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Unformatted text preview: dTb/dt = (Tw Tb) (hA/mbcb) dTw/dt = (Tb Tw) (hA/mwcw) 4th order Runge Kutta (Contd) n The Formulation: k1 = x*dT/dtT = T(t) k2 = x*dT/dtT = T(t) + 0.5 k1 k3 = x*dT/dtT = T(t) + 0.5 k2 k4 = x*dT/dtT = T(t) + k3 T(t+x) = T(t) + (1/6)k1 + (1/3)k2 + (1/3)k3 + (1/6)k4 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 Temperature of the bath = 294 K Temperature of the bar = 509 K n After 30 seconds Temperature of the bath = 295.7 K 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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 Fall '08
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