Showing papers in "International Journal of Heat and Mass Transfer in 1981"

Abstract: The present work analyzes the effects of a solid boundary and the inertial forces on flow and heat transfer in porous media. Specific attention is given to flow through a porous medium in the vicinity of an impermeable boundary. The local volume-averaging technique has been utilized to establish the governing equations, along with an indication of physical limitations and assumptions made in the course of this development. A numerical scheme for the governing equations has been developed to investigate the velocity and temperature fields inside a porous medium near an impermeable boundary, and a new concept of the momentum boundary layer central to the numerical routine is presented. The boundary and inertial effects are characterized in terms of three dimensionless groups, and these effects are shown to be more pronounced in highly permeable media, high Prandtl-number fluids, large pressure gradients, and in the region close to the leading edge of the flow boundary layer.

Abstract: This study extends previous work of Bergles and Webb to establish a broad range of Performance Evaluation Criteria (PEC) applicable to single phase flow in tubes. The equations include the effects of shellside enhancement and fouling and are applicable to roughness and internally finned tubes. Detailed procedures are outlined to calculate the performance improvement and to select the ‘optimum’ surface geometry. PEC are presented for four design cases:(1) reduced heat exchanger material; (2) increased heat duty; (3) reduced log-mean temperature difference; and (4) reduced pumping power. The 11 cases discussed include fixed flow area and variable flow area. Appropriate PEC for two-phase exchangers area also discussed.

Abstract: After highlighting the problems associated with the conventional numerical implementations of Stefan problems using the enthalpy formulation, a simple development is described which leads to very accurate solutions. The extension of this technique to two dimensional problems is then demonstrated using a straightforward explicit method. An implicit scheme for one dimensional problems, based upon the above development, is then described which can cope with any size phase change temperature range and the influence of internal heating, simultaneously. Finally, the utility of this scheme is demonstrated by its application to a welding problem.

Abstract: The inverse conduction problem arises when experimental measurements are taken in the interior of a body, and it is desired to calculate temperature and heat flux values on the surface. The problem is shown to be ill-posed, as the solution exhibits unstable dependence on the given data functions. A special solution procedure is developed for the one-dimensional case which replaces the heat conduction equation with an approximating hyperbolic equation. If viewed from a new perspective, where the roles of the spatial and time variables are interchanged, then an initial value problem for the damped wave equation is obtained. Since the formulation is well-posed, both analytic and numerical solution procedures are readily available. Sample calculations confirm that this approach produces consistent, reliable results for both linear and nonlinear problems.

Abstract: A nonlinear problem of thermal, mass and dynamic interaction between a vapour-gas bubble and a liquid is considered with account for temperature nonuniformity in the bubble and interdiffusion of the vapour-gas mixture components. A numerical solution is obtained for the problem of radial bubble motion induced by a sudden pressure change in the liquid — a situation which, in particular, corresponds to the behaviour of bubbles beyond a shock-wave front when the latter enters a bubble curtain. Considered also are vapour-gas bubbles oscillating in the liquid under the influence of a sound field. The capillary effects and phase transitions, taken together, are shown to produce a new resonant frequency of small vapour bubbles which differs from that described by Minnaert. The expressions for the frequency and the thermal damping ratio of bubble oscillations are obtained. The effective coefficients of heat transfer between radially oscillating bubbles and the liquid are determined.

Abstract: Optical tomography has been applied to an off-axis turbulent methane-air free jet to determine the mean methane concentration throughout the mixing region. Optical tomography is a multi-angular absorption technique which involves making M line of sight absorption measurements (projections) at N angles. These M × N measurements are then used to reconstruct the original two-dimensional flow field. Absorption measurements were made on methane using the near resonance 3.39 μm line of a He-Ne laser. Mean concentration measurements were obtained at three positions downstream of the jet exit plane. Comparisons with the results of previous workers for the axial and radial mean concentration profiles show good agreement. Additionally, the sensitivity of the reconstructed results to the number of angles and scans used is briefly described. The results demonstrate the unique capabilities of optical tomography for flow field diagnostics.

Abstract: An extensive series of measurements of gas bubble diameters on detachment into flowing liquids has been performed. The test liquids were water, water with surface active agent, and ethylene glycol. By use of different surfaces equilibrium contact angles ranging from 22 to 90° were obtained. Based on these results new expressions are proposed for the surface tension and drag forces experienced by a bubble attached to a solid surface.

Abstract: The lowest surface temperature possible for the existance of spray evaporative cooling is determined experimentally to be a linear function of the impinging spray mass flux. A conduction-controlled analytical model of droplet evaporation gives fairly good agreement with experimental measurements at atmospheric pressure. At reduced pressures droplet evaporation rates are decreased significantly such that an optimum operating pressure exists for each desired surface heat flux. The initiation of the 'Leidenfrost state' provides the upper surface temperature bound for spray evaporative cooling.

Abstract: An approach to pool film boiling on a horizontal surface on the basis of the Reynolds analogy is suggested. Within the framework of the model considered, the influence of vapour film thickness and vapour velocity on Taylor instability of the interface has been investigated. Four limiting solutions have been obtained for laminar and turbulent vapour flow in the film with and without allowance for friction at the liquid-vapour interface. The relations suggested practically correlate all of the available experimental data with an accuracy of ± 25 %. The boundary of the region where heat-transfer rate depends on the size of the heating surface has been established and an empirical formula allowing for this effect has been obtained.

Abstract: Experiments were performed to study freezing on a finned vertical tube when either conduction in the solid or natural convection in the liquid controls the heat transfer. Conduction is the controlling mode when the liquid is at its fusion temperature, whereas natural convection controls when the liquid temperature is above the fusion value. The phase change medium was a paraffin, 99% pure n-eicosane, with a fusion temperature of 36.4°C. Auxiliary experiments were also performed with an unfinned tube to obtain comparison data. For conduction control, the enhancement of freezing due to finning is less than the area ratio of the finned and unfinned tubes, whereas for natural-convection control the enhancement is very nearly equal to the area ratio. The liquid-solid interface is a thicket of whisker-like crystals when conduction controls but is straight (i.e. vertical). On the other hand, the interface is smooth but tapered when natural convection controls—yielding bottom-heavy frozen specimens. When conduction controls, freezing continues more or less indefinitely, whereas natural convection severely retards the freezing and ultimately terminates it altogether.

Abstract: An analysis is presented for the flow and heat transfer in an interrupted-plate passage, which is an idealization of the offset-fin heat exchanger. The plates are considered to be of finite thickness. The effect of the plate thickness on the flow field and heat transfer is investigated through numerical solutions of the governing equations. The flow field is found to be quite complex. It contains recirculation zones behind the trailing edges of the plates, and there occurs significant deflection of the through flow. Whereas this greatly increases the pressure drop required for a given flow rate, the heat transfer from the thick plates does not improve sufficiently. Detailed results are presented for a number of thickness ratios and for a range of the Reynolds number. The overall results are compared with available experimental data.

Abstract: The present work analyzes the problem of condensation in porous insulation. Specific consideration is given to a steady-state one-dimensional formulation, representing a porous slab exposed to two different humid environments on both sides. The analysis includes both the convective and the diffusive transport mechanisms along with phase change. Condensation (or freezing) is shown to take place in a wet zone in which the air-vapor mixture is saturated. When the two external environments are not saturated, the wet zone is bounded by two dry zones with no condensation. The effect of condensation, due to release of latent heat, on the overall thermal performance is found to be significant. Both the condensation rate and the resulting increase in heat transfer depend on the Peclet number, the Lewis number, and the Biot number, as well as on the temperatures and humidities of the two external environments.

Abstract: Starting from the first principles, and with one experimentally obtained parameter, an expression for stagnation heat transfer is derived, applicable to round, impinging jets. The results obtained with a row of air jets impinging on an electrically-heated surface in a small-scale setup characteristic of a typical turbine blade have been found compatible with the average heat transfer from a geometrically similar, steam-heated surface scaled up ten times, and comparable with the results of other investigators. These findings were linked to the flow fields likely to exist in the gas turbine blades, internally cooled by a row of round jets or a single jet of equivalent width. The magnitude of heat-transfer coefficients obtained here with impinging jets approaches that normally associated with forced convection of water and evaporative cooling.

Abstract: Measurements in a slightly heated turbulent boundary layer, with essentially identical origins for momentum and thermal fields, indicate that the constants in the velocity and temperature logarithmic regions do not vary with Reynolds number. The extent of these regions, as a proportion of the boundary layer thickness, is approximately constant, independent of the momentum thickness Reynolds number Rm, when R m ⪞ 3100 . The deviation from the temperature logarithmic law in the outer layer is reasonably well described by expressions analogous to those which describe the velocity “ wake ”. The maximum value of this deviation increases with Rm over the range 990–4750 but is approx. constant for Rm > 4750, and equal to about half the maximum velocity deviation. Distributions of r.m.s. velocity and temperature scale moderately well with wall variables in the inner part of the sublayer at all Rm. Scaling on outer flow variables is only approximately achieved when R m ⪞ 3100 . The only noticeable effect of Rm on the turbulent Prandtl number and turbulence structure parameters is observed at the smallest Reynolds numbers investigated.

Abstract: Measurements of critical heat flux and rate of droplet entrainment due to bubble bursting are made with boiling liquid films flowing downwards on the outside surface of a uniformly heated vertical tube. The critical condition occurs first at the exit end of the heating section. The critical heat flux shows three types of characteristics by increasing the liquid film flow rate at the exit end of the heating section. The data are expressed in terms of the film flow rate and the film Weber number at the exit end. The relationship between the droplet entrainment rate and the evaporation rate of the film is also discussed.

Abstract: The present paper develops a formulation of the boundary element method for the analysis of axisymmetric transient heat conduction problems. The axisymmetric time-dependent fundamental solution is obtained by directly integrating the three-dimensional one. Due to its complexity, series expansions have to be introduced in order to make possible the analytical evaluation of the time integrals that appear in the formulation. Several results of numerical analyses are presented, including problems with time-dependent boundary conditions, and they demonstrate the feasibility of using boundary elements in space and time to solve axisymmetric heat conduction problems.

Abstract: The variable time step method introduced by Douglas and Gallie for solving a one-dimensional Stefan problem with constant heat flux at the fixed end is extended to cover a more general boundary condition. The numerical results are obtained for solidification of a liquid initially at its fusion temperature. A method due to Goodling and Khader is discussed in detail and some practical aspects of its implementation are investigated. The same problem is solved by the “modified variable time step” method earlier suggested by the present authors. The results from all the methods are almost identical. An approximate analytical solution is obtained by the heat-balance integral method.

Abstract: The heat transfer through vertical partitions surrounded by thermally-stratified fluids is studied theoretically and experimentally. The theory is based on the Oseen linearization method. The analytical results show the effect of thermal stratification on the partition temperature, fluid flow and heat flux. The relationship between overall heat transfer (Nusselt number) and the degrees of thermal stratification on both sides of the partition is determined. The experimental part of the study confirms the heat transfer features predicted analytically. In particular, it is shown that the theoretical Nusselt number calculation is in good agreement with experimental measurements. It is shown also that the net heat transfer between the two ends of a rectangular enclosure is proportional to (1 + n)−0.61, where n is the number of vertical partitions inserted in the middle of the enclosure.

Abstract: The onset of downwards penetration of a bubbly water pool above a perforated plate was studied with both air and steam upflows. An interpolative scaling length is developed empirically, which, when introduced into the Wallis countercurrent flow equation, fits the air-water data for a variety of perforatedplate geometries, as well as full-length tube bundle data with saturated water and steam. The same equation, when suitably corrected for steam condensation in the immediate neighborhood of the plate, fits the steam-water data also. Implications for the cooling of overheated nuclear reactor cores are discussed.

Abstract: The problems of steady film condensation outside a wedge or a cone embedded in a porous medium filled with a dry saturated vapor are investigated. As in classical film condensation problems, it is assumed that (a) the condensate and the vapor are separated by a distinct boundary with no two-phase zone in between, and (b) the condensate has constant properties. Within the boundary layer approximations, similarity solutions have been obtained for the temperature and flow fields in the condensate. Moreover, a closed form solution has been obtained for the Nusselt number which depends on the square root of the Rayleigh number and the dimensionless film thickness. The latter is found to be a function of a dimensionless parameter related to the degree of wall subcooling. Asymptotic cases for small and large wall subcoolings are also considered. As in the classical film condensation problems, it is found that the ‘Nusselt’-type approximation (for small wall subcooling) overestimates the film thickness while underestimates the Nusselt number. An approximate expression for Nusselt number in terms of the degree of wall subcooling explicitly is also obtained.

Abstract: Improved theoretical results for heat transfer through individual drops and for the mean distribution of drop sizes are used as a basis for assessing the validity of the basic assumption of dropwise condensation theory [1] i.e. that the mean heat flux can be found from steady calculation of the heat transfer through individual drops and a steady distribution of drop sizes.

Abstract: Because of the increasing need for precise information on engine processes, this study developed and experimentally verified models for the instantaneous heat transfer in an engine exhaust port. Experimental measurements were made of the instantaneous cylinder pressure and instantaneous exhaust gas temperature for a range of engine operating conditions. The pressure measurements were used to obtain the instantaneous cylinder gas state and the temperature measurements were used to validate the heat transfer models. The exhaust port heat transfer was dominated by jet induced large-scale fluid motion as opposed to wallshear generated fluid motion. An analysis based on the jet velocity through the valve opening correctly estimated the heat transfer due to this large-scale motion. Models for the instantaneous exhaust port heat transfer provided excellent agreement with measurements as a function of engine operating conditions.

Abstract: Phase-change energy storage devices have an inherent disadvantage due to the insulating properties of the phase-change materials (PCM's) used. Such systems are difficult to analyze theoretically due to the nonlinearities of the moving liquid-solid interface and the presence of natural convection as shown by several recent numerical and experimental investigations. Previous work has been unsuccessful in predicting the performance of phase-change devices in the presence of fins and natural convection. This study presents a simplified numerical model based on a quasi-linear, transient, thin fin equation, which predicts the fraction of melted PCM, and the shape of the liquid-solid interface as a function of time with sufficient accuracy for engineering purposes. Experimental results are compared in dimensionless form with model predictions, and show fairly good agreement. To achieve high heat-transfer rates with a fixed amount of PCM and metal fin material, the model indicates that melting the PCM in a pure conduction mode with closely spaced thin fins is preferable to melting PCM with thicker fins spread further apart, even in the presence of natural convection.

Abstract: Experiments and analyses are reported for an open, free convection loop. The loop is U-shaped with the lower segment heated; the vertical legs are adiabatic and are connected to an isothermal reservoir. The loop is filled with water or a water-saturated porous medium. Experimental results include the starting transients and the friction factors and heat transfer rates at steady state for flow Reynolds numbers from 4 to 1000. Oscillations are observed with the onset of boiling. Single-phase stability analyses confirm the unstable rest states and the stable steady-states observed in the experiments, and reveal a conditional instability of the steady states. Numerical simulations of the starting transients are obtained and are compared with experiment. Results are applicable to geothermal, solar, and industrial open-loop thermosyphons.

Abstract: This paper is part of a series of papers by the author providing the exact transient temperature distribution in bodies heated by disk heat sources. The body in this paper is a semi-infinite cylinder with a uniform disk source centered at the end and uniformly heated. Results are given by infinite series, tables, figures and approximate relations. Care has been taken to provide methods for efficient evaluation of the infinite series because direct evaluation can require thousands of terms. Alternative exact methods are provided that require as few as three terms. The solution is intrinsically important but it is also a basic building block for spatially and time varying heat fluxes for finite as well as semi-infinite cylinders. This is discussed briefly herein and references for more extensive treatment are provided. The solution is also a basic one for the new numerical procedure called the surface element method.

Abstract: This article examines the buoyancy induced circulation occurring on both sides of a vertical impermeable partition separating two semi-infinite porous reservoirs maintained at different temperatures. The circulation is found to consist of two counterflowing boundary layers which interact thermally across the partition, transferring heat from the hot side to the cold side. The net heat transfer rate is calculated and the effect of the thickness and conductivity of the partition on the heat transfer rate is determined. It is demonstrated that the insertion of a vertical impermeable partition in the middle of a vertical porous layer reduces significantly the net heat transfer rate through the layer.

Abstract: A methodology is set forth for the numerical solution of transient two-dimensional diffusion-type problems (e.g. Heat conduction) in which one of the boundaries of the solution domain moves with time. The moving boundary is immobilized by a coordinate transformation, but the transformed coordinates are, in general, not orthogonal. Furthermore, with respect to a given control volume in the new coordinate system, mass appears to pass through the control surface which bounds the volume, and this mass movement brings about a convection-like transport of energy. The energy equation for a moving, nonorthogonal control volume is derived in general and then specialized to the transformed coordinate system associated with the immobilization of the moving boundary. A fully implicit scheme is used to discretize the control volume energy equation. The spatial derivatives are discretized by either of two schemes depending on the size of the pseudo-convection relative to the diffusion. The energy balance at the moving boundary of the solution domain is also transformed and discretized. A numerical procedure is then developed for solving the discretized energy equations. The use of the control volume formulation and the solution methodology will be illustrated for a specific physical situation in a companion paper that follows this paper in the journal.