Convection laminar natural

Here we terminate laminar forced convection and proceed to laminar natural convection. 

Consider a heated vertical plate in a quiescent fluid. The plate heats the fluid in its neighborhood, which then becomes lighter and moves upward. The force resulting from the product of gravity and density difference and causing this upward motion is called buoyancy. The fluid moving under the effect of buoyancy develops a vertical boundary layer about the plate. Within the boundary layer the temperature decreases from the plate temperature to the fluid temperature, while the velocity vanishes on the plate walls and beyond the boundary layer and has a maximum in between (Fig. 5.13). Actually, in a manner similar to forced convection, the momentum boundary layer of natural convection is expected to be thicker for larger Prandtl numbers than the thermal boundary layer. However, the characteristic velocity for the enthalpy flow across should be scaled relative to Ss rather than 5, 

In the preceding study on forced convection we neglected the buoyancy force relative to the inertial force. Here, we neglect the inertial force relative to the buoyancy force. The momentum balance for the control volume involving a fluid of height x and thickness 5 (Fig. 5,14) gives then 

For an estimate on rw in a manna similar to the estimate on qw [recall Eq. (5.19)], we may assume, in terms of a mean velocity U for the upward motion, 

For the thermal energy, consider the balance between the axial enthalpy flow and the transversal convection for the control volume shown in Kg. 5.15. Thus, 

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

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

As explained in Chapter 1, natural or free convective heat transfer is heat transfer between a surface and a fluid moving over it with the fluid motion caused entirely by the buoyancy forces that arise due to the density changes that result from the temperature variations in the flow, [1] to [5]. Natural convective flows, like all viscous flows, can be either laminar or turbulent as indicated in Fig. 8.1. However, because of the low velocities that usually exist in natural convective flows, laminar natural convective flows occur more frequently in practice than laminar forced convective flows. In this chapter attention will therefore be initially focused on laminar natural convective flows. 

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. 

Newell, M.E. and Schmidt, F.W., Heat Transfer by Laminar Natural Convection Within Rectangular Enclosures , J. Heat Transfer, Vol. 92, pp. 159-168, 1970. 

Al-Arabi, M., and Y. K. Salman Laminar Natural Convection Heat Transfer from an Inclined Cylinder, Int. J. Heat Mass Transfer, vol. 23, pp. 45-51, 1980. Holman, J. P. "Heat Transfer," 4th ed., McGraw-Hill Book Co., New York, 1976. 

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. 

A. Bejan and C. L. Tien, Laminar Natural Convection Heat Transfer in a Horizontal Cavity with Different End Temperatures, /. Heat Transfer (100) 641-647,1978. 

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. 

G. M. Harpole and I. Catton, Laminar Natural Convection About Downward Facing Heated Blunt Bodies to Liquid Metals, J. Heat Transfer (98) 208-212,1976. 

T. H. Kuehn and R. J. Goldstein, Numerical Solution to the Navier-Stokes Equations for Laminar Natural Convection About a Horizontal Isothermal Circular Cylinder, Int. J. Heat Mass Transfer (23) 971-979,1980. 

J. L. Lage and A. Bejan, The Ra-Pr Domain of Laminar Natural Convection in an Enclosure Heated From the Side, Numerical Heat Transfer Part A (19) 21-41,1991. 

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. M. Yovanovich and K. Jafarpur, Bounds on Laminar Natural Convection From Isothermal Disks and Finite Plates of Arbitrary Shape From All Orientations and Prandtl Numbers, ASME HTD (264) 93-110,1993. 

For a laminar natural convection, Nu varies according to the relationship [37] ... 

For laminar natural convection of air at a horizontal plate heated from... 

Rao, A.K., 1963. Laminar natural convection flow with suction or injection. Appl. Sci. Res. All, 1-9. 

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