Darcy-Brinkman-Forchheimer流动模型,分析了幂律型非牛顿流体在填充多孔介质平板通道中强迫对流传热过程充分发展的黏性耗散效应,并比较了三个不同的黏性耗散项Darcy项、Al-Hadhrami项和Forchheimer项对流动传热率的影响。推导出了无量纲轴向流速分布和无量纲温度分布的计算表达式,并在恒热流边界条件下,利用经典Runge-Kutta法进行数值求解。模拟结果表明,布林克曼数Br、达西数Da、综合惯性参数F和幂律指数n等重要参数对无量纲温度分布有着较大的影响,同时发现不同的黏性耗散效应对流动传热特性也有着重要的影响。     

冲击热负荷作用下垂直自然循环传热特性的试验研究

鉴于对炼钢转炉锅炉研究的重要意义，设计了一套简单、可靠的试验系统，对炼钢转炉余热锅炉周期性的不稳定传热过程进行试验模拟。对其在冲击热负荷下垂直自然循环的传热特性进行了深入的试验研究，得到其传热特性的一般变化规律，并分析了冲击热负荷和工质欠焓对其传热特性的影响，通过回归试验数据得到传热系数的准则关系式。对改善炼钢转炉余热锅炉的传热特性和水循环安全性提出了建议。     

Heat transfer analysis of solar-driven high-temperature thermochemical reactor using NiFe-Aluminate RPCs

Converting solar energy efficiently into hydrogen is a promising way for renewable fuels technology. However, high-temperature heat transfer enhancement of solar thermochemical process is still a pertinent challenge for solar energy conversion into fuels. In this paper, high-temperature heat transfer enhancement accounting for radiation, conduction, and convection heat transfer in porous-medium reactor filled with application in hydrogen generation has been investigated. NiFe-Aluminate porous media is synthesized and used as solar radiant absorber and redox material. Experiments combined with numerical models are performed for analyzing thermal characteristics and chemical changes in solar receiver. The reacting medium is most heated by radiation heat transfer and higher temperature distribution is observed in the region exposed to high radiation heat flux. Heat distribution, O₂ and H₂ yield in the reacting medium are facilitated by convective reactive gas moving through the medium's pores. The temperature gradient caused by thermal transition at fluid-solid interface could be more decreased as much as the reaction chamber can store the transferred high-temperature heat flux. However, thermal losses due to radiation flux lost at the quartz glass are obviously inevitable.     

Blood flow in a stenotic artery with temperature-dependent viscosity

We investigate the effects of temperature-dependent viscosity variations on the flow and heat transfer characteristics in an artery in the presence of stenosis. The dimensionless governing equations have been solved using the implicit finite difference method. The local skin friction coefficient and the local Nusselt number at the lower and upper walls are found to be stronger with the increase of stenosis. With the change of position of the upper stenosis, the skin friction and the Nusselt number at the lower plate demonstrate distinct characteristics. A remarkable result is that when the viscosity variation parameter is increased, the vortices following the stenosis become smaller in size. Moreover, the size of vortices increases with the increase of stenosis, whereas it is found to decrease owing to the change of position of the upper stenosis.     

A numerical study of film condensation on a metallic foam-sintered plate with considering convection and super-cooling effects

A numerical solution was presented for film condensation on a vertical plate sintered with metallic foam. In the metallic foam region, the Brinkman-Darcy model was employed to establish the fluid flow equation, and the thermal equilibrium model was used to describe local heat transfer. Through introduction of dimensionless distance, namely, the ratio of the coordinate normal to the plate and the local film thickness, the computational domain was regularized in a rectangular zone. The effects of convection and explicit heat of super-cooled liquid on the condensation film were considered. The temperature and velocity profile, film thickness, and the local and average Nu number were obtained. The effects of Ja and Da number on the velocity profile and heat transfer performance were investigated. The numerical model was verified through comparison of the predicted results with those in the literature, which neglected convection and explicit heat of super-cooling effects. Convection and explicit heat of super-cooling can play a positive role in reducing the velocity level in the film. The two effects played a positive role in heat transfer improvement when the dimensionless location along the gravity direction (X) was > 0.15, which was associated with reduced film thickness. The two effects also had a mild influence on the linear distribution of dimensionless temperature. The heat transfer performance deteriorated with an increase in Ja number or Da number.     

Optimal homotopy asymptotic method for heat transfer in hollow sphere with robin boundary conditions

In this article, we have investigated heat transfer from a hollow sphere using a powerful and relatively new semi‐analytic technique known as the optimal homotopy asymptotic method (OHAM). Robin boundary conditions are applied on both the inner and outer surfaces. The effects of Biot numbers, uniform heat generation, temperature‐ dependent thermal conductivity, and temperature parameters on the dimensionless temperature and heat transfer are investigated. The results of OHAM are compared with a numerical method and are found to be in good agreement. It is shown that the dimensionless temperature increases with an increase in Biot number at the inner surface and temperature and heat generation parameters, whereas it decreases with an increase in the Biot number at the outer surface and the dimensionless thermal conductivity and radial distance parameters. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res 43(2): 124‐133, 2014; Published online 20 June 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21067     

Thermal analysis of natural convection and radiation in porous fins

In this study, the effects of radiation and convection heat transfer in porous media are considered. The geometry considered is that of a rectangular profile fin. The porous fin allows the flow to infiltrate through it and solid-fluid interaction takes place. This study is performed using Darcy's model to formulate heat transfer equation. To study the thermal performance, three types of cases are considered viz. long fin, finite length fin with insulated tip and finite length fin with tip exposed. The theory section addresses the derived governing equation. The effects of the porosity parameter S_h, radiation parameter G and temperature ratio C_T on the dimensionless temperature distribution and heat transfer rate are discussed. The results suggest that the radiation transfers more heat than a similar model without radiation.     

The effects of micro-structured surfaces on multi-nozzle spray cooling

Experiments were conducted to investigate heat transfer characteristics of spray cooling with eight nozzles for micro-structured surfaces included cubic pin fins and straight pin fins of different sizes. Liquid volume flow rate ranged from 2.46 × 10⁻² m³/s/m² to 3.91 × 10⁻² m³/s/m² and the corresponded inlet pressures changed from 0.28 MPa to 0.6 MPa by keeping the inlet water temperature between 20.4 °C and 24.31 °C. And the input power of heat block varied from 180 W to 1080 W. The results show that the heat transfer performances of straight fins2 and straight fins3 are the best in single phase zone, but the cubic pin fins is better in two phase zone. Notably, the critical point between single phase zone and two phase zone shifts to left with the increasing of liquid volume flow rate. Moreover, with the liquid volume flow rate increasing, the heat transfer coefficient increases as well, but straight fins1 and polished surface are not sensitive to this change. For a deeper analysis of the heat transfer enhancement, a dimensionless number (DM) is created to characterize heat transfer performance of different microstructures in single phase heat transfer. We verified the dimensionless number using experimental results in this study and previous literature. Furthermore, the micro-structured surfaces have negligible effects on temperature distribution except for cubic pin fins.