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In this paper, a novel Bian stone thermal therapy assisted by using solar radiation is proposed for safe thermal therapy on patients. A mathematical model is developed based on heat balance, and the performance of heat transfer from the novel Bian stone thermal therapy system to human body is studied. Sensitivity analysis is also performed. Fluid heated by solar radiation is channeled through a pipe to heat the Bian stone. For stronger solar radiation, or smaller or shorter pipe, the Bian stone attains the initial body temperature faster, and the novel thermal therapy system shows better performance and can therefore be used on patients earlier during the day. Early use of the thermal therapy system is a very important factor because the lowest ambient temperature is normally obtained early in the morning. Moderate water flow velocity is suitable by considering good mixing effect and power savings. The stone-body contact surface area has little influence on the critical heating time for the Bian stone to reach the initial body temperature after sunrise. This work lays a solid foundation for safe use of the solar assisted Bian stone thermal therapy. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a one-phase supercooled Stefan problem, with a nonlinear relation between the phase change temperature and front velocity, is analysed. The model with the standard linear approximation, valid for small supercooling, is first examined asymptotically. The nonlinear case is more difficult to analyse and only two simple asymptotic results are found. Then, we apply an accurate heat balance integral method to make further progress. Finally, we compare the results found against numerical solutions. The results show that for large supercooling the linear model may be highly inaccurate and even qualitatively incorrect. Similarly as the Stefan number β →1+ the classic Neumann solution which exists down to β =1 is far from the linear and nonlinear supercooled solutions and can significantly overpredict the solidification rate. [Copyright &y& Elsevier]

Abstract: In this paper the two main drawbacks of the heat balance integral methods are examined. Firstly we investigate the choice of approximating function. For a standard polynomial form it is shown that combining the heat balance and refined integral methods to determine the power of the highest order term will either lead to the same, or more often, greatly improved accuracy on standard methods. Secondly we examine thermal problems with a time-dependent boundary condition. In doing so we develop a logarithmic approximating function. This new function allows us to model moving peaks in the temperature profile, a feature that previous heat balance methods cannot capture. If the boundary temperature varies so that at some time t >0 it equals the far-field temperature, then standard methods predict that the temperature is everywhere at this constant value. The new method predicts the correct behaviour. It is also shown that this function provides even more accurate results, when coupled with the new CIM, than the polynomial profile. Analysis primarily focuses on a specified constant boundary temperature and is then extended to constant flux, Newton cooling and time dependent boundary conditions. [Copyright &y& Elsevier]

Abstract: The slip effect of gaseous flow in a micro-scale channel is dominant when the characteristic length is less than about 10μm under atmospheric conditions. The slip flow in a channel whose wall temperature is specified can be analyzed by solving the momentum and energy equations with taking into account the slip velocity and temperature jump. However, when there is slip, the shear work due to the slip at the wall should be included to calculate the heat flux from the wall. Unfortunately, the need of inclusion of the shear work in the heat balance equation has not been physically explained. In this paper, the physical reason of the inclusion of the shear work in the heat balance equation is physically explained from the point of view of both conservation law of energy and the kinetic theory of gases. [Copyright &y& Elsevier]

Abstract: The work in this paper deals with the development of momentum and thermal boundary layers when a power law fluid flows over a flat plate. At the plate we impose either constant temperature, constant flux or a Newton cooling condition. The problem is analysed using similarity solutions, integral momentum and energy equations and an approximation technique which is a form of the Heat Balance Integral Method. The fluid properties are assumed to be independent of temperature, hence the momentum equation uncouples from the thermal problem. We first derive the similarity equations for the velocity and present exact solutions for the case where the power law index . The similarity solutions are used to validate the new approximation method. This new technique is then applied to the thermal boundary layer, where a similarity solution can only be obtained for the case . [Copyright &y& Elsevier]

Abstract: When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires no knowledge of an exact solution and generally produces significantly better results than all previous HBI models. The method is illustrated by first applying it to standard thermal problems. A Stefan problem with an analytical solution is then discussed and results compared to the approximate solution. An ablation problem is also analysed and results compared against a numerical solution. In both examples the agreement is excellent. A Stefan problem where the boundary temperature increases exponentially is analysed. This highlights the difficulties that can be encountered with a time dependent boundary condition. Finally, melting with a time-dependent flux is briefly analysed without applying analytical or numerical results to assess the accuracy. [Copyright &y& Elsevier]

Abstract: The paper presents the geometry of infinite regular polyhedrons that can be used to construct the heat exchange units. The basic structural component of the infinite solid consists of six hexagons, which meet in the common vertex. The mathematical model of heat and mass transfer inside the labyrinth heat exchanger is shown. The first and the second Kirchhoff’s laws are used to simulate fluid flow distribution at hydraulic network created with connected basic solids. Heat balance equations are adopted to describe forced convection heat transfer inside developed heat exchanger. Good accordance among the experimental data and calculation results over whole simulation range is obtained. The efficiency and thermal characteristic of the labyrinth heat exchanger is presented in the form of graphs. [Copyright &y& Elsevier]