mws_mec_ode_txt_runge4th_Examples

# mws_mec_ode_txt_runge4th_Examples - Chapter 08.04...

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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

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mws_mec_ode_txt_runge4th_Examples - Chapter 08.04...

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