Natural convection plates

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... 

C. Laminar, local, flat plate, natural convection vertical plate... 

I. Turbulent, local flat plate, natural convection, vertical plate Turbulent, average, flat plate, natural convection, vertical plate Nsk. = — = 0.0299Wg=Ws = D x(l + 0.494W ) )- = 0.0249Wg=W2f X (1 + 0.494WE )- [S] Low solute concentration and low transfer rates. Use arithmetic concentration difference. Ncr > 10 " Assumes laminar boundary layer is small fraction of total. D [151] p. 225... 

O. Laminar flow, vertical parallel plates, forced and natural convection... 

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. 

In forced convection, the velocity of the liquid must be characterized by a suitable characteristic value Vih e.g. the mean velocity of the liquid flow through a tube or the velocity of the edge of a disk rotating in the liquid, etc. For natural convection, this characteristic velocity can be set equal to zero. The dimension of the system in which liquid flow occurs has a certain characteristic value /, e.g. the length of a tube or the longitudinal dimension of the plate along which the liquid flows or the radius of a disk rotating in the liquid, etc. Solution of the differential equations (2.7.5), (2.7.7) and (2.7.8) should yield the value of the material flux at the phase boundary of the liquid with another phase, where the concentration equals c. ... 

Figure 9.11 (a) Laminar burning rate of a vertical plate under natural convection by Kim, deRis... 

A major fallacy is made when observations obeying a known physical law are subjected to trend-oriented tests, but without allowing for a specific behaviour predicted by the law in certain sub-domains of the observation set. This can be seen in Table 11 where a partial set of classical cathode polarization data has been reconstructed from a current versus total polarization graph [28], If all data pairs were equally treated, rank distribution analysis would lead to an erroneous conclusion, inasmuch as the (admittedly short) limiting-current plateau for cupric ion discharge, albeit included in the data, would be ignored. Along this plateau, the independence of current from polarization potential follows directly from the theory of natural convection at a flat plate, with ample empirical support from electrochemical mass transport experiments. 

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. 

In electrochemical reactors, the externally imposed velocity is often low. Therefore, natural convection can exert a substantial influence. As an example, let us consider a vertical parallel plate reactor in which the electrodes are separated by a distance d and let us assume that the electrodes are sufficiently distant from the reactor inlet for the forced laminar flow to be fully developed. Since the reaction occurs only at the electrodes, the concentration profile begins to develop at the leading edges of the electrodes. The thickness of the concentration boundary layer along the length of the electrode is assumed to be much smaller than the distance d between the plates, a condition that is usually satisfied in practice. 

Laminar Natural Convection to a Vertical Plate with First-Order Homogeneous Reaction... 

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... 

From Table 2, for natural convection from a vertical plate with GrPr = 1.533 x 109,... 

Dimensionless velocity profiles in natural convective boundary layer on a vertical plate for various values of Prandtl number. 

Eqs. (8.120) and (8.121) represent the limiting boundary layer solution for natural convective flow through a vertical plane duct. For the particular case of Pr = 0.7, the similarity solution for natural convective boundary layer flow on a vertical plate... 

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. 

Transition to turbulence in the natural convective flow over a vertical plate. 

Available analyses of turbulent natural convection mostly rely in some way on the assumption that the turbulence structure is similar to that which exists in turbulent forced convection, see [96] to [105]. In fact, the buoyancy forces influence the turbulence and the direct use of empirical information obtained from studies of forced convection to the analysis of natural convection is not always appropriate. This will be discussed further in Chapter 9. Here, however, a discussion of one of the earliest analyses of turbulent natural convective boundary layer flow on a flat plate will be presented. This analysis involves assumptions that are typical of those used in the majority of available analyses of turbulent natural convection. 

This analysis is based on the use of the momentum and energy integral equations which for natural convective flow over a vertical plate are ... 

Solution. The following integrals arise in the approximate solution for turbulent natural convective boundary layer flow over a flat plate discussed above ... 

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. 

Using the similarity solution results, derive an expression for the maximum velocity in the natural convective boundary layer on a vertical flat plate. At what position in the boundary layer does this maximum velocity occur ... 

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. 

Natural convective flow over a vertical plate. 

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. 

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