Natural convection, laminar vertical

Some of the more commonly used methods of obtaining solutions to problems involving natural convective flow have been discussed in this chapter. Attention has been given to laminar natural convective flows over the outside of bodies, to laminar natural convection through vertical open-ended channels, to laminar natural convection in a rectangular enclosure, and to turbulent natural convective boundary layer flow. Solutions to the boundary layer forms of the governing equations and to the full governing equations have been discussed. 

Ihe role played by the Reynolds number in forced convection is played by the Grashof number in natural convection. As such, the Grashof number provides the main criterion in determining whether the fluid flow is laminar or turbulent in natural convection. For vertical plates, for e.Kample, the critical... 

M. M. Yovanovich and K. Jafarpur, Models of Laminar Natural Convection From Vertical and Horizontal Isothermal Cuboids for All Prandtl Numbers and All Rayleigh Numbers Below 1011, ASME HTD (264) 111-126,1993. 

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... 

H. Vertical tubes, laminar flow, forced and natural convection... 

The corresponding laminar natural convection burning rate on a vertical surface was... 

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

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... 

In order to. illustrate how natural convection in a vertical channel can be analyzed, attention will be given to flow through a wide rectangular channel, i.e., to laminar, two-dimensional flow in a plane channel as shown in Fig. 8.15. This type of flow is a good model of a number of flows of practical importance. 

Oosthuizen, P.H., A NumericaLStudy of Laminar Free Convective Row Through a Vertical Open Partially Heated Plane Duct , Fundamentals of Natural Convection/Electronic Equipment Cooling, ASME HTD, Vol. 32, pp. 41-48, 22nd National Heat Transf. Conf. and Exhibition, Niagara Falls, New York, 1984. 

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... 

G. Vertical tubes, laminar flow, forced and natural convection Nsh, e = 1.62JV 1 0.0742 d/L a [T] Approximate solution. Use minus sign if forced and natural convection oppose each other. Good agreement with experiment. N NsJ g p d3 MGz-, DlQr- 9 L pv2 [127]... 

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. 

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... 

Natural convection also occurs in vertical tubes, increasing the rate of heat flow, when the fluid flow is upward, to above that found in laminar flow only. The effect is marked at values of Nct between 10 and 10,000 and depends on the magnitude of the quantity NatNpfD/L. 

The intersection points of the pure natural convection and pure forced convection equation also provide valuable information on the conditions for which forced and natural convection are equally important. For example, for laminar flow along the heated isothermal vertical plate in Fig. 4.6 if Eq. 4.33a for NulV is equated to the forced convection Nusselt number given by... 

Vertical Plates. If Eq. 4.33a (Eq. 4.336 should be used if Ra < 104 is of interest) and Eq. 4.33c are used for laminar and turbulent natural convection, respectively, and if Eq. 4.154 and Nuf = (0.037Re08 - 871.3) Pr1 3 are used, respectively, for laminar and turbulent forced convection, then Eq. 4.155 gives the laminar-laminar (i.e., laminar forced convection and laminar natural convection) intersection, while the laminar-turbulent intersection is given by... 

Y. Asako, H. Nakamura, and M. Faghri, Three-Dimensional Laminar Natural Convection in a Vertical Air Slot With Hexagonal Honeycomb Core, J. Heat Transfer (112) 130-136,1990. 

J. R. Dyer, The Development of Laminar Natural Convection Flow in a Vertical Uniform Heat Flux Duct, Int. J. Heat Mass Transfer (18) 1455-1465,1975. 

W. W. Humphreys and J. R. Welty, Natural Convection With Mercury in a Uniformly Heated Vertical Channel During Unstable Laminar and Transitional Flow, AIChE Journal (21/2) 268-274, 1975. 

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. 

M-H Chun and K-T Kim, A Natural Convection Heat Transfer Correlation for Laminar and Turbulent Film Condensation on a Vertical Surface, Proc. ASMEIJSME Thermal Eng. Conf, Reno, 2, pp. 459-464,1991. 

For large pipe diameters and large temperature differences AT between pipe wall and bulk fluid, natural convection effects can increase li(Pl). Equations are also available for laminar flow in vertical tubes. 

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. ... 

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