1. Make up: Project presentation class at the end of the semester
Announcement
No Class on
Thursday, October 25th
Make up: Project presentation class at the end of the semester

2. Lecture Objectives:
Review Linearization of nonlinear equation for unsteady state problems

3. 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

4. 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

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. Impacts on HW3
…..

10. 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

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

12. Modeling steps Define the domain Analyze the most important phenomena
and define the most important elements
Discretize the elements and
define the connection
Write energy and mass balance
equations
Solve the equations
Present the result
ES program
Preprocessor
Solver
Postprocessor

13. Characteristic parameters
Conduction (and accumulation) solution method
finite dif (explicit, implicit), response functions
Time steps
Meteorological data
Radiation and convection models (extern. & intern.)
Windows and shading
Infiltration models
Conduction to the ground
HVAC and control models

14. Weather File Typical Meteorological Year TMY, TMY2, TMY3

15. eQUEST (DOE2) US Department of Energy & California utility customers
eQUEST - interface for the DOE-2 solver
DOE-2 - one of the most widely used ES program
- recognized as the industry standard
eQUEST very user friendly interface
Good for life-cycle cost and parametric analyses
Not very large capabilities for modeling of different HVAC systems
Many simplified models
Certain limitations related to research application
- no capabilities for detailed modeling