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Fins: Overview

Fins: Overview. Straight fins of (a) uniform and ( b ) non-uniform cross sections; ( c ) annular fin, and ( d ) pin fin of non-uniform cross section. Fins

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Fins: Overview

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  1. Fins: Overview Straight fins of (a) uniform and (b) non-uniform cross sections; (c) annular fin, and (d) pin fin of non-uniform cross section. • Fins • extended surfaces that enhance fluid heat transfer to/from a surface in large part by increasing the effective surface area of the body • combine conduction through the fin and convection to/from the fin • the conduction is assumed to be one-dimensional • Applications • fins are often used to enhance convection when h is small (a gas as the working fluid) • fins can also be used to increase the surface area for radiation • radiators (cars), heat sinks (PCs), heat exchangers (power plants), nature (stegosaurus)

  2. Fins: The Fin Equation • Solutions

  3. Bessel Equations Form of Bessel equation of order  with solution J = Bessel function of first kind of order  Y = Bessel function of second kind of order  Form of modified Bessel equation of order  with solution I = modified Bessel function of first kind of order  K = modified Bessel function of second kind of order 

  4. Bessel Functions – Recurrence Relations OR AND

  5. Fins: Fin Performance Parameters • Fin Efficiency • the ratio of actual amount of heat removed by a fin to the ideal amount of heat removed if the fin was an isothermal body at the base temperature • that is, the ratio the actual heat transfer from the fin to ideal heat transfer from the fin if the fin had no conduction resistance • Fin Effectiveness • ratio of the fin heat transfer rate to the heat transfer rate that would exist without the fin • Fin Resistance • defined using the temperature difference between the base and fluid as the driving potential

  6. Fins: Efficiency

  7. Fins: Efficiency

  8. Fins: Arrays • Arrays • total surface area • total heat rate • overall surface efficiency • overall surface resistance

  9. Fins: Thermal Circuit Equivalent Thermal Circuit Effect of Surface Contact Resistance

  10. sinh Function

  11. Fourier Series Consider a set of eigenfunctionsϕn that are orthogonal, where orthogonality is defined as for m ≠ n An arbitrary function f(x) can be expanded as series of these orthogonal eigenfunctions or Due to orthogonality, we thus know all other ϕnAmϕmintegrate to zero because m ≠ n Thus, the constants in the Fourier series are

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