MIT2_094S11_hw_10_sol

# MIT2_094S11_hw_10_sol - 2.094 FINITE ELEMENT ANALYSIS OF...

This preview shows pages 1–3. Sign up to view the full content.

2.094 F INITE E LEMENT A NALYSIS OF S OLIDS AND F LUIDS S PRING 2008 Homework 10 - Solution Instructor: Prof. K. J. Bathe Assigned: 05/06/2008 Due: 05/13/2008 Problem 1 (10 points): The governing differential equation is 2 2 p dd vk dx dx c θ ρ = The non-dimensional form is 2 2 1 e dX Pe dX ΘΘ = where L RL Θ = , x X h = and /( ) e p vh v c h Pe k αρ == The principle of virtual temperature for a unit area is 2 2 11 () ee d d dX dX dX boundary terms dX Pe dX Pe dX dX Θ Θ −+ ∫∫ Therefore, 1 e d dX boundary terms dX Pe dX dX Θ Θ ⎡⎤ += ⎢⎥ ⎣⎦ If we use two-node elements, then for i-th element 1 (1 ) ) 22 i ii rr ΘΘΘ + =− ++ Page 1 of 4

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

View Full Document
() 1 2 1 ii i dd d r d dX dr dX dr ΘΘ Θ Θ Θ + == = + Hence [] 1 0 1 1 ) 1 1 ( 1 11 2 1 (1 ) 1 2 ˆ ˆ 2 ) 2 1111 22 ˆ T T e i i e i i e i i e i d dX dX Pe dX dX d dr dX Pe dX dX r dr Pe r Pe P Θ Θ Θ Θ Θ + + ⎡⎤ + ⎢⎥ ⎣⎦ =+ ⎧⎫ ⎛⎞ ⎪⎪ ⎜⎟ =− + ⎨⎬ + ⎝⎠ ⎩⎭ −+ = ˆ e i ee e Pe Pe Θ −− + where 1 ˆ T i Θ + =
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 02/24/2012 for the course MECHANICAL 2.094 taught by Professor Klaus-jürgenbathe during the Spring '11 term at MIT.

### Page1 / 5

MIT2_094S11_hw_10_sol - 2.094 FINITE ELEMENT ANALYSIS OF...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online