1. Equation solvers Scilab http://www.scilab.org/ Matlab
Free versions / open source codes:
Scilab
MathCad:
Mathematica:
LabView:
EES:
Modelica: ….

2. Lecture Objectives: Review the previous lectures
Prepare for the exam – solve some example problems
Discuss the final project assignment

3. Review Heat transfer Thermal analysis of building elements
External and internal boundary conditions
Weather data for boundary conditions
Modeling procedures
Numerical methods for solving of model equations

4. Review of heat transfer
How to model:
Convection at surfaces
Radiation between surfaces
Conduction through building elements
Steady state or unsteady state

5. Building elements

6. Weather data (TMY2 database)
Use them for External boundary conditions
Convection
Long-wave Radiation
Solar radiation
Direct
Diffuse
Reflected (diffuse)

7. Discretization

8. Discretization for conduction
T – temperature [C]
ρ – density [kg/m3]
cp – specific capacity [J/kgK]
k- conductivity [W/mK]
time [sec]
x distance [m]
Section considered in the
following discussion
Discretization in space
Discretization in time

9. Finite volume (difference) method
Boundaries of control volume
Fir each node conservation of energy:
explicit
implicit

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

11. Unsteady-state conduction Implicit method with linearization
b1T1 + +c1T2+=f(Tair,T1,T2)
a2T1 + b2T2 + +c2T3+=f(T1 ,T2, T3)
Air 1 2 3 4 5 6
Air
a3T2 + b3T3+ +c3T4+=f(T2 ,T3 , T4)
………………………………..
a6T5 + b6T6+ =f(T5 ,T6 , Tair)
Matrix equation
M × T = F
for each time step
M × T = F

12. Numerical methods PROBLEM Unsteady-state Steady-state
System of equations for
unsteady state process
(nonlinear)
System of equations
for steady state process
(nonlinear)
Explicit
Implicit
Implicit
Linearization
(Matrix solver)
Nonlinear
(Newton-Raphson
method)
For each time step

13. Modeling steps Define the domain
Analyze the most important phenomena and define the most important elements
Discretize the elements and define the connection
Write the energy and mass balance equations
Solve the equations (use numeric methods or solver)
Present the result

14. Practice for the Exam Example #1
Walmart store
(L>>H, D>>H)
H-5m
L=200 m
D=100m
door
Plenum (air)
Room (air)
Floor
concrete
QHVAC
insulation
acoustic tile TR TF
Lconcrete
Linsulation
Lplenum
Ltile
mS ,TS

15. Practice for the Exam Example #2
You are considering using the ventilated windows for ventilation of your new building and a sales person claims that it will reduce your annual energy bill by 10%. To check this claims you decided to model the performance of this window for your climate condition.
TRA
QHVAC
Building fan creates under pressure in the room
TRA
Building fan creates pressure in the room
QHVAC
Air cavity open to outdoor air at the top, and to indoor air at the bottom

16. Heat transfer for double glazed window

17. Final project: Graduate students – individual
- detailed modeling: your model or advance use of software
Undergraduate students – group of 2 students
- Energy analysis of buildings
form Integrated design course or
any other building or building system
I can provide several ideas but your ideas are encouraged…
Send me a ½ page proposal with your ideas till Wednesday, November 7
Will meet with each student in my office and define/finalize the project assignment