Heat Transfer Handbook part 33. 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. | STRIP ON A FINITE CHANNEL WITH COOLING 311 on the strip which may have the following values 1 p -2 to approximate an isothermal strip provided that a c 1 2 p 0 for an isoflux distribution and 3 p 2 which gives a parabolic flux distribution. The three flux distributions are q x Q 1 Ln a2 x2 Q 2La Va2 x2 Lna2 for p 1 for p 0 for p 2 The dimensionless spreading resistance relationship based on the mean source temperature is kLRs r p 3 2 A 2 p 1 2 sin nne _ ----z ----- zzr Zj Jp i 2 nne n2 I 2 nne J n2 where nn Bitanh nnT nn tanh nnT Bi n 1 2 3 . and the three dimensionless system parameters and their ranges are 0 a 1 c 0 Bi hc TO k 0 T - TO c The general relationship gives the following three relationships for the three flux distributions kLRs 1 sin nne T z 2 - 2T J0 nni Pn for p 1 tt2 n2 n 1 1 sin2 nne . E for p 0 n 1 2 sin nnt 7 --------- J1 nne Pn for p 2 n n 1 n The influence ofthe cooling along the bottom surface on the spreading resistance is given by the function pn which depends on two parameters Bi and t. If the channel is relatively thick . t pn 1 for all values n 1 to and the influence of Are parameter Bi becomes negiigible. When t the finite channel may be modeled as though it were infinitely thick. This special case is presented next. 312 THERMAL SPREADING AND CONTACT RESISTANCES STRIP ON AN INFINITE FLUX CHANNEL If de relative thickness of the rectangular channel becomes very large . t rc the anlhttcneCtpe given hbcvn appecaet the anlhttcneCtpe hppacpathtn fca tCn tnflnttely tttek flux ehannel. The dtmenetcnleee epaeadtnr aeetetanee fca thte pacblem depends cn twc paaameteae the aelattve etze cf cVc strip e and the heat flux dtetatbuttcn paaametea p. The theee eelattcnehtpe fca the dtmenetcnleee epaeadtnr aeetetanee aee cbtatned facm the aelattcnehtpe rtven abcve wtth pn 1. Numeateal valuee fca LkRs fca thaee valuee cf p aae rtven tn Table . Facm the tabulated valuee tt ean be eeen that the epaeadtnr aeetetanee
