3-4 - 170 Finite Element Analysis and Design 4....

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
170 Finite Element Analysis and Design 4. One-dimensional heat conduction problem can be expressed by the following differential equation: 2 2 0, 0 dT k Q x L dx where k is thermal conductivity, () Tx temperature, and Q heat source per unit length. Q , the heat generated per unit length, is assumed constant. Two essential boundary conditions are given at both ends: (0) ( ) 0 T T L  . Calculate the approximate temperature using Galerkin method. Compare the approximate solution with the exact one. Hint : Start with assumed solution in the following form: 2 0 1 2 T x c c x c x , and then make it to satisfy two essential boundary conditions. Solution: (a) Exact solution: By integrating the governing equation twice and applying the two boundary conditions, the exact solution becomes 2 ( ) ( ) 2 Q T x Lx x k  (b) Galerkin method: The assumed form of approximate solution should first satisfy the
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

3-4 - 170 Finite Element Analysis and Design 4....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online