Vertical plates, natural convection

Hong, J.-T., Tien, C.-L. and Kaviany. M., Non-Darcean Effects on Vertical Plate Natural Convection in Porous Media with High Porosity . Int. J. Heat Mass Transfer, Vol. 28, pp. 2149-2157. 1985. 

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]... 

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... 

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... 

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

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

The adequaey of the Boussinesq approximations has been tested for natural eonveetion from a vertical plate (S31) and for mixed convection from a hori-... 

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... 

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... 

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

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

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. 

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. 

Eckert, E.R.G. and Carlson, W.O., Natural Convection in an Air Layer Enclosed Between Two Vertical Plates with Different Temperatures , Int. J. Heat Mass Transfer, Vol. 2, pp. 106-120, 1961. 

Henkes, R.A.W.M. and Hoogendoom. C.J., Comparison of Turbullence Models for the Natural Convection Boundary Layer Along a Heated Vertical Plate , Int. J. Heat Mass Transfer, Vol. 32, pp. 157-169, 1989. 

Numerically predicted variation of Nusselt number variation with Reynolds number in turbulent assisting mixed convective flow over a vertical plate. (Based on results obtained by Patel K., Armaly B.F., and Chen T.S., Transition from Turbulent Natural to Turbulent Forced Convection Adjacent to an Isothermal Vertical Plate , ASME HTD, Vol. 324, pp. 51-56, 1996. With permission.)... 

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. 

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