Heat loss calculation in thermal simulation

An appraisal is presented for four different methods that are usually incorporated in thermal simulators to estimate the rate of heat loss to surroundings. The methods are the analytical solution using a superposition theorem, the analytical solution using a numerical approximation to the convolution integral, the semi-analytical solution, and the numerical solution. This appraisal includes expressing the equations in a form that can be incorporated into a fully implicit simulator, computer programming complexity, and the computer CPU time and memory storage requirements. A steam flood problem is used for the comparison, and the gas recovery, oil recovery, and heat loss performances for a reservoir in one and two dimensions are presented. It is found that the numerical solution is sensitive to grid size in the overburden, the semi-analytical solution is the simplest to program but its prediction is the least accurate, the analytical solution is the most expensive, whereas the analytical-numerical solution combines both accuracy and acceptable storage requirements, and therefore, it is recommended for use in thermal simulation.     

Heat transfer in the cylindrical rarefied Couette flow

The efficiency of the self-similar interpolation method is demonstrated with reference to the solution of the problem of heat transfer in a rarefied gas between two coaxial cylinders rotating relative one another. The analytical solution of the problem is compared with the results obtained by direct statistical simulation. The most interesting result is the energy flux nonmonotonicity and the reversal of its sign with variation in the Knudsen number.     

Heat transfer in vertical annular laminar flow of two immiscible liquids

The paper investigates heat transfer in annular laminar undisturbed flow of two immiscible liquids, with constant heat-flux generated at the wall of the tube. It presents an analytical solution for the fully developed temperature field. This is used to obtain a more general solution from a model, describing the temperature field as a superposition of the fully developed and the developing fields. This superposition model is solved by an orthogonal collocation method. An asymptotic model for short entry lengths is also described. Calculations for a kerosene-water system, show that the superposition solution converges to the entrance solution below 100 diameters and converges asymptotically to the solution of the fully developed temperature field beyond 5000 diameters. The effect of the wavy interface is assessed experimentally for annular kerosene-water flow, by comparing predicted and measured temperature profiles. It is found that experimental profiles are considerably flatter and measured Nusselt numbers for the kerosene phase are accordingly higher by 40–320% as compared to the undisturbed flow analyses.     

Heat and mass transfer in direct contact hygroscopic condensation

A theoretical analysis of direct contact hygroscopic-condensation of cold vapor on hot films is presented. The condensation of the relatively low temperature, low pressure, vapors on a hot film of an hygroscopic brine solution may occur due to the reduced vapor pressure of a sufficiently concentrated solution. The driving force for condensation is the difference between the partial pressure of water in the brine and the partial pressure of the condensing water vapor. The condensation is also governed by simultaneous mass transfer mechanisms, due to a non-isothermal absorption, with a possible opposing thermal driving force in the condensing vapor phase. The overall performance is determined by the accumulating effects of the various resistances to heat and mass transfer. The present study is aimed to elucidate the controlling mechanisms associated with this absorption-condensation process, and suggest overall transfer rates at the laminar and turbulent flow regimes.     

Heat conduction between confocal elliptical surfaces using the theory of a Cosserat shell

This paper is concerned with steady-state heat conduction in rigid shell-like interphase regions. By analogy this work may provide insight into related problems of electric, dielectric and magnetic behavior. Although the field equations for three-dimensional linear Fourier heat condition are rather simple, the solution of problems in shell regions is significantly complicated when the shell has a general geometry and variable thickness. Here, the problem of heat conduction between confocal elliptical surfaces is solved within the context of the theory of a Cosserat shell. This problem is of particular interest because the Cosserat solution can be compared with an exact solution and the influences of variable shell thickness and strong variations of the temperature field through the shell’s thickness can be explored independently. The results show that the Cosserat approach is reasonably accurate even for moderately thick shells, moderate ellipticity, and moderately strong variation of the temperature through the shell’s thickness.     

Heat transfer in the assimilation of a pre-heated jet into non-uniform streams

 The flow assimilation of a pre-heated jet into non-uniform external streams has been examined. Two possible families of downstream velocity and temperature profiles are identified. The formulation of the problem allows for a comprehensive numerical solution over the entire flow and temperature field downstream of the jet source. The role of the respective families of downstream asymptotes is elucidated, and consistency is demonstrated between a spatial stability analysis of the profiles and the numerical results. Received on 12 May 2000     

Heat transfer in channels in the laminar flow of a non-newtonian liquid with slip

We consider the case of quasi-isothermal heat transfer in the laminar flow of a non-Newtonian medium with slip in circular and plane channels. The calculation is based on the simultaneous solution of the equations of energy, motion, and a rheological relation with the specific boundary conditions which takes into account discontinuity in the velocity and temperature on the heat-transfer surface.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 146–151, September–October, 1971.     

Heat and mass transfer in a dispersive medium

Macroscopic equations for the conservation of heat (or the mass of a diffusing impurity) in a continuous medium containing distributed particles of a dispersed phase are formulated neglecting the effect of random fluctuations of the medium and particles by the transfer process. The problem of convective heat conduction or diffusion near an isolated particle is also formulated, the solution of which permits calculation of all the parameters entering into the indicated equations. This problem has been solved in the particular case of small Peclet numbers, which characterize heat and mass exchange in the vicinity of a single particle.     

Heat transfer in unsteady laminar flow through a channel

The temperature distribution in unsteady laminar flow of a viscous incompressible fluid in a flat channel is investigated, when the pressure gradient is an arbitrary function of time. Two techniques are presented (i) explicit finite difference scheme, and (ii) Chebyshev polynomial solution. Using both the techniques, several cases of pressure gradient are considered, with special attention paid to the linearly varying case.     

Heat wave phenomena in solids subjected to time dependent surface heat flux

Hyperbolic heat conduction in a plane slab, infinitely long solid cylinder and solid sphere with a time dependent boundary heat flux is analytically studied. The solution is based on the separation of variables method and Duhamel’s principle. The temperature distribution, the propagation and reflection of the temperature wave and the effect of geometry on the shape of the wave front are studied for the case of a rectangular pulsed boundary heat flux. Comparisons with the solution obtained for Fourier heat conduction are performed by considering the limit of a vanishing thermal relaxation time.     

Laminar Heat Transfer of a Swirled Flow in a Conical Diffuser. Self-similar Solution

Heat transfer in a laminar swirled air flow in the divergent channel between a disk and a cone whose vertex touches the disk is studied. A self-similar solution of the Navier-Stokes and energy equations is derived using group analysis. An exact numerical solution of the problem is obtained for different radial-to-tangential velocity ratios at the channel inlet.     

Heat transfer analysis of a particle-containing channel flow

This paper describes an analytical model of heat transfer in a two-dimensional, steady, nonreacting particle-containing channel flow. An idealized gas flow of specified uniform velocity between insulated parallel plates is assumed and the nonvaporizing particles are conceptualized as contained within an thin sheet injected at the symmetry plane. Two dimensionless parameters that affect the solution are described. These are the effective gas diffusivityK and the dimensionless particle number densityP. The linear, coupled differential equations governing the energy exchange between the gas and liquid phases are solved by means of the Green's function technique. This procedure yields a Volterra integral-series equation as the solution of the gas-phase energy equation. A series solution of this integral equation is obtained by the method of successive substitutions and terms up to second order are calculated.     

Heat transfer characteristics of water and APG surfactant solution in a micro-channel heat sink

The steady increase in internal heat production of cost and high performance electronic components has lead researchers to seek improved ways to remove the heat generated. Single-phase liquid flow has been considered as a potential solution for solving this cooling problem. However, when considering that any solution needs to be of low cost and low mass fluxes and yet retain low temperature gradients across the electronic components, it seems that two-phase boiling flow is preferred. Surfactant solutions have been introduced in connection with enhancement of the boiling processes. We investigated the effects of surfactant solution flows through a micro-channel heat sink. The experimental setup included a high-speed IR radiometer and a CCD camera that were used to characterize the test module. The module consisted of inlet and outlet manifolds that distributed surfactant solutions through an array of 26 parallel micro-channels. The experimental results have shown that there exists an optimal solution concentration and mass flux for enhancing heat removal. Surfactant solution boiling flows were also found to stabilize the maximum and average surface temperatures for a wide range of applied heat fluxes. In addition, the use of surfactant solutions at low mass fluxes has led to CHF enhancement when compared to regular water flows. In the last part of this work, possible explanations for the observed non-ionic surfactant effects are presented.     

Convergence of Anisotropically Decaying Solutions of a Supercritical Semilinear Heat Equation

We consider the Cauchy problem for a semilinear heat equation with a supercritical power nonlinearity. It is known that the asymptotic behavior of solutions in time is determined by the decay rate of their initial values in space. In particular, if an initial value decays like a radial steady state, then the corresponding solution converges to that steady state. In this paper we consider solutions whose initial values decay in an anisotropic way. We show that each such solution converges to a steady state which is explicitly determined by an average formula. For a proof, we first consider the linearized equation around a singular steady state, and find a self-similar solution with a specific asymptotic behavior. Then we construct suitable comparison functions by using the self-similar solution, and apply our previous results on global stability and quasi-convergence of solutions.     

Heat transfer of a micropolar fluid by the presence of radiation

An analysis of the steady flow of a micropolar fluid past an unmoving plate by the presence of radiation is considered. Numerical solution for temperature field has been derived and the effect of the radiation parameter on the temperature field is discussed.     

A Numerical Verification of Nontrivial Solutions for the Heat Convection Problem

A computer assisted proof of the existence of nontrivial steady-state solutions for the two-dimensional Rayleigh-Bénard convection is described. The method is based on an infinite dimensional fixed-point theorem using a Newton-like operator. This paper also proposes a numerical verification algorithm which generates automatically on a computer a set including the exact nontrivial solution. All discussed numerical examples take into account of the effects of rounding errors in the floating point computations.     

Heat flow in a channel with discontinuity of the temperature on the wall

We study the temperature field in the flow of a viscous fluid in a circular tube when there is an abrupt change in the boundary condition for the temperature on the walls at a section of the channel. Following the classical studies [1, 2], this problem has often been considered (for example, in [3, 4, 5]) under different assumptions about the type of flow, the form of the boundary conditions, and the values of the Péclet number. The solutions hitherto obtained are frequently cumbersome and do not exhaust all situations of physical interest. In the present paper, we find the solution to the problem for the case of Poiseuille flow, boundary conditions of the first kind for the temperature, and arbitrary values of the Péclet number. We establish an expression that determines the Nusselt number at different sections of the channel. The results of calculations based on the obtained formulas are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Shidkosti i Gaza, No. 5, pp. 194–198, September–October, 1979.     

Heat transfer during bubble formation

The flow around a gas bubble forming at a submerged orifice without vaporisation is analysed both with and without heat transfer taking place from the bubble surface. The results of experiments are given in which high-speed photography was used to study air bubbling through four different sizes of orifice into water, for the isothermal and diabatic case. A numerical solution of the dimensionless equations using Hamming's modified predictor-corrector method gave excellent agreement with experimental measurements of the bubble volume-time history for both stages of growth as well as predicting accurately the transition point between the two stages. Most of the heat transfer was found to occur almost immediately after the start of bubble growth