Horizontal plates, natural convection

Dropkin, D., and E. Somerscales Heat Transfer by Natural Convection in Liquids Confined by Two Parallel Plates Which Are Inclined at Various Angles with Respect to the Horizontal, J. Heat Transfer, vol. 87, p. 71, 1965. 

Habne, E. W. P. Heat Transfer and Natural Convection Patterns on a Horizontal Circular Plate, Int. J. Heat Mass Transfer, vol. 12, p. 651, 1969. 

Goldstein, R. J., E. M. Sparrow, and D. C. Jones Natural Convection Mass Transfer Adjacent to Horizontal Plates, Ini. J. Heat Mass Transfer, vol. 16, p. 1025, 1973. 

Consider the natural-convection equations available. Heat-transfer coefficients for natural convection may be calculated using the equations presented below. These equations are also valid for horizontal plates or discs. For horizontal plates facing upward which are heated or for plates facing downward which are cooled, the equations are applicable directly. For heated plates facing downward or cooled plates facing upward, the heat-transfer coefficients obtained should be multiplied by 0.5. 

Natural Convection over Surfaces 510 Vertical Plates (Fj = constant) 512 Verbeal Plates (4 = constant) 512 Vertical Cylinders 512 Inclined Plates 512 Horizontal Plates 513 Horizontal Cylinders and Spheres 513... 

Mass How Rate ttirougn ttie Space beLV, een Plates 519 9-5 Natural Convection Inside Enclosures 521 effective Thermal Conductivity 522 Horizontal Rectangular Enclosures 523 Inclined Rectangular Enclosures 523 Vertical Rectangular Enclosures 524 Concentric Cylinders 524 Concentric Spheres 525 Combined Natural Convection and Radiation 525... 

Consider a 0.6 m X 0.6-m thin square plate in a room at 30°C. One side of the plate is maintained at a temperature of 90°C, while the other side is insulated, as shown in Fig. 9-15. Determine the rate of heat transfer from the plate by natural convection if the ptate is (a) vertical, (W horizontal with hot surface facing Up, and (c) horizontal with hot surface facing down. 

The characteristics of heat transfer through a horizontal enclosure depend ou whether the hotter plate is at the top or at the bottom, as shown in Fig. 9-22. When the hotter plate is at the top, no convection currents develop in the enclosure, since Ihe lighter fluid is always on top of the heavier fluid. Heat transfer in tlris case is by pure conduction, and we have Nu - 1. When the hotter plate is at the bottom, the heavier fluid will be on top of the lighter fluid, and there will be a tendency for Ihe lighter fluid to topple the heavier fluid and rise to the top, where it comes in contact with the cooler plate and cools down. Until that happens, however, heat transfer is still by pure couduc-tion and Nu — I. When Ra > 1708, the buoyant force overcomes the fluid resistance and initiates natural convection currents, which are observed to be in the form of hexagonal cells called BSnard cells. For Ra > 3 X 10, the cells break down and the fluid motion becomes turbulent. 

Flat-plate solar collectors are often tilted up toward the sun in order to intercept a greater amount of direct solar radiation. The tilt angle from the horizontal also affects the rate of heat loss from the collector. Consider a 1.5-m-high and 3-m-wide solar collector th.al is lilted at an angle fioin the horizontal. The back side of the absorber is heavily insulated. The absorber plate and the glass cover, which are spaced 2.5 cm from eachother, are maintained at temperatures of 80°( and 40°C, respectively. Determine llie rale of heat loss from the absorber plate by natural convection for 0 = 0°, 30, and 90. ... 

In a production facility, thin square plates 2 m X 2 m in siie coming out of the oven at 270°C are cooled by blowing ambient air at I8°C horizontally parallel to their surfaces. Determine the air velocity above which the natural convection effects on heat transfer are less than 10 percent and thus are negligible. 

Consider a flat-plate solar collector placed horizontally on the flat roof of a house. The collector is 1.5 m wide and 6 m long, and the average temperature of ihe exposed surface of Ihe collector is 42 C, Determine ihe rale of heal loss from the collector by natural convection duiing a calm day when Ihe ambient air temperature is 8 C. Also, determine the heat loss by radiation by taking Ihe eniissivily of the collector surface to be 0.9 and the effective sky temperature to be - 15 C. /l/iswers 1750 W, 2490 W... 

Corwider a horizontal 0.7-m-wide and O.S5-m-long plate in a room at 30°C. Top side of the plate is insulated while the bottom side is maintained at 0°C. The rate of heal transfer from the room air to the plate by natural convection is... 

The simulations were performed assuming that the flow is laminar. Additionally, the contact angle is assumed to be known. The initial velocity is assumed to be zero everywhere in the domain. The initial fluid temperature profile is taken to be linear in the natural convection thermal boundary layer and the thermal boundary layer thickness, 5j, is evaluated using the correlation for the turbulent natural convection on a horizontal plate as, Jj. =1. 4(vfiCil ... 

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. 

Natural Convection between Two Horizontal Parallel Plates.523... 

Globe, S., and Dropkin, D., Natural Convection Heat Transfer in Liquids Confined between Two Horizontal Plates, J. Heat Transfer 81C, 24, (1959). 

In Chapter 5, we learned the foundations of convection. Integrating the governing equations for laminar boundary layers, we obtained expressions for the heat transfer associated with forced convection over a horizontal plate and natural convection about a vertical plate. We also found analytically, as well as by the analogy between heat and momentum, that the thermal and momentum characteristics of laminar flow over a flat plate are related by... 

Table 6.7 Natural convection correlations for horizontal plates...

S. Globe and D. Dropkin, Natural convection heat transfer in liquids confined between two horizontal plates, J. Heat Transfer, C81,24-29,1959. 

The natural convection currents surrounding a hot, horizontal pipe are more complicated than those adjacent to a vertical heated plate, but the mechanism of the process is similar. The layers of air immediately next to the bottom and sides of the pipe are heated and tend to rise. The rising layers of hot air, one on each side of the pipe, separate from the pipe at points short of the top center of the pipe and form two independent rising currents with a zone of relatively stagnant and unheated air between them. 

FIGURE 4.10 Definition sketch for natural convection on a horizontal upward-facing plate of arbitrary planform. Only the top heated surface of area A is heated. 

The problem of natural convection in a cavity without interior solids is exemplified by the two situations sketched in Fig. 4.25. In both situations, the fluid-filled cavity is bounded by two isothermal parallel plates that are inclined at angle 0 from horizontal, spaced at distance L, and held at different temperatures. The temperature Th is assumed to be larger than Tc, so cavities with 0 = 0° are described as horizontal with heating from below, those with 0 = 90° are described as vertical with heating from the side, and those with 0 = 180° are described as horizontal with heating from above. 

Horizontal Flow. For laminar flow over the upper surface of a horizontal heated plate (or over the bottom surface of a cooled plate), the center of the mixed convection regime can again be estimated by equating the forced convection Nusselt number from Eq. 4.154 to that for natural convection from Eq. 4.39c (for detached turbulent convection). This results in... 

M. Al-Arabi and M. K. El-Riedy, Natural Convection Heat Transfer From Isothermal Horizontal Plates of Different Shapes, Int. J. Heat Mass Transfer (19) 1399-1404,1976. 

I. Catton and D. K. Edwards, Effect of Side Walls on Natural Convection Between Horizontal Plates Heated From Below, J. Heat Transfer (89) 295-299,1967. 

A. M. Clausing and J. J. Berton, An Experimental Investigation of Natural Convection from an Isothermal Horizontal Plate, /. Heat Transfer (111) 904-908,1989. 

D. W. Hatfield and D. K. Edwards, Edge and Aspect Ratio Effects on Natural Convection From the Horizontal Heated Plate Facing Downwards, Int. J. Heat Mass Transfer (24/6) 1019-1024,1981. 

K. Kitamura and F. Kimura, Heat Transfer and Fluid Flow of Natural Convection Adjacent to Upward-Facing Horizontal Plates, Int. J. Heat Mass Transfer (38/17) 3149-3159,1995. 

The experimental data plotted in Figs. 1 through 6 represent the highest values reported and show the broad superheat range typical of nucleate boiling, which is often due to different nucleation conditions. For comparison, the heat flow density (the peak flux of natural convection pool boiling on a horizontal plate as given by Kutateladze)... 

Natural convection from horizontal plates. For horizontal flat plates Eq. (4.7-4) is also used with the constants given in Table 4.7-1 and simplified equations in Table 4.7-2. The dimension L to be used is the length of a side of a square plate, the linear mean of the two dimensions for a rectangle, and 0.9 times the diameter of a circular disk. 

For laminar natural convection of air at a horizontal plate heated from... 

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