Frost formation in vertical channels under natural convection

Processes involving heat transfer from a humid air stream to a cold plate, with simultaneous deposition of frost, are of great importance in a variety of refrigeration equipment. In this paper, frost growth on a cold, vertical plate in free convection has been experimentally investigated. The cold plate (0.095 m high, 0.282 m wide) was placed in vertical channels open at the top and bottom in order to permit the natural circulation of ambient air. The channels, rectangular in shape, were 2.395 m high and 0.36 m wide, with the depth set equal either to 20 mm, or 10 mm, or 6 mm in order to infer the influence of channel flow area on the natural convection and frost formation. The cold plate temperature and the air relative humidity were varied in the −40 to −4 °C and 31–85% range, respectively, with the air temperature held fixed at 27 °C (±1 °C). Several quantities (thickness, temperature and mass of frost, heat flux at the cold plate), were measured during the time-evolution of the process (7.5 h from the frost growth inception), and are presented as functions of the input parameters (relative humidity and cold plate temperature); in particular, the role exerted by the plate confinement on the frost growth is discussed. Data are recast in order to identify compact parameters able to correlate frost mass, thickness and density data.     

Der Einflu\ der freien Konvektion in laminaren und turbulenten Grenzschichtströmungen mit Stoffaustausch

The paper presents numerical solutions of the boundary layer equations for forced convection flows in which buoyancy effects caused by temperature and concentration gradients are important. Critical parameters for the onset of the free convection effects and for boundary layer separation were determined when the forced and free convection act in opposite directions. Results are given for laminar boundary layers and boundary layers in the transition regime with mass transfer.     

Frost formation on a vertical plate in simultaneously developing flow

It is well recognized that frost formation on heat exchanger surfaces seriously affects the performance of a refrigeration system. Consequently, defrosting is essential, yet it is only effective when both analytical tools and comprehensive experimental data on frost formation are available. In air conditioning units, frost formation most commonly takes place in the entrance region of the heat exchanger. Therefore, in this study, an experimental investigation was undertaken to characterize the effect of environmental conditions on the frost growth occurring on a vertical plate in the hydrodynamically and thermally developing region. Several experiments were performed while four environmental parameters, inlet air temperature, inlet air humidity, air velocity and cooling surface temperature, were varied. The thickness, mass, and density of the frost layer were determined from the measured data and empirical correlations were reduced from dimensionless parameters.     

Thermal interaction between natural convection on one side of a vertical wall and forced convection on the other side

An analysis is made for the conjugate heat transfer problem of natural convection on one side of a vertical wall and forced convection on the other side. The natural convection mode is treated analytically by employing the Oseen linearization approach developed by Gill. The forced convection boundary layer is analyzed on the basis of the integral technique. The two solutions are matched on the separating wall so as to satisfy the continuity of heat flux between the two fluids. The analysis shows that the complexion of this two-fluid problem is governed by a dimensionless conjugate parameter, R, which relates the heat transfer effectiveness of forced convection mode to that of free convection mode. The boundary conditions at the wall are not prescribed in the analysis in advance, rather, determined among the results. The heat transfer and flow characteristics in the two counter-flowing boundary layers are presented graphically. Heat transfer results of engineering importance are determined as a function of the conjugation parameter. Received on 19 August 1998     

Coupled thermo-mechanical analysis of shape memory alloy circular bars in pure torsion

Pure torsion of shape memory alloy (SMA) bars with circular cross section is studied by considering the effect of temperature gradient in the cross sections as a result of latent heat generation and absorption during forward and reverse phase transformations. The local form of energy balance for SMAs by taking into account the heat flux effect is coupled to a closed-form solution of SMA bars subjected to pure torsion. The resulting coupled thermo-mechanical equations are solved for SMA bars with circular cross sections. Several numerical case studies are presented and the necessity of considering the coupled thermo-mechanical formulation is demonstrated by comparing the results of the proposed model with those obtained by assuming an isothermal process during loading–unloading. Pure torsion of SMA bars in various ambient conditions (free and forced convection of air, and forced convection of water flow) subjected to different loading–unloading rates are studied and it is shown that the isothermal solution is valid only for specific combinations of ambient conditions and loading rates.     

No slip boundary effects in non-Darcian mixed convection from a vertical wall in saturated porous media. Analytical solution

An analytical study is made for wall effects in non-Darcy mixed convection from vertical impermeable surfaces embedded in a saturated porous medium. The governing equations are transformed into a dimensionless form by non-similar transformation to cover both forced and natural convection dominated regimes. Two different dimensionless parameters that measure the strength of mixed convection were found in both regimes. The parameters of forced convection dominated regime can be related to those of natural convection dominated regime. An approximate analytical solution for the governing equations was obtained. Temperature and velocity profiles for both regimes are presented. Received on 9 September 1997     

Experimental techniques in natural convection

Experimental techniques in natural convection heat transfer employed in the author's laboratory are introduced. The techniques are mostly related to visualization of flow, temperature field, and heat flux distribution in fluids. Three topics are presented, the first being natural convection in a horizontal rectangular liquid layer driven by surface tension and buoyancy. The patterns of flow were visualized by suspending fine aluminum flakes in the liquid. At the same time, the distribution of the temperature gradient in the liquid was visualized by an optical method making use of the refraction of light. The second topic is the onset of oscillatory convection in the Czochralski growth melt. In this case a forced flow due to rotation of the crystal and the vessel is superimposed on the buoyancy convection, resulting in an oscillatory flow under certain circumstances. The flow pattern and the temperature distribution in the liquid were visualized simultaneously by suspending in the liquid a microencapsulated temperature-sensitive liquid crystal. Periodical oscillation of the flow and the temperature was clearly recognized. The third topic is the rollover of double liquid layers that were stratified stably due to a density difference. A small-scale experiment was carried out to clarify the basic mechanism of rollover. The tracer method was used to visualize boundary layer flow along the vertical side wall and the shadowgraph technique to visualize the density distribution in the liquid layers. The article emphasizes the importance of visual observation in the investigation of natural convection phenomena.     

An analytical study of frost nucleation and growth during the crystal growth period

An analytical study was made to clarify the fundamental nature of the early stage of crystal growth period of frost formation phenomena. A suitable model was developed by using the principles of crystallization and nucleation theory. The effect of four dominant parameters of frost formation; plate temperature, air temperature, air humidity ratio and Reynolds number, was studied. Ice crystal density variation with temperature reported by cloud physicists is used in the model to predict the density variation of frost during the crystal growth period. The temperature variation in the frost layer is formulated and vapor diffusion through the frost layer is taken in the consideration.     

Self-similar thermal boundary layers on plane and axisymmetric bodies

This paper proposes an approximate solution procedure for the prediction of the forced convection heat transfer through self-similar laminar boundary layers. The differential equations governing the viscous and thermal boundary layers have been reduced to a pair of algebraic equations for the boundary layer shape factor and the boundary layer thickness ratio. The local Nusselt number predicted under various pressure gradients turns out to be in excellent agreement with that of the exact solution over a wide range of the Prandtl number.     

Conjugate parallel-flowing free and forced convection boundary layers on vertical wall sides

The paper describes an analytical study of two parallel-flowing boundary layers of free and forced convection modes on the facing sides of a vertical thin wall. The two layers are analyzed separately within the framework of boundary layer theory, and coupled by the matching conditions at wall. Numerical data are obtained for a wide range of a dimensionless conjugation parameter + relating the heat transfer effectiveness of two convection modes. Based on these data, an expression for calculating the conjugate mean Nusselt number as a function of +-parameter is found by means of a curve-fitting method.     

An experimental investigation of combined turbulent free and forced evaporation

The wide variation in correlations available in the literature for predicting water evaporation rates in a moving air stream necessitated a new investigation to determine which correlations can be considered reliable. Water evaporation measurements were made from a heated pool (a class-A pan) into a low speed wind tunnel. The evaporation regime examined combined turbulent free and turbulent forced convection over the range 0.1 < Gr_m/Re² < 10.0. The data includes the range in which combined convection modes are important, as well as the limits where either free or forced convection effects may dominate. The data are compared to several evaporation correlations based on laboratory wind tunnel data. These historical correlations do not produce consistent estimates in predicting evaporation rates. It is believed that the apparent inconsistencies arise because many correlations do not adequately describe the appropriate evaporation regimes for which they are valid. A new correlation using the combined free/forced convection Sherwood number has been developed to predict evaporation rates for a moving air stream. This correlation allows the results of this study to be extended to other evaporating conditions (i.e. variation in surface geometry and air turbulence levels) than those described here. For a 95% confidence limit, the Sherwood number correlation matches the data within ±7.9%.     

Heat transfer by combined free and forced convection in vertical tubes

The influence of free convection on forced convection heat transfer becomes important in laminar flows. Numerical methods have been applied for a study of mixed convection in vertical tubes for the following conditions: temperature-dependent fluid density, constant wall temperature and parabolic profile of axial velocity at the tube entrance. Both cases: heating and cooling have been considered.     

Integral treatment of subcooled forced convection film boiling on a flat plate

Subcooled forced convection film boiling on a flat plate has been analysed by means of an integral method. Following the two phase boundary layer theory, the momentum and energy equations for both liquid and vapor layers are considered along with the compatibility conditions on the liquid-vapor interface. Subsequently, the governing equations are reduced to a set of algebraic equations which can readily be solved for given parameters. Comparison of the present solution with the Cess and Sparrow solution reveals an excellent performance of the present solution procedure. The effects of superheating, subcooling and liquid Prandtl number on the hydrodynamic and heat transfer characteristics are fully discussed. Furthermore, the asymptotic formulas are derived for the local Nusselt number and skin friction coefficient through a careful examination of the physical limiting conditions.     

On the second fundamental problem of combined free and forced convection through vertical noncircular ducts

Analysis of combined free and forced convection through vertical noncircular ducts is carried out using a variational technique. Fully developed flow with uniform axial heat input and uniform peripheral heat flux is assumed. All fluid properties are considered invariant with temperature except the variation of density in the buoyancy term of the equation of motion. The condition of uniform peripheral heat flux is utilized in deriving the variational expression. This procedure releases the thermal boundary condition from satisfying exactly the condition at the wall. A finite-difference procedure is carried out. For pure forced convection case, a particularly simple variational expression is presented. Nusselt numbers for combined free and forced convection are computed for rectangular, rhombic and elliptical ducts. An exact solution is presented for laminar forced convection through elliptic ducts. Variational results are in agreement with this exact solution. The present results are compared with those in the published literature wherever possible, and good agreement is obtained.     

Conjugate heat exchange and hydrodynamics for a viscous incompressible fluid moving in a rectangular cavity

Numerical simulation was performed of the motion of a viscous incompressible nonisothermal fluid in an open rectangular cavity under conditions of forced convection and conjugate heat exchange. The effect of the jet dynamic parameter (Reynolds number) and fluid flow conditions on the character of motion and heat exchange of viscous incompressible nonisothermal fluids in rectangular cavities is studied. A hydrodynamic pattern of viscous flow in an open cavity under forced convection conditions (in the conjugate and nonconjugate formulations of the problem) is obtained. The effect of parameters of the model on the character of motion is studied. Temperature profiles for the solid and fluid phases are obtained. The effect of parameters of the model on the character of temperature distribution in both phases is studied.     

薄膜涂层材料中的广义瑞利波

基于弹性动力学的线性理论，建立了涂层材料中广义瑞利波传播的理论分析模型，并 且由波动方程和边界条件推导了波的频散方程．分析了慢层和快层对相速度频散的影响，给 出了不同层厚-波长比和不同涂层-基体密度比情况下广义瑞利波相速度的理论解．算例分 析分别比较了慢层和快层结构中波的相速度、群速度，以及随深度衰减的位移与应力振 幅．另外，相速度曲线和位移振幅曲线与文献中给出的结果吻合，验证了理论模型和分析过 程的正确性．     

A study of frost growth and densification on flat surfaces

The present study advances a theoretical and experimental investigation of the frost growth and densification on flat surfaces. This study focuses on the most important factors affecting the frost formation process, i.e. the surrounding air temperature, humidity and velocity, and the surface temperature. The processes of frost growth and densification were investigated experimentally in order to provide a physical basis for the development of a theoretical model to predict the variation of the frost layer thickness and mass with time. The mathematical model was based on mass and energy balances within the frost layer, assuming the frost as a porous medium and accounting for the supersaturation of the moist air on the frost surface. The governing equations for mass and heat diffusion were integrated analytically, giving rise to a semi-algebraic formulation which requires numerical integration of only one time dependent ordinary differential equation. When compared with experimental data, the model predictions of the frost thickness as a function of time agreed to within ±10% error bands. The experimentally-validated model was then used to predict the frost layer growth and densification with respect to the operation conditions such as plate surface temperature, air stream temperature, humidity and velocity.     

Laboratory observations of double-diffusive convection using high-frequency broadband acoustics

High-frequency broadband (200–300 kHz) acoustic scattering techniques have been used to observe the diffusive regime of double-diffusive convection in the laboratory. Pulse compression signal processing techniques allow (1) centimetre-scale interface thickness to be rapidly, remotely, and continuously measured, (2) the evolution, and ultimate merging, of multiple interfaces to be observed at high-resolution, and (3) convection cells within the surrounding mixed layers to be observed. The acoustically measured interface thickness, combined with knowledge of the slowly varying temperatures within the surrounding layers, in turn allows the direct estimation of double-diffusive heat and buoyancy fluxes. The acoustically derived interface thickness, interfacial fluxes and migration rates are shown to support established theory. Acoustic techniques complement traditional laboratory sampling methods and provide enhanced capabilities for observing the diffusive regime of double-diffusion in the ocean.     

Comparison of multicomponent fuel droplet vaporization experiments in forced convection with the Sirignano model

The vaporization of multicomponent fuel droplets was studied experimentally in a heated flow and the results were compared to the model proposed by Abramzon and Sirignano. The droplet was suspended on a permanent holder which was set up in a thermal wind-tunnel. This wind-tunnel was fitted with a video recording system and an infra-red camera. The period during which the droplet was suspended on the holder before the opening of the hot air flow damper was recorded. This first sequence corresponds to the droplet vaporization in natural convection, whose initial experiment conditions, especially diameter, temperature, composition of the droplet, are well known. Then the damper was turn on, and the sequence of forced convection begun. The initial diameter of the droplet was recorded by the video system. The other initial conditions of this second sequence cannot be determined experimentally. The distribution of temperature in the droplet and the surface temperature, the mass fraction distribution in the droplet and the surface mass fraction were unknown. These unknown parameters were determined by coupling our experiment with a model using “the film concept” in natural convection. Experimental results were compared with the calculations and found satisfactory, in natural convection as well as in forced convection initiated by this method. The method was tested in the case of a fuel mixture droplets (heptane–decane) for different initial concentrations and variable durations of the sequence in natural convection.     

Convective heat transfer from a rotating or nonrotating axisymmetric body

An analysis of steady laminar mixed-convection heat transfer from a rotating or nonrotating axisymmetric body is presented. A mixed-convection parameter is proposed to serve as a controlling parameter that determines the relative importance of the forced and the free convection. In addition, a rotation parameter is introduced to indicate the relative contributions of the flow forced convection and the rotational forced convection. The values of both these two parameters lie between 0 and 1. Furthermore, the coordinates and dependent variables are transformed to yield computationally efficient numerical solutions that are valid over the entire range of mixed convection from the forced-convection limit (rotating or nonrotating bodies) to the pure free-convection limit (non-rotating bodies) and the entire regime of forced convection from the pure flow forced-convection limit (nonrotating bodies) to pure rotational forced-convection limit (rotating bodies). The effects of mixed-convection intensity, body rotation, fluid suction or injection, and fluid Prandtl number on the velocity profiles, the temperature profiles, the skin-friction parameter, and heat transfer parameter are clearly illustrated for both cases of buoyancy assisting and opposing flow conditions.