K.G.T. Hollands

Correlation equations for free convection heat transfer in horizontal layers of air and water

Abstract New experimental measurements are reported on the natural convective heat transport through a horizontal layer of air, covering the Rayleigh number range from sub-critical to 4 × 106. When these data are combined with Goldstein and Chus data for air, the full set of data points are demonstrated to bear a Nusselt number dependence which is asymptotic to a 1 3 power on the Rayleigh number as the Rayleigh number approaches infinity. The asymptotic coefficient of proportionality is consistent with that predicted by a simple “conduction layer model” which is described. Knowledge of the asymptote has permitted a simple but accurate correlation equation to be obtained, valid for the full range of Rayleigh number. By extension, a similar correlation equation is also obtained for water.

Experimental Nusselt numbers for a cubical-cavity benchmark problem in natural convection

Abstract Experimental natural convection Nusselt numbers are reported for a cubical, air-filled cavity that has one pair of opposing faces isothermal at different temperatures, Th and Tc, the remaining faces having a linear variation from Tc to Th. Average Nusselt numbers at the cold face are given for Rayleigh numbers Ra equal to 104, 105, 106, 107 and 108, and for three angles of inclination φ of the isothermal faces from horizontal: namely φ = 0, 45 and 90°. The 95% confidence limits on the measured Nusselt number Nu are typically 1% of the Nu. Unexpectedly, two Nusselt numbers were found at φ = 0° and Ra = 105, depending on the initial conditions. The results are intended to provide data for a recently-defined benchmark problem in CFD.

On a physically-realizable benchmark problem in internal natural convection

Abstract A new natural convection ‘benchmark problem’ for validating CFD codes is defined. In the subject problem, a cubical air-filled cavity, tilted at 0, 45°, or 90°, has one pair of opposing faces at different temperatures, Th and Tc, respectively, the remaining faces having a linear variation from Tc to Th. In contrast to some other benchmark problems, this problem is physically-realizable. Experimental techniques to establish the thermal boundary conditions and to measure the Nusselt number to 1% accuracy are reported. Measured Nusselt numbers at Rayleigh number equal to 4×104 are shown to agree with CFD predictions to within ±0.3%.

Experimental study of the stability of differentially heated inclined air layers

Abstract This paper reports the experimental determination of the critical Rayleigh numbers governing the stability of horizontal, vertical and inclined air layers in the conduction regime. The experimental method consists of measuring the heat flux in the immediate neighbourhood of the instability and extrapolating this data to the state of pure conduction. The measured critical Rayleigh number for the horizontal case is within 1 per cent of the accepted value (1708). In the vertical case, the measured value of the critical Grashof number is 11 000 ± 510, which is in very close agreement to the value of 11 024 predicted by Unny. In the inclined case results are presented at angles from the horizontal 15, 30, 45, 60, 75, 80 and 85 degrees. The results are in agreement with the predictions of Unny and Hart to within a maximum deviation of about 20 per cent. The Nusselt number in the neighbourhood of the instability is also reported.

Coupled radiative and conductive heat transfer across honeycomb panels and through single cells

In the absence of natural convection, heat flows through a gas-filled honeycomb by conduction and radiation. For the parameter ranges of interest in a plastic honeycomb inside a flat plate solar collector, the conduction and radiation are strongly coupled. The total heat transfer across the panel was studied experimentally and theoretically. The experimental approach precisely measured the total heat transfer under varying conditions. The theoretical approach proposed several models, established their governing equations, and solved the equations by either numerical or analytical methods. A model based on grey surfaces, specular sidewalls, and one-dimensional conduction yielded results within 6% of measurements.

On Natural Convection Heat Transfer From Three-Dimensional Bodies of Arbitrary Shape

A simple expression is developed for the natural convection heat transfer from three-dimensional bodies of arbitrary shape immersed in an extensive fluid. The expression applies to both laminar and turbulent regimes and requires the calculation of purely geometric properties of the bodies. Experiments were performed with air, covering a Rayleigh number (Ra) range of from 10 to 10{sup 8}, on different body shapes oriented in various directions: for example, circular or square disks, a short circular cylinder of height equal to diameter and a similar cylinder but with hemispherical ends, prolate and oblate spheroids of various aspect ratio, and an apple core shape. Comparison between the predictions of the expression and the experimental results of this work and those gathered from several other sources ranging up to Ra = 10{sup 14} showed very good agreement, with an average rms difference of 3.5% for Ra < 10{sup 8} and 22% for 10{sup 8} < Ra < 10{sup 14}.

Numerical predictions of natural convection in a trombe wall system

Abstract In a Trombe wall passive heating system, air from a room is circulated by natural convection through a narrow channel formed by a window on one side and a wall on the other. The circulating flow delivers the solar energy collected by the wall and window to the room. The present paper analyses an idealized Trombe wall system in which the flow is laminar and two-dimensional and the window and wall are isothermal. A dimensional analysis shows that, for a given geometry, the flow and heat transfer are characterized by two Rayleigh numbers. Flow and heat transfer predictions over a wide range of operating conditions were performed using a finite-volume method. These predictions are believed to be the first that fully account for the interaction between the room and channel, and which include the important case where the window temperature is lower than the room temperature.

An analysis of a counterflow spray cooling tower

Abstract The cooling tower analyzed in this study is void of fill. It is vertical with the air stream moving uniformly upwards and the water stream, dispersed into droplets, moving uniformly down. The droplets are introduced at the top of the tower with zero velocity, uniform temperature and a known size distribution. The analysis takes into account the fact that at any given height all droplets are not at the same temperature. Results are presented in the form of a correction factor on a simplified solution which neglects this fact. The effect on the correction factor of all pertinent dimensionless groups is examined.

Numerical Solution of an Open Cavity, Natural Convection Heat Exchanger

An open-cavity natural convection heat exchanger is one in which the flow on one side is driven by buoyancy forces and in which the efect of associated piping, values, and fittings on that side can be ignored, since the exchanger is effectively exposed there to an extensive fluid of unifrom temperature. This paper reports a finite volume numerical solution of the full set of equations governign the flow ont he natural convection side of such a heat exchagner. The exchangers dimensionless performance is shown to depend on five dimensionless groups: a modified Rayleigh number Ra*, a flow number F describing the forced convection heat capacity, a Biot number Bi describing the effect of forced convection side heat transfer coefficient, an aspect ratio A{sub R}, and the Prandtl number Pr. A parametric study is performed for suitable ranges of Ra*, F, and Bi, and for Pr = 6 and AR = 0.1. The results are presented in terms of a Nusselt number, a dimensionless flow rate, and the exchanger effectiveness as a function of these variables.

Modeling of gaseous radiant exchange with the smooth (reordered) band model

The smooth band model (also called the reordered band model) shows promise of providing the foundation for a radiant analysis method for enclosures containing participating gases. Existing models for the smooth absorption coefficient distribution, however, are not totally satisfactory. This paper presents a new model for the smooth absorption coefficient that addresses the problems with the current models. The new model is exercised on some benchmark calculations of total gas emissivity to test its accuracy. Also, a demonstration problem involving a spherical enclosure with reflective walls is solved to illustrate the utility of the smooth band model, as well as the ease of calculation.