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Unformatted text preview: Â¡ dTb/dt = (Tw â€“ Tb) (hA/mbcb) Â¡ dTw/dt = (Tb â€“ Tw) (hA/mwcw) 4th order Runge Kutta (Contâ€™d) n The Formulation: Â¡ k1 = x*dT/dtT = T(t) Â¡ k2 = x*dT/dtT = T(t) + 0.5 k1 Â¡ k3 = x*dT/dtT = T(t) + 0.5 k2 Â¡ k4 = x*dT/dtT = T(t) + k3 Â¡ T(t+x) = T(t) + (1/6)k1 + (1/3)k2 + (1/3)k3 + (1/6)k4 Â¡ x = time step Solution with MATLAB n Need the temperature of the bar after 10 & 30 seconds n Using a step size of 0.1 seconds n After 10 seconds Â¡ Temperature of the bath = 294 K Â¡ Temperature of the bar = 509 K n After 30 seconds Â¡ Temperature of the bath = 295.7 K Â¡ Temperature of the bar = 318.5 K Plot 5 10 15 20 25 30 35 200 300 400 500 600 700 800 900 1000 T b T w Te m pe rat ur e (K ) Time (seconds) Conclusion n With time, the temperature of the bar and the water bath approach the same value, leading to thermal equilibrium...
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This note was uploaded on 06/23/2011 for the course ME 218 taught by Professor Unknown during the Fall '08 term at University of Texas.
 Fall '08
 Unknown

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