Chapter 5 Numerical Methods in Heat Conduction 5-54E A long solid bar is subjected to steady two-dimensional heat transfer. The unknown nodal temperatures and the rate of heat loss from the bar through a 1-ft long section are to be determined. Assumptions 1Heat transfer through the body is given to be steady and two-dimensional. 2 Heat is generated uniformly in the body. 3 The heat transfer coefficient also includes the radiation effects. PropertiesThe thermal conductivity is given to be k= 16 Btu/h.ft⋅°C. Analysis The nodal spacing is given to be Δx=Δx=l=0.2 ft, and the general finite difference form of an interior node for steady two-dimensional heat conduction is expressed as TTTTTglklefttoprightbottomnodenode+++−+=402&(a) There is symmetry about the vertical, horizontal, and diagonal lines passing through the center. Therefore, 9731TTTT===and , and are the only 3 unknown nodal temperatures, and thus we need only 3 equations to determine them uniquely. Also, we can replace the symmetry lines by insulation and
This is the end of the preview. Sign up
access the rest of the document.
This note was uploaded on 01/22/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.