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Heat Transfer Handbook part 121. 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. | TRANSPORT LIMITATIONS 1197 TABLE 16.2 Expressions for the Effective Capillary Radius rc for Several Wick Structures Structure rc Data Circular cylinder artery reff _ r r radius of iiqmd low passagee or tunnel wicks Rectangular groove reff _ w w groove width Triangular groove w reff _ T cos ß reff _ w w groove width Parallel wires P half-included angle w wire spacing Wire screens Packed spheres w dw 1 N screen mesh number w wire spacing dw wire diameter rs sphere radius reff _ 2 _ 2N rc _ 0.41rs Source Chi 1976 with permission. The differential liquid pressure drop in the wick structure assuming one-dimensional laminar flow can be expressed as dPi ini i x dx KAwPl 16.12 where K represents the wick permeability. The wick permeability is related directly to the porosity of the wick stnicuire which is defined as flee at io of pore volume to total volume or e Vpore Vtot and is given by K _ 2e rh 2 fi Rei 16.13 As the hydraulic radius of flee porous it cu e ss typccally small and flee liquid flow velocity is low the liquid flow can be assumed laminar. Thus the values of f Re can be assumed constant and depend only on the flow passage shape where typical values of the permeability for different wick structures are given in Table 16.3. Assuming one-dimensional vapor flow the differential vapor pressure drop can be expressed in terms of the pressure drops due to frictional forces and dynamic pressure or dPv f Re vmv x 2mv dmv x dx 2Avr2v p A2 p dx 16.14 Recognizing that the total vapor mass flow rate and liquid mass flow rate are equal at steady-state conditions the mass flow rate through the system can be expressed in terms of hie l t transport rate and the latent heat of vaooriaalion of flic fluid or 1198 HEAT PIPES TABLE 16.3 Expressions of Wick Permeability K for Several Wick Structures Wick Structure K Expression r 2 Circular artery K 8 Open rectangular grooves K h fl Re w e porosity s s groove pitch 2w8 rh w 28 w groove width 8 groove depth fl Re from a below 2r2 .
