Lecture Objectives: Answer questions related to HW 2 Write energy balance equations Show Matlab example Start analyzing unsteady state Conducting

Homework assignment 1b Top view Te_o Te_i Tinter_surf Tair_in IDIR Styrofoam Te_o Tinter_surf Te_i 2.5 m Tair_in Surface to surface radiation 8 m 8 m IDIR Idif Tw_i South East Tw_o IDIR Tair_out Idif Glass Surface to surface radiation

MatLab Example Example code is posted on the class website MatLab at: http://www.ece.utexas.edu/it/student-licensing

Conductive heat transfer k - conductivity of material Steady-state Unsteady-state Boundary conditions Dirichlet Tsurface = Tknown Neumann TS1 TS2 L h Tair

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

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

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

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

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

Explicit methods information progressing during the calculation Tw Ti To

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

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