Flat plates natural convection

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... 

C. Laminar, local, flat plate, natural convection vertical plate (Va., = = 0.508 Ni (0.952 + [T] Low MT rates. Dilute systems, Ap/p 1. NqtNsc < 108. Use with arithmetic concentration difference, x = length from plate bottom. [141] p. 120... 

J. Perforated flat disk Perforated vertical plate. Natural convection. Characteristic length = disk diameter d NSh = O.INscNg Characteristic length = L, electrode height [E]6 x 109 < NsJia. < 1012 and 1943 hole diameter [E]l x 1010 < JVsJVGr < 5 x 1013 and 1939 < N < 2186 Average deviation + 10% [162]... 

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. 

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. 

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

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 ... 

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. 

Warner, C. Y., and V. S. Arpaci An Experimental Investigation of Turbulent Natural Convection in Air at Low Pressure along a Vertical Heated Flat Plate, Int. J. Heat Mass Transfer, vol. 11, p. 397, 1968. 

Consider a vertical hot flat plate immersed in a quiescent fluid body. We assume the natural convection flow to be steady, laminar, and two-dimensional, and the fluid to be Newtonian with constant properties, including density, with one exception the density difference p — is to be considered since it is this density difference between the inside and the outside of the boundary layer that gives rise to buoyancy force and sustains flow. (This is known as the Boussines.q approximation.) We take the upward direction along the plate to be X, and the direction normal to surface to be y, as shown in Fig. 9-6. Therefore, gravelly acts in the —.t-direclion. Noting that the flow is steady and two-dimensional, the.t- andy-compoijents of velocity within boundary layer are II - u(x, y) and v — t/(.Y, y), respectively. 

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. ... 

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... 

Consider natural convection in flow past a flat plate.[6] The velocity distribution is governed as in example 4.13. In addition, the temperature T is governed by ... 

To illustrate the use of the transport equations, the following problem is posed. An electrochemical cell containing vertical flat sheets of copper as the anode and cathode is operated with an aqueous CUSO4 electrolyte. The copper plates are connected to a DC power supply so that oxidation and reduction reactions proceed at the anode and cathode (Cu -1- 2e — Cu at the cathode Cu -> Cu -I- 2e at the anode). For the case when there is no forced or natural convection during current flow, we derive a simple expression between the constant applied current density and the steady-state cupric ion concentration profile. The cation flux and current density equations for the flat plate electrode/no convection cell are... 

Combined forced and free convection at a vertical flat plate, where the forced convection velocity is in the same direction as the natural convection flow (the so-called assisting mixed convection case). Here, researchers have combined Sherwood numbers for the pure forced and natural convection cases in the following way [15, 24-26] ... 

Let the medium between the flat surfaces of two bodies (now a fluid because of practical reasons) flow with a mean velocity V (Fig. 1.13). This flow results from either an imposed pressure drop or an induced buoyancy, respectively called forced and natural convection. Lettheinlettemperatureofthefluidbe72. (Note that the fluid temperature need not be Tz- Selection of Tz for this temperature eliminates temperature gradient near plate 2 and simplifies the following development.) The convection heat transfer from plate 1 is defined as the conduction in the fluid next to plate 1 (in view of the fact... 

Evaluate the heat loss by natural convection, forced convection, and radiation from a flat plate at a uniform temperature Tm to ambient air or water at a temperature Tm. The temperature difference between the wall and ambient is 100 K. The heat transfer coefficients for natural and forced convection in air are 10 and 200 W/mz-K, and in water are 500 and 10,000 W/m2 -K, respectively. Plot the various heat losses from the plate as a function of Tm/ TW - Tm) for To, = 0,400,800, and 1200 K. Note the effect of convection relative to radiation as a function of temperature. 

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... 

C. Y. Warner and V. S. Arpaci, An experimental investigation of turbulent natural convection in air at low pressure for a vertical heated flat plate, InL J. Heat Mass Transfer, 11,397-406,1968. 

Discussion of Correlation for Specific Shapes. The equation for elliptical cylinders fits the approximate analysis of Raithby and Hollands [224] but has not been verified by experiment except in the limiting cases of a vertical plate (C/L = 0) and a circular cylinder (C/L = 1.0). The vertical plate predictions by Eq. 4.48 are slightly different than those based on the more accurate specialized equations given in the section on external natural convection in flat plates. 

E. K. Levy, P. A. Eichen, W. R. Cintani, and R. R. Shaw, Optimum Plate Spacings for Laminar Natural Convection Heat Transfer From Parallel Vertical Isothermal Flat Plates Experimental Verification, J. Heat Transfer (97) 474-476,1975. 

An important heat-transfer system occurring in process engineering is that in which heat is being transferred from a hot vertical plate to a gas or liquid adjacent to it by natural convection. The fluid is not moving by forced convection but only by natural or free convection. In Fig. 4.7-1 the vertical flat plate is heated and the free-convection boundary layer is formed. The velocity profile differs from that in a forced-convection system in that the velocity at the wall is zero and also is zero at the other edge of the boundary layer since the free-stream velocity is zero for natural convection. The boundary layer initially is laminar as shown, but at some distance from the leading edge it starts to become turbulent. The wall temperature is T K and the bulk temperature T. ... 

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. 

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