D. G. Kroger, Dept. ofMech. Eng., University of Stellenbosch, South Africa M. Burger, Dept. ofMech. Eng., University of Stellenbosch, South Africa

The convection heat transfer coefficient between a horizontal surface and the natural environment is determined experimentally. It is shown that heat is transferred due to natural and forced convection. The results are compared to values obtained by other investigators. A good correlation is obtained between a new semi-empirical equation and experimental results.

Introduction

Consider the energy balance that is applicable to a unit area of horizontal surface that is exposed to the natural environment on a clear, dry, sunny day, as shown in figure 1, i. e.

has = h(Ts — Ta) +Є so(Ts4 — Tsky4) — kg(dT/dz)

where /hasis the incident solar radiation absorbed per unit horizontal area. Figure 1: Heat Fluxes at ground surface exposed to the environment.

For diffuse surfaces as is constant. According to Duffie and Beckman [1] the surfaces of most solar collectors are such that the absorptivity is some function of the beam incidence angle, which for horizontal surfaces, is the zenith angle of the sun i. e.

lba„ + laas = lba, [і + 2.0345 x 10^вг -1.99 x 10^0? + 5.324 x 1O-6^ — 4.799x 10^в‘ ]

+,A

(3)

where /h = /b + /d, /b and /d are the beam and diffuse solar radiation respectively and0zis the zenith angle.

The first term on the right-hand side of equation (1) represents the convective heat transfer between the surface and the ambient air. The objective of this study is to determine the heat transfer coefficient h.

The second term on the right-hand side of equation (1) represents the long-wave radiation between the surface and the environment. In this term, the Kelvin sky temperature can be approximated by (Swinbank [2])

Tsky = 0.0552 Ta1’5

The third term on the right-hand side of equation (1) represents the heat that is conducted into the surface or ground. If the ground is insulated, this term is negligible and the heat transfer coefficient is given by

The results of tests that were conducted on surfaces exposed to the natural environment during windy conditions are reported by Duffie and Beckman [1], Watmuff, Charters and Proctor [3], Clarke [4] and Test, Lessman and Johary [5]. It should however be noted that the tests by Test, Lessman and Johary [5] were done on an inclined surface of 40°. In general the convective heat transfer coefficients for these tests are expressed as

h = a + bvw (6)

where a and b are supposed to be constants. Examples of these correlations are shown in figure 2. A correlation by Vehrencamp [6] that differs from equation (6) is also shown as well as a dimensionless equation according to Lombaard and Kroger [7]. Note the significant discrepancies between the equations.

It is obvious that equation (6) cannot adequately express the heat transfer coefficient. Equation (6) is not dimensionless and does not make provision for changes in thermo­physical properties. Furthermore, when the wind speed vw = 0, heat that is transferred due to natural convection is not constant, but is a function of the temperature difference between the surface and the ambient air as given by Bejan [8].

Nu = cRa13

or

where Tm = (Ts + Ta)/2 is the mean air temperature.

Many laboratory experiments have been conducted to determine the heat transfer coefficient due to turbulent natural convection from a heated horizontal upward-facing surface (Fujii and Imura [9], Rohsenow et al. [10], Lloyd and Moran [11], Al-Arabi and El — Riedy [12], Clausing and Berton [13]). Values of c range between 0.13 and 0.16. In part, this range of values for c is due to the fact that the test surfaces were made up of different materials and had different sizes. In some tests uniform surface temperatures were maintained while in other cases it was claimed that the heat flux was uniform.

Lombaard and Kroger [7] conducted experiments on an insulated 1m x 1m horizontal plate exposed to the natural environment. This truly uniform "heat flux” (solar radiation) test gave a value of c = 0.227.

Al-Arabi and El-Riedy [12] refer to the work of Kraus who tested 160mm x 160mm to 260mm x 260mm heated horizontal surfaces and obtained a coefficient of c = 0.137 and Kamal and Salah who studied a horizontal rectangular plate 504mm x 200mm maintained at constant temperature and concluded that for a plate of infinite size (for which case the edge effects could be neglected) the value of the coefficient was c = 0.135. Al-Arabi and El-Riedy [12] carried out experiments on upward facing heated plates at constant temperature. They tested square plates having dimensions varying from 50mm to 450mm, circular plates ranging from 100mm to 500mm in diameter and rectangular plates of 150mm wide and lengths of 250mm to 600mm. All their mean results are well correlated by a coefficient of c = 0.155. They also conducted an experiment on a square plate to find the heat transfer coefficient in the central part of the plate, which was not influenced by edge effects. The resultant coefficient had a value of c = 0.145.

According to the studies by Al-Arabi and El-Riedy [12], it would thus appear that for an infinite plate horizontal surface at constant temperature, c = 0.14 (average of 0.135 and 0.145). According to Kroger [14] the value of the constant for uniform heat flux is я/2 times this value i. e. 0.22. This value is close to the 0.227 found by Lombaard and Kroger [7].

Kroger [14] theoretically analysed the problem of convection heat transfer on a horizontal surface exposed to the natural environment. He shows that the dimensionless convective heat transfer coefficient is given by

1/3

In this approximate semi-empirical equation the constant c has a theoretical value of 0.243. The effective friction coefficient, Cf, has to be determined experimentally under windy conditions.

Experiment

Experiments were conducted at the Solar Energy Laboratory of the University of Stellenbosch, Stellenbosch, South Africa (Latitude -33.93°, Longitude 341.15° west). The experimental apparatus consisted of a 1m x 1m polystyrene plate having a thickness of 50mm, which was surrounded by an open area covered with a large black plastic sheet as shown schematically in figure 3. The plate was put on the black sheet to simulate an infinite black surface and to minimise edge effects.

The surface temperature measurements were obtained from six type T thermocouples that were embedded on the surface of the plate. Another four type T thermocouples were placed at different heights above the solar collector, as shown in figure 3, to measure the temperature gradient above the collector.

A weather station was used to measure ambient air temperature, barometric pressure, humidity, wind speed and wind direction. The wind speed was measured at 0.15m and 1.0m above ground level. Solar radiation was measured with a Kipp & Zonen pyranometer. All data was collected in one minute intervals and averaged over ten minutes.

Examples of experimental measurements as a function of solar time on a particular day are shown graphically in figure 4, 5, 6 and 7.

6 7 8 9 10 11 12 13 14 15 16 17 18 19

Solar time

Figure 6: Measured wind speed and direction at a height of 0.15m above ground level.

Figure 7: Measured wind speed and direction at a height of 1m above ground level.

Results and discussion

As shown in figure 8 the experimental results for the dimensional heat transfer coefficient are well correlated by an expression having the same form as equation (8), i. e.

і

0.9 0.8 0.7 0.6 0.5 0.4 — 0.3 0.2 0.1 — 0

w LM9 (T. — T)_

Figure 8: Experimental results of the dimensional heat transfer coefficient.

The value of the coefficient c of 0.2128 is close to the expected value of 0.14(^/ 2) = 0.22.

The value of the effective friction factor based on a height of 1m above ground level is Cf = 0.0046.

In general the velocity distribution is close to the 1/7th power law as shown in figure 9.

Only experimental data taken during the period 10:00 to 14:00 was considered since the nature of equation (5), used to evaluate the heat transfer coefficient, is such that it becomes very sensitive to small errors in temperature measurement before and after these times, as is shown in figure 10 for an error of +1°C in surface temperature.

Conclusion

The convection heat transfer coefficient between an infinite horizontal surface and the natural environment has been studied experimentally. The experimental data is well correlated by equation (9) in the range of 0m/s < vw < 4m/s, measured 1m above ground level. The value of the effective skin friction coefficient, based on a height of 1m above ground level, is found to be Cf = 0.0046.

Nomenclature
a	Constant	Ih	Solar irradiation, W/m2
b	Constant	k	Thermal conductivity, W/mK
c	Constant	L	Length, m
Cf	Friction coefficient	P	Pressure, N/m2
cp	Specific heat, J/kgK	T	Temperature, K
g	Gravitational acceleration, m/s2	vw	Wind speed, m/s
h	Heat transfer coefficient, W/m2K	z	coordinate
Dimensionless numbers
Nu	hL Nusselt number, к	Ra	Rayleigh number, P g^s — TmPk
Greek letters
a	Absorptivity	P	Density, kg/m3
є	Emissivity	Az	Zenith angle, °
и	Dynamic viscosity, kg/ms

Subscripts

a Air or ambient g Ground m Mean

nc Natural convection

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