Free Convection from Horizontal Plates

The average heat-transfer coefficient from horizontal flat plates is calculated with Eq. (7-25) and the constants given in Table 7-1. The characteristic dimension for use with these relations has traditionally [4] been taken as the length of a side for a square, the mean of the two dimensions for a rectangular surface, and 0.9d for a circular disk. References 52 and 53 indicate that better agreement with experimental data can be achieved by calculating the characteristic dimension with 

The experiments of Ref. 44 have produced the following correlations for constant heat flux on a horizontal plate. For the heated surface facing upward, 

In these equations all properties except /3 are evaluated at a temperature Te defined by 

Section 7-7 discusses an extension of these equations to inclined surfaces. 

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Assume that one-half of the heat transfer by free convection from a horizontal cylinder occurs on each side of the cylinder because of symmetry considerations. Going by this assumption, compare the heat transfer on each side of the cylinder with that from a vertical flat plate having a height equal to thd circumferential distance from the bottom stagnation point to the top stagnation point on the cylinder. Discuss this comparison. 

G. D. Raithby and K. G. T. Hollands, Laminar and Turbulent Free Convection From Elliptic Cylinders, With a Vertical Plate and Horizontal Circular Cylinder as Special Cases, J. Heat Transfer (98) 72-80,1976. 

A flat-plate solar collector is 1 m square and is inclined at an angle of 200 with the horizontal. The hot surface at 160°C is placed in an enclosure which is evacuated to a pressure of 0.1 atm. Above the hot surface, and parallel to it, is the transparent window which admits the radiant energy from the sun. The hot surface and window are separated by a distance of 8 cm. Because of convection to the surroundings, the window temperature is maintained at 40°C. Calculate the free-convection heat transfer between the hot surface and the transparent window. 

A flat plate 1 by 1 m is inclined at 30° with the horizontal and exposed to atmospheric air at 30°C and 1 atm. The plate receives a net radiant-energy flux from the sun of 700 W/m2, which then is dissipated to the surroundings by free convection. What average temperature will be attained by the plate ... 

Wang, X.A. (1982). An experimental study of mixed, forced, and free convection heat transfer from a horizontal flat plate to air, ASME J. Heat Transfer 104 139-144. 

H. Imura, R. R. Gilpin, and K. C. Cheng, An Experimental Investigation of Heat Transfer and Buoyancy Induced Transition From Laminar Forced Convection to Turbulent Free Convection Over a Horizontal Isothermally Heated Plate, J. Heat Transfer (100) 429-434,1978. 

H-T. Lin, K-Y. Wu, and H-L. Hoh, Mixed Convection from an Isothermal Horizontal Plate Moving in Parallel or Reversely to a Free Stream," Int. J. Heat Mass Transfer, 36, pp. 3547-3554,1993. 

For the heated vertical plate and horizontal cylinder, the flow results from natural convection. The stagnation configuration is a forced flow. In each case the flow is of the boimdai7 Kiyer type. Simple analytical solutions can be obtained when the thickness of the du.st-free space is much smaller than that of the boundary layer. In this case the gas velocity distribution can be approximated by the first term in an expansion in the distance norroal to the surface. Expressions for the thickness of the dust-free space for a heated vertical surface and a plane stagnation flow are derived below. 

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