mws_mec_ode_txt_runge4th_Examples

mws_mec_ode_txt_runge4th_Examples - Chapter 08.04...

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

08.04.1 Chapter 08.04 Runge-Kutta 4th Order Method for Ordinary Differential Equations-More Examples Mechanical Engineering Example 1 A solid steel shaft at room temperature of C 27 o is needed to be contracted so that it can be shrunk-fit into a hollow hub. It is placed in a refrigerated chamber that is maintained at C 33 o . The rate of change of temperature of the solid shaft is given by  33 588 5 10 42 5 10 35 1 10 33 2 10 69 3 10 33 5 2 2 3 3 5 4 6 6 θ . θ . θ . θ . θ . . dt d θ C 27 0 θ Using the Runge-Kutta 4 th order method, find the temperature of the steel shaft after 86400 seconds. Take a step size of 43200 h seconds. Solution 33 588 5 10 42 5 10 35 1 10 33 2 10 69 3 10 33 5 2 2 3 3 5 4 6 6 θ . θ . θ . θ . θ . . dt d θ 33 588 5 10 42 5 10 35 1 10 33 2 10 69 3 10 33 5 2 2 3 3 5 4 6 6 θ . θ . θ . θ . θ . . t, θ f h k k k k i i 4 3 2 1 1 2 2 6 1 For 0 i , 0 0 t , 7 2 0 0 0 1 , t f k 27 , 0 f   33 27 588 . 5 27 10 42 . 5 27 10 35 . 1 27 10 33 . 2 27 10 69 . 3 10 33 . 5 2 2 3 3 5 4 6 6 0.0020893 h k h t f k 1 0 0 2 2 1 , 2 1 43200 0020893 . 0

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 06/12/2011 for the course EML 3041 taught by Professor Kaw,a during the Spring '08 term at University of South Florida.

Page1 / 6

mws_mec_ode_txt_runge4th_Examples - Chapter 08.04...

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

View Full Document
Ask a homework question - tutors are online