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Published byFarida Hardja Modified over 6 years ago
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Announcement MATHCAD for solving system of equation for HW1b
Tomorrow 5:30 pm this studio (computer lab)
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Lecture Objectives: Discuss HW1b
Answer your questions Analyze the unsteady-state heat transfer numerical calculation methods
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Unsteady-state heat transfer (Explicit – Implicit methods)
Example: To - known and changes in time Tw - unknown Ti - unknown Ai=Ao=6 m2 (mcp)i=648 J/K (mcp)w=9720 J/K Initial conditions: To = Tw = Ti = 20oC Boundary conditions: hi=ho=1.5 W/m2 Tw Ti To Ao=Ai Conservation of energy: Time [h] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 To 20 30 35 32 10 15 Time step Dt=0.1 hour = 360 s
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Explicit – Implicit methods example
Conservation of energy equations: Wall: Air: After substitution: For which time step to solve: + or ? Wall: Air: + Implicit method Explicit method
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Implicit methods - example
After rearranging: 2 Equations with 2 unknowns! = To Tw Ti =36 system of equation Tw Ti =72 system of equation Tw Ti
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Explicit methods - example
=360 sec = To Tw Ti =360 To Tw Ti =720 To Tw Ti Time There is NO system of equations! UNSTABILE
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Problems with stability !!! Often requires very small time steps
Explicit method Problems with stability !!! Often requires very small time steps
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Explicit methods - example
= To Tw Ti =36 To Tw Ti =72 To Tw Ti Stable solution obtained by time step reduction 10 times smaller time step Time =36 sec
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Explicit methods information progressing during the calculation
Tw Ti To
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Unsteady-state conduction - Wall
q Dx Nodes for numerical calculation
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Discretization of a non-homogeneous wall structure
Section considered in the following discussion Discretization in space Discretization in time
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