1 / 12

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

jacobd
Download Presentation

Fins: Overview

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related