Heat Transfer Handbook part 26. 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. | PERIODIC CONDUCTION 241 and the steady periodic temperature distribution is given by Bi j e 5 e- X cos 2nr - Vn X - p Bi2 2Bi 2 1 2 where e T - a . X x 2naz t 2n. . 3 Bi h 2 m a P arctan i r Note that as h to Bi to and P 0 eqs. reduce to eq. with 7 m Ti .The presence of the factor Bi Bi 2Bi 2 1 2 in eq. shows that convection enhances the damping effect and that it also increases the phase angle by an amount P arctan 1 1 Bi . Finite Plane Wall with Periodic Surface Temperature Consider a plane wall of thickness L with the face at x 0 insulated and the face at x L subjected to a periodic temperature change of hie form T L t Ti a cos mt where Ti is the initial temperature of the wall and the instated boundary condttfon at x 0 gives dT 0 t 0 dx The steady periodic solution is T x t Ti a L -1 L cos Lt Jx I . l L 2 J I 2 l1 2a JJ where the numerical values of 1 as a function of x L and w 2a 1 2L are supplied in Table and 2 which is also a function of x L and w 2a 1 2L is given by 9 9 - 69 92 arctan-------------- 9 a 6 - c d 242 CONDUCTION HEAT TRANSFER TABLE Values of the Amplitude Decay Function as a Function of x L and a w 2a 1 2L Ơ x L 0 œ where ộa cos 1 2 L cosh 1 2 L ộ6 cos ộc sin ộd sin rn X1 2 x 2az 1 2 J 2a rn X1 2 x 2a cosh sinh sinh rn X1 2 x 2a 1 2 2a rn X1 2 x 2a Infinitely Long Semi-infinite Hollow Cylinder with Periodic Surface Temperature Consider an infinitely long cylinder of inside radius ri .
