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Announcement

Announcement . MATHCAD for solving system of equation for HW2 Tomorrow 8 am ECJ 302 (computer lab). Lecture Objectives:. Discuss HW1a Finish with energy balance equations and provide example HW1b Analyze the unsteady-state heat transfer numerical calculation methods .

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Announcement

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  1. Announcement • MATHCAD for solving system of equation for HW2 • Tomorrow 8 am ECJ 302 (computer lab)

  2. Lecture Objectives: • Discuss HW1a • Finish with energy balance equations and provide example • HW1b • Analyze the unsteady-state heat transfer numerical calculation methods

  3. Air balance – steady stateConvection on internal surfaces + Infiltration = Load Uniform temperature Assumption • h, and Qsurfaces as many as surfaces • infiltration – mass transfer (mi – infiltration) Qair= Qconvective+ Qinfiltration T outdoor air Qconvective= ΣAihi(TSi-Tair) Ts1 mi Qinfiltration= Σmicp(Toutdoor_air-Tair) Q2 Q1 In order to keep constant air Temperate, HVAC system needs to remove cooling load Tair h1 h2 QHVAC= Qair= m·cp(Tsupply_air-Tair) HVAC

  4. Top view Glass Teast_o Teast_i Tinter_surf Tair_in Surface radiation IDIR Idif Tsouth_i conduction Tsouth_o Tair_out Styrofoam Surface radiation Idif IDIR Homework assignment 1b 2.5 m 10 m 10 m South East

  5. Example: Unsteady-state heat transfer(Explicit – Implicit methods) 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 step Dt=0.1 hour = 360 s

  6. Conservation of energy equations: Explicit – Implicit methods example Wall: Air: After substitution: For which time step to solve: +  or  ? Wall: Air: +  Implicit method  Explicit method

  7. Implicit methods - example After rearranging: 2 Equations with 2 unknowns!  =0 To Tw Ti  =36 system of equation Tw Ti  =72 system of equation Tw Ti

  8. Explicit methods - example  =360 sec  =0 To Tw Ti  =360 To Tw Ti  =720 To Tw Ti Time There is NO system of equations! UNSTABILE

  9. Explicit method Problems with stability !!! Often requires very small time steps

  10. Explicit methods - example  =0 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

  11. Explicit methods information progressing during the calculation Tw Ti To

  12. Unsteady-state conduction - Wall q Nodes for numerical calculation Dx

  13. Discretization of a non-homogeneous wall structure Section considered in the following discussion Discretization in space Discretization in time

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