They are related to one another gtw t 3 gr 2 gtw

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Unformatted text preview: esults –  Analy'cal results –  Numerical inves'ga'ons –  Semi ­analy'c or empirical models •  Natural convec'on results are always presented in terms of the following groups, Rayleigh # and Grashof #. They are related to one another: gβ(Tw − T∞ ) 3 Gr = ν2 gβ(Tw − T∞ ) 3 Ra = Gr Pr Ra = αν 6 Convec'on Heat Transfer •  Free convec'on from a ver'cal flat plate is a boundary layer problem, but more complex. •  The basic equa'ons which have been solved are: 1 ∂u ∂v β= − T [K ] ∂x + ∂y =0 ∂u ∂u ∂ 2u u +v = gβ(T − T∞ ) + ν 2 ∂x ∂y ∂y€ ∂T ∂T ∂ 2T u +v =α 2 ∂x ∂y ∂y T β is the thermal expansion coefficient. For gases it is given by the above equa'on. All other fluids it is tabulated. •  Unlike forced convec'on, the equa'on of mo'on is coupled to the energy equa'on, € which makes analysis more complex. 7 Convec'on Heat Transfer •  Ver'cal Flat Plate* Nux = 0.503Ra1 / 4 f (Pr) x 4 Nu0 − L =...
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