On an indirect integral equation approach for stationary heat transfer in semi-infinite layered domains in R3 with cavities

Regions containing internal boundaries such as composite materials arise in many applications.We consider a situation of a layered domain in IR3 containing a nite number of bounded cavities. The model is stationary heat transfer given by the Laplace equation with piecewise constant conductivity. The heat ux (a Neumann condition) is imposed on the bottom of the layered region and various boundary conditions are imposed on the cavities. The usual transmission (interface) conditions are satised at the interface layer, that is continuity of the solution and its normal derivative. To eciently calculate the stationary temperature eld in the semi-innite region, we employ a Green's matrix technique and reduce the problem to boundary integral equations (weakly singular) over the bounded surfaces of the cavities. For the numerical solution of these integral equations, we use Wienert's approach [20]. Assuming that each cavity is homeomorphic with the unit sphere, a fully discrete projection method with super-algebraic convergence order is proposed. A proof of an error estimate for the approximation is given as well. Numerical examples are presented that further highlights the eciency and accuracy of the proposed method.

Computer methods for the heat conduction equation

The merits of various numerical methods for the solution of the one and two dimensional heat conduction equation with a radiation boundary condition have been examined from a practical standpoint in order to determine accuracies and efficiencies. It is found that the use of five increments to approximate the space derivatives gives sufficiently accurate results provided the time step is not too large; further, the implicit backward difference method of Liebmann (27) is found to be the most accurate method. On this basis, a new implicit method is proposed for the solution of the three-dimensional heat conduction equation with radiation boundary conditions. The accuracies of the integral and analogue computer methods are also investigated.

Pet food from bovine origin drying by green heat pump technology and fluidization

Bovine intestine was dried in a heat pump fluid bed combination. Minimum fluidisation velocity was calculated by Ergun Equation and some relations were established.

Heat-Transfer During Dropwise Condensation

A comprehensive model is developed for previous termheat transfernext term during previous termdropwise condensationnext term based on the assumption that previous termheat transfernext term takes place through the bare surface in between drops to form nuclei at nucleation sites during the waiting period required for nucleation. The dynamics of drop formation and surface renewal, and the presence of non-condensable gases in the vapour have been considered. The resulting equation expresses the dependence of the vapour-side previous termheat transfernext term coefficient on the previous termheatnext term flux, properties of the vapour, previous termcondensationnext term coefficient, mole fraction of non-condensable gases in the vapour, free area available for previous termcondensation,next term surface roughness and surface thermal properties. The equation is tested with the available data and the agreement is found to be satisfactory.

Pressure shocks in relativistic viscous heat-conducting fluids

In this paper we have studied the propagation of pressure shocks in viscous, heat-conducting, relativistic fluids. Velocities of wave fronts and growth equations for the strength of the waves are obtained in the case of low and high temperatures with variable transport coefficients. On the basis of numerical integrations the growth equation results have been discussed. In the case of constant transport coefficients and for all admissible values of ratio of specific heats of the fluid, an analytical solution for the velocity of the wave as a function of distance along the normal trajectory to the wave front, has been obtained.

Two-dimensional heat conduction with phase change in a semi-infinite mould

Analytical solution of a 2-dimensional problem of solidification of a superheated liquid in a semi-infinite mould has been studied in this paper. On the boundary, the prescribed temperature is such that the solidification starts simultaneously at all points of the boundary. Results are also given for the 2-dimensional ablation problem. The solution of the heat conduction equation has been obtained in terms of multiple Laplace integrals involving suitable unknown fictitious initial temperatures. These fictitious initial temperatures have interesting physical interpretations. By choosing suitable series expansions for fictitious initial temperatures and moving interface boundary, the unknown quantities can be determined. Solidification thickness has been calculated for short time and effect of parameters on the solidification thickness has been shown with the help of graphs.

Heat transfer to power-law fluids in thermal entrance region with viscous dissipation for constant heat flux conditions

An analytical solution of the heat transfer problem with viscous dissipation for non-Newtonian fluids with power-law model in the thermal entrance region of a circular pipe and two parallel plates under constant heat flux conditions is obtained using eigenvalue approach by suitably replacing one of the boundary conditions by total energy balance equation. Analytical expressions for the wall and the bulk temperatures and the local Nusselt number are presented. The results are in close agreement with those obtained by implicit finite-difference scheme. It is found that the role of viscous dissipation on heat transfer is completely different for heating and cooling conditions at the wall. The results for the case of cooling at the wall are of interest in the design of the oil pipe line.

Development of an efficiency equation for solar evaporator- collectors

Considering the growing energy needs and concern for environmental degradation, clean and inexhaustible energy sources, e.g solar energy are receiving greater attention for various applications. The use of solar energy systems for low temperature applications reduces the burden on conventional fossil fuels and has little or no harmful effects on the environment. The performance of a solar system depends to a great extent on the collector used for the conversion of solar radiant energy to thermal energy. A solar evaporatorcollector (SEC) is basically an unglazed flat plate collector where refrigerant, like R134a, is used as the working fluid. As the operating temperature of SEC is very low, it collects energy both from solar irradiation and ambient energy leading to a much higher efficiency than the conventional collectors. The capability of SEC to utilize ambient energy also enables the system to operate at night. Therefore it is not appropriate to use for the evaluation of performance of SEC by conventional efficiency equation where ambient energy and condensation is not considered as energy input in addition to irradiation. In the National University of Singapore, several Solar Assisted Heat Pump (SAHP) systems were built for the evaluation of performance under the metrological condition of Singapore for thermal applications of desalination and SEC was the main component to harness renewable energy. In this paper, the design and performance of SEC are explored. Furthermore, an attempt is made to develop an efficiency equation for SEC and maximum efficiency attained 98% under the meteorological condition of Singapore.

On latent heat of vaporization, surface tension, and temperature

A semitheoretical equation for latent heat of vaporization has been derived and tested. The average error in predicting the value at the normal boiling point in the case of about 90 compounds, which includes polar and nonpolar liquids, is about 1.8%. A relation between latent heat of vaporization and surface tension is also derived and is shown to lead to Watson's empirical relation which gives the change of latent heat of vaporization with temperature. This gives a physico-chemical justification for Watson's empirical relation and provides a rapid method of determining latent heats by measuring surface tension.

Heat transfer to newtonian fluids in coiled pipes in laminar flow

Data on pressure drop and heat transfer to aqueous solutions of glycerol flowing in different types of coiled pipes are presented for laminar flow in the range of NRe from 80 to 6000. An empirical correlation is set up which can account the present data as well as the data available in literature within ±10 per cent deviation. Conventional momentum and heat transfer analogy equation is used to analyse the present data.

Numerical procedure for second order non-linear ordinary differential equations and application to heat transfer problem

In this paper, we have first given a numerical procedure for the solution of second order non-linear ordinary differential equations of the type y″ = f (x;y, y′) with given initial conditions. The method is based on geometrical interpretation of the equation, which suggests a simple geometrical construction of the integral curve. We then translate this geometrical method to the numerical procedure adaptable to desk calculators and digital computers. We have studied the efficacy of this method with the help of an illustrative example with known exact solution. We have also compared it with Runge-Kutta method. We have then applied this method to a physical problem, namely, the study of the temperature distribution in a semi-infinite solid homogeneous medium for temperature-dependent conductivity coefficient.

Non-linear couette flow with heat transfer using the B-G-K model

In recent years a large number of investigators have devoted their efforts to the study of flow and heat transfer in rarefied gases, using the BGK [1] model or the Boltzmann kinetic equation. The velocity moment method which is based on an expansion of the distribution function as a series of orthogonal polynomials in velocity space, has been applied to the linearized problem of shear flow and heat transfer by Mott-Smith [2] and Wang Chang and Uhlenbeck [3]. Gross, Jackson and Ziering [4] have improved greatly upon this technique by expressing the distribution function in terms of half-range functions and it is this feature which leads to the rapid convergence of the method. The full-range moments method [4] has been modified by Bhatnagar [5] and then applied to plane Couette flow using the B-G-K model. Bhatnagar and Srivastava [6] have also studied the heat transfer in plane Couette flow using the linearized B-G-K equation. On the other hand, the half-range moments method has been applied by Gross and Ziering [7] to heat transfer between parallel plates using Boltzmann equation for hard sphere molecules and by Ziering [83 to shear and heat flow using Maxwell molecular model. Along different lines, a moment method has been applied by Lees and Liu [9] to heat transfer in Couette flow using Maxwell's transfer equation rather than the Boltzmann equation for distribution function. An iteration method has been developed by Willis [10] to apply it to non-linear heat transfer problems using the B-G-K model, with the zeroth iteration being taken as the solution of the collisionless kinetic equation. Krook [11] has also used the moment method to formulate the equivalent continuum equations and has pointed out that if the effects of molecular collisions are described by the B-G-K model, exact numerical solutions of many rarefied gas-dynamic problems can be obtained. Recently, these numerical solutions have been obtained by Anderson [12] for the non-linear heat transfer in Couette flow,

Exact solution for the unsteady flow and heat transfer between eccentrically rotating disks

The unsteady heat transfer associated with flow due to eccentrically rotating disks considered by Ramachandra Rao and Kasiviswanathan (1987) is studied via reformulation in terms of cylindrical polar coordinates. The corresponding exact solution of the energy equation is presented when the upper and lower disks are subjected to steady and unsteady temperatures. For an unsteady flow with nonzero mean, the energy equation can be solved by prescribing the temperature on the disk as a sum of steady and oscillatory parts

Study of magnetic field effect on the specific heat and entropy in DyBa2Cu3O7-x

The change in the specific heat by the application of magnetic field up to 161 for high temperature superconductor system for DyBa2Cu3O7-x by Revaz et al. [23] is examined through the phenomenological Ginzburg-Landau(G-L) theory of anisotropic Type-II superconductors. The observed specific heat anomaly near T-c with magnetic field is explained qualitatively through the expression <Delta C > = (B-a/T-c) t/(1 - t)(alpha Theta(gamma)lambda(2)(m)(0)), which is the anisotropic formulation of the G-L theory in the London limit developed by Kogan and coworkers; relating to the change in specific heat Delta C for the variation of applied magnetic field for different orientations with c-axis. The analysis of this equation explains satisfactorily the specific heat anomaly near T-c and determines the anisotropic ratio gamma as 5.608, which is close to the experimental value 5.3 +/- 0.5given in the paper of Revaz et al. for this system. (C) 2010 Elsevier B.V. All rights reserved.