Plate heated, natural convection

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. 

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 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... 

For the purpose of discussion, it can however, be assumed that at steady state Thotface = Tuquidus in which case h becomes the heat transfer coefficient for a vertical plate undergoing natural convection heating. The magnitude of h is then of the order of 425 [W/m -K] for a cooler immersed in only silicate slag. More precise estimates accounting for different material properties can be made using [20, 23, 24] ... 

Convective heat transfer is classified as forced convection and natural (or free) convection. The former results from the forced flow of fluid caused by an external means such as a pump, fan, blower, agitator, mixer, etc. In the natural convection, flow is caused by density difference resulting from a temperature gradient within the fluid. An example of the principle of natural convection is illustrated by a heated vertical plate in quiescent air. 

Natural convection occurs when a solid surface is in contact with a fluid of different temperature from the surface. Density differences provide the body force required to move the flmd. Theoretical analyses of natural convection require the simultaneous solution of the coupled equations of motion and energy. Details of theoretical studies are available in several general references (Brown and Marco, Introduction to Heat Transfer, 3d ed., McGraw-HiU, New York, 1958 and Jakob, Heat Transfer, Wiley, New York, vol. 1, 1949 vol. 2, 1957) but have generally been applied successfully to the simple case of a vertical plate. Solution of the motion and energy equations gives temperature and velocity fields from which heat-transfer coefficients may be derived. The general type of equation obtained is the so-called Nusselt equation hL I L p gp At cjl... 

If a beaker containing water rests on a hot plate, the water at the bottom of the beaker becomes hotter than that at the top. Since the density of the hot water is lower than that of the cold, the water in the bottom rises and heat is transferred by natural convection. In the same way air in contact with a hot plate will be heated by natural convection currents, the air near the surface being hotter and of lower density than that some distance away. In both of these cases there is no external agency providing forced convection currents, and the transfer of heat occurs at a correspondingly lower rate since the natural convection currents move rather slowly. 

The details of natural convective flows over surfaces other than flat plates have only recently been studied experimentally (A7, Jl, P3, SI2). We consider a heated sphere in an infinite, stagnant medium. Flow is directed toward the surface over the bottom hemisphere and away from the surface over the top hemisphere with a stagnation point at each pole (P3, S12). The lower pole is considered the forward stagnation point. 

Coefficients of heat transfer by natural convection from bodies of various shapes, chiefly plates and cylinders, are correlated in terms of Grashof, Prandtl, and Nusselt numbers. Table 8.9 covers the... 

Heat transfer by natural convection across an enclosed space, called an enclosure or, sometimes, a cavity, occurs in many real situations, see [34] to [67]. For example, the heat transfet between the panes of glass in a double pane window, the heat transfer between the collector plate and the glass cover in a solar collector and in many electronic and electrical systems basically involves natural convective flow across an enclosure. 

A 0.3-m vertical plate is maintained at a surface temperature of 65°C imd is exposed to stagnant air at a temperature of 15°C and standard ambient pressure. Compare the natural convective heat transfer rate from this plate w ith that which would result from forcing air over the plate at a velocity equal to the maximum velocity that occurs in the natural convective boundary layer. 

A 30-cm high vertical plate has" a surface temperature that varies linearly from 15°C at the lower edge to 45°C at the upper edge. This plate is exposed to air at 1S°C and ambient pressure. Use the computer program for natural convective boundary layer flow to determine how the local heat transfer rate varies with distance up die plate from the lower edge. 

Air flows by natural convection through the channel formed between 2 20-cm high plates kept at a temperature of 50°C. If the distance between the 2 plates is 3 cm and if the ambient air temperature is 20°C, find the rate of heat transfer from the 2 plates to the air and the mean velocity of the air through the channel. 

Gryzagoridis, J., Natural Convection from a Vertical Rat Plate in the Low Grashof Number Range , Int. J. Heat Mass Transfer, Vol. 14, pp. 162-164, 1971. 

Bah ani, P.A. and Sparrow, E.M., Experiments on Natural Convection from Vertical Parallel Plates with Either Open or Dosed Edges , ASME J. Heat Transfer, Vol. 102, pp. 221-227, 1980. 

Bar-Cohen, A. and Rohsenow, W.M.. "Thermally Optimum Spacing of Vertical Natural Convection Cooled, Parallel Plates , J. Heat Transfer, Vol. 106. p. 116. 1984. 

The side of i small laboratory furnace can be idealized as a vertical plate 0.6 m high and 2.5 m wide. The furnace sides are at 40°C and the surrounding air is at 25°C. If air is blown vertically over the side of the fur.iace, estimate the lowest forced air velocity that would cause the heat-transfer coefficient to depart noticeable from its natural convection value. 

A heat pump system utilizes a heat exchanger buried in water-saturated soil as a heat source. The heat exchanger basically consists of a series of vertical plates with height of 30 cm and a width of 10 cm. These plates are effective Is at a uniform temperature of 5°C. The soil can be assumed to have a permeability of 10 0 nr and apparent thermal conductivity of 0.1 W/m-K. The temperature of the saturated soil far from the heat exchanger is 30°C. Assuming natural convective flow and that there is no interference between the flows over the individual plates, find the mean heat transfer rate to a plate. 

Discuss how the analysis of natural convective flow over a vertical flat plate in a saturated porous medium must be modified if there is a uniform heat flux rather than a uniform temperature at the surface. 

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. 

As a first example of low-density heat transfer let us consider the two parallel infinite plates shown in Fig. 12-14. The plates are maintained at different temperatures and separated by a gaseous medium. Let us neglect natural-convection effects. If the gas density is sufficiently high so that A — 0, a linear temperature profile through the gas will be experienced as shown for the case of A. As the gas density is lowered, the larger mean free paths require a greater distance from the heat-transfer surfaces in order for the gas to accommodate to the surface temperatures. The anticipated temperature profiles are shown in... 

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. 

However, the experimental studies relate to spatial growth of disturbances as the flow system is always excited by fixed frequency sources. Hence a spatial theory is preferred to study the stability of non-isothermal flows. Despite the distinction between temporal and spatial methods, the neutral curve, however, is identical. Iyer Kelly (1974) reported results using linear spatial theory under parallel flow approximation for free-convection flow past heated, inclined plates. Tumin (2003) also reports the spatial stability of natural convection flow on inclined plates providing the eigen spectrum. 

Figure 6.7 Heat transfer by natural convection from a plate to an infinite medium.

---