## 1r s riln rj 1rj X h 0r 0 j kj hi

This expression results from the application of the conduction equation across the wall components and the convection equation at the wall boundaries. Then, by noting that in steady state each expression for heat must be equal, we can write the expression for U, which contains both convection and conduction effects. The U factor is extremely useful to engineers and architects in a wide variety of applications.

However, there is no difference in heat-transfer rate; that is,

Qo = UiAiToverall = UoAoToverall so it is apparent that

UiAi = UoAo for cylindrical systems.

Finned Surfaces. Many heat-exchange surfaces experience inadequate heat transfer because of low heat-transfer coefficients between the surface and the adjacent fluid. A remedy for this is to add material to the surface. The added material in some cases resembles a fish "fin," thereby giving rise to the expression "a finned surface." The performance of fins and arrays of fins is an important item in the analysis of many heat-exchange devices. Figure I.5 shows some possible shapes for fins.

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