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Heat Transfer Handbook part 118. The Heat Transfer Handbook provides succinct hard data, formulas, and specifications for the critical aspects of heat transfer, offering a reliable, hands-on resource for solving day-to-day issues across a variety of applications. | INTERNAL NATURAL CONVECTION 1167 Figure 15.10 Asymptotes of the function Nu RaH Prp for convection in a porous layer heated from below. From Bejan 1995. In this formulation Nu is a function of two groups RaH and Prp in which Prp accounts for the transition from Darcy to Forchheimer flow Fig. 15.10 . In this formulation the Darcy flow result of eq. 15.115 becomes Nu 1 Rrh 1 40 PT7 40 Rrh Prp 15.118 The experimental data for convection in the entire regime spanned by the asymptotes given by eqs. 15.116 and 15.118 are correlated by Nu RRh c Prp 1 2 15.119 1168 POROUS MEDIA where n -1.65 and c 1896 are determined empirically based on measurements reported by many independent sources. The effects of fluid inertia and other departures from Darcy flow are discussed in detail in Nield and Bejan 1999 . The correlations of ss-115.115 115.119 refer to layers with length heihhr ratios considerably greater than 1. They apply when the length lateral dimension L perpendicular to gravity of the confined system is g t r than the horizontal tength scale of a sîngte convective cell i.e. g t r than H RaH1 2 according to the scale analysis of Bejan 1984 . Natural convection studies have also been reported for porous layers confined in rectangular parallelpipeds heated from below. horizontal circular cylinders. and horizontal annular cylinders. The general conclusion is that the lateral walls have a convection-suppression effect. For example. in a circular cylinder of diameter D and height H Fig. 15.9 . in the limit D H the critical condition for the onset of convection is Bau and Torrance. 1982 RaH 13.56 -D 15.120 In inclined porous layers that deviate from the horizontal position through an angle 9 Fig. 15.9c . convection sets in at Rayleigh numbers that satisfy the criterion Combarnous and Bories. 1975 RaH 3948 15.121 cos 9 where it is assumed that the boundaries are isothermal and impermeable. The average heat transfer rate at high Rayleigh numbers can be estimated by x 4n2s2 Nu 1 V
