sion, is dynamic fluid viscosity, υ is the kinematic fluid viscosity, *h*c is the heat

transfer conductance, α is the thermal diffusivity, and *k *is the thermal conductiv-

ity of the fluid. *Pr *is the Prandtl number and *Gr *is the Grashof number. The two

remaining undefined terms, ∆*T *and *L*, are dependent on the boundary conditions

and geometry of the problem. In the simplest case, ∆*T *will be the temperature dif-

ference between a warm surface and a cold surface. The variable *L *is a character-

width is often used; other examples are discussed below. Correlations for *Nu *are

found in the form of

(10)

when a specific material, such as air, is specified, or

(11)

for the general case of natural convection in fluids or gases.

Heat transfer by radiation between two surfaces can have a large effect on the

heat transfer correlations. Experiments and analytical or numerical analysis can

include these effects or they can be removed. Radiation is primarily reflected in

the heat transfer conductance *h*. Generally, *h *should be considered to be the sum

vection. It is not always clear when examining heat transfer correlations if this is

the case, or if *h *represents merely *h*c.

A vertical rectangular cavity (enclosure) is defined as an enclosure bounded by

two vertical surfaces held at different temperatures. The other two parallel sur-

faces, top and bottom, are taken as insulated (Gebhart et al. 1988). Heat transfer

occurs only at the vertical surfaces. The characteristic length *L *for this geometry is

the distance between the hot and cold walls, and the characteristic temperature

∆*T *is the difference between the vertical wall temperatures. For an air-filled square

enclosure, Ostrach (1972) summarized the following numerical results for the

average Nusselt number in the form of eq 11.

Reference

eq

Newell and Schmidt (1969)

0.0547

0.397

(12)

Han (1967)

0.0782

0.3594

(13)

Elder (1965)

0.231

0.25

(14)

He reported tolerable agreement between these correlations and experiments.

Recently, de Vahl Davis and Jones (1983) presented a numerical benchmark

solution for air in a square vertical enclosure at *Ra *values from 103 to 106. Fitting

an equation to their Nusselt number data at the cold surface yields

(15)

Equations 1215 are drawn on Figure 2.

Correlations have also been developed for vertical enclosures with aspect ra-

tios (height/width) other than one. Gebhart et al. (1988) present several correla-

tions of the form

4

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