1. Lecture Objectives:
Review linearization of nonlinear equation for unsteady state problems
Learn about whole building modeling equations

2. 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

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

4. 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

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

6. 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

7. 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

8. HW3
Discuss the Analysis

9. Weather File for boundary conditions
Typical Meteorological Year
TMY, TMY2, TMY3

10. From Homework Assignment 3
Solution
from previous years
Day 1
Day 2
Day 3

11. Next HW (Project 1) We will use software: http://www.doe2.com/equest/
Soon we will have a class in the computer lab

12. 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