problem4-53 - PROBLEM 4.53 KNOWN Volumetric heat generation...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
PROBLEM 4.53 K NOWN: Volumetric heat generation in a rectangular rod of uniform surface temperature. FIND: (a) Temperature distribution in the rod, and (b) With boundary conditions unchanged, heat eneration rate causing the midpoint temperature to reach 600 K. g SCHEMATIC: ASSUMPTIONS: (1) Steady-state, two-dimensional conduction, (2) Constant properties, (3) Uniform volumetric heat generation. ANALYSIS: (a) From symmetry it follows that six unknown temperatures must be determined. Since all nodes are interior ones, the finite-difference equations may be obtained from Eq. 4.35 written in the form ( ) ( ) i neighbors T 1 4 T 1 4 q x y k = + Δ ± Δ . With ( ) q x y 4k Δ Δ ± = 62.5 K, the system of finite-difference equations is (1) ( ) 1 s 2 4 s T 0.25 T T T T 15.625 = + + + + (2) ( ) 2 s 3 5 1 T 0.25 T T T T 15.625 = + + + + (3) ( ) 3 s 2 6 2 T 0.25 T T T T 15.625 = + + + + (4) ( ) 4 1 5 1 s T 0.25 T T T T 15.625 = + + + + (5)
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern