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Heat Transfer Handbook part 27

Heat Transfer Handbook part 27. 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. | CONDUCTION-CONTROLLED FREEZING AND MELTING 251 An improvement on the quasi-steady-state solution can be achieved with the regular perturbation analysis provided by Aziz and Na 1984 . The improved version of eq. 3.374 is pL t ----------- k Tf - To 4 r 2 f f 4St rf - ro 1 In rf ro 3.375 If the s Lii I ace of die cyl inder is convectively cooled die boundary condition is dT k dr r ro h T ro t Tœ 3.376 and tfo quasi-stoade-stato solutions for St o in this ease is r T Tf Tœ k hro ln rf ro In rf Tf 3.377 t pL k Tf - Tœ _2 rf ro .2 r2 1 2k hro 3.378 1 1 4 f Noting that tfo quasi-stoade-stato solutions suef as eqs. 3.377 and 3.378 strietly apply only wfon St o Huang and Sfif 1975 usod tfom as zoro-ordor solutions in a rogular portureation sorios in St and gonoratod two additional torms. Tfo tfroo-torm portureation solution providos an improvomont on oqs. 3.377 and 3.378 . Inward Cylindrical Freezing Consider a saturated liquid at the freezing temperature contained in a cylinder of inside radius ri. If the surlace temperature is suddnnly reduced to and kept at T0 such that T0 Tf the liquid freezes inward. The governing equation is 1 d 9T r dr y dr J 1 dT a dt 3.379 with initial and boundary eonditions T ri t To T rf o Tf dT dr r rf drf pL-f dt 3.38oa 3.38oe 3.38oe 252 CONDUCTION HEAT TRANSFER Equations 3.373 and 3.374 also give the quasi-steady-state solutions in this case except that r0 now becomes ri. If the surface oooligg is due to coriveciiori from a fluid at temperatoe Tm with heat transfer coefficient h the quasi-steady-state solutions for T and t ate Tf - T. T T. --------f.---------- œ ln rf n - k hr2 r In - ri k A hri 3.381 pL t Ir2ln f 1 r2 - r2 1 k Tf - T. - _2 f ri 4 V i hri 3.382 Outward Spherical Freezing Consider a situation where saturated liquid at the freezing temperature Tf is in contact with a sphere of radius r0 whose surface temperature To is less than Tf. The differential equation for the solid phase is 1 d2 Tr _ 1 dT r dr2 a dt 3.383 which is to be .