TAILIEUCHUNG - Heat Transfer Handbook part 31

Heat Transfer Handbook part 31. 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. | SPREADING RESISTANCE WITHIN A COMPOUND DISK WITH CONDUCTANCE 291 For all values in the range 0 Bi to and for all values t tanh 8 t 1 for all n 1. Therefore 1 for values n 1. Characteristics of Bn When t1 tanh 8nr 1 n 1 for all 0 Bi to therefore Bn 1 for n 1. Special Cases of the Compound Disk Solution The general solution for the compound disk may be used to obtain spreading resistances for several special cases examined previously by many researchers. These special cases arise when some of the system parameters go to certain limits. The special cases fall into the following two categories isotropic half-space semi-infinite flux tube and finite disk problems and layered half-space and semi-infinite flux tube problems. Figures and show the several special cases that arise from the general case presented above. Results for several special cases are discussed in more detail in subsequent sections. Half-Space Problems If file dimensions of the oompouud dssk b t become very large relative to the radius a and the first layer thickness t1 the general solution approaches the solution for the case of a single layer in perfect thermal contact with an isotropic half-space. In this case e 0 t1 0 and the spreading resistance depends on the four system parameters a t1 k1 k2 and the heat flux parameter p. If we set t1 0 or k1 k2 the general solution goes to the special case ofa circular heat source in perfect contact with an isotropic half-space. In this case the spreading resistance depends on two system parameters a k2 and the heat flux parameter p. The dimensionless spreading resistance is now defined as 4k2aRs and it is a constant depending on the heat flux parameter. The total resistance is equal to the spreading resistance in both cases because the one-dimensional resistance is negligible. The half-space problems are shown in Figs. and . Semi-infinite Flux Tube Problems The general solution goes to the semi-infinite flux tube .

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