1. Lecture Objectives: Discuss HW3
Linearization of nonlinear equation for unsteady state problems

2. Linearization of radiation equations Surface to surface radiation
Equations for internal surfaces - closed envelope Ti Tj
Linearized equations:
Calculate h based on temperatures
from previous time step
Or for your HW3

3. Linearized radiation means linear system of equations
Calculated based on temperature values
from previous time step B0 C0 T0 F0 A1 B1 C1 T1 F1 A2 B2 C2 T2 F2
These coefficient will have
Some radiation convection coefficients x = A3 B3 C3 T3 F3 A4 B4 C4 T4 F4 A5 B5 C5 T5 F5 A6 B6 T6 F6

4. Impacts on HW3
…..

5. Energy balance for air unsteady-state heat transfer
QHVAC

6. System of equation for more than one element
Roof
air
Left wall
Right wall
Floor
Elements are connected by:
Convection – air node
Radiation – surface nodes

7. Example
Tair is unknown and it is solved by system of equation :

8. System of equations (matrix) for single zone (room)
8 elements
Three diagonal matrix for each element x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
Air equation

9. System of equations for a building
Matrix for the whole building
4 rooms
Rom matrixes
Connected by common wall elements and airflow in-between room – Airflow simulation program (for example CONTAM)
Energy Simulation program “meet” Airflow simulation program

10. Next assignment: Project 1
We will use software:
Soon we will have a class in the computer lab