1. Lecture Objectives: Answer questions related to HW 1
Learn about Internal and External Surface Convection
Learn about conduction

2. HW1
1) Using the equations provided in the attached paper sheet and the basic properties of view factors calculate the view factors for internal characteristic surfaces:
FSS , FSE , FSI
FES , FEE , FEI
FIS , FIE , FII
2) Using the geometry of the building, period of the year, and provided data in the excel file calculate:
- incident angle of direct solar radiation on all external surfaces for period of 24 hours,
- direct (ID) and diffuse (Id) components of solar radiation for period of 24 hours.
For the ground surface assume reflectivity of rground = 0.2.
3) Using both a) Swinbank Cole model and b) Berdahl and Martin model (provided in class notes) and data provided in the excel file calculate the equivalent sky temperature for the period of 24 hours.

3. Convection
How to calculate h ? What are the parameters that affect h ? What is the boundary layer ?

4. Laminar and Turbulent Flow forced convection

5. Forced convection governing equations
1) Continuity
2) Momentum
u, v – velocities
n – air viscosity
Non-dimensionless momentum equation
Using
L = characteristic length and U0 = arbitrary reference velocity
ReL
Reynolds number

6. Forced convection governing equations
Energy equation for boundary layer 
T –temperature, a – thermal diffusivity a=k/rcp,
k-conductivity, r - density, cp –specific cap.
Non-dimensionless energy equations
Air temperature outside
of boundary layer
Wall temperature
Reynolds number
Prandtl number
Momentum diffusivity
Inertial force
Thermal diffusivity
Viscous force

7. Simplified Equation for Forced convection
General equation
For laminar flow:
For turbulent flow:
For air: Pr ≈ 0.7, n = viscosity is constant, k = conductivity is constant
Simplified equation:
Or:

8. Natural convection

9. GOVERNING EQUATIONS Natural convection
Continuity
Momentum which includes gravitational force
Energy
u, v – velocities , n – air viscosity , g – gravitation, b≈1/T - volumetric thermal expansion
T –temperature, – air temperature out of boundary layer, a –temperature conductivity

10. Characteristic Number for Natural Convection
Non-dimensionless governing equations
Using
L = characteristic length and U0 = arbitrary reference velocity Tw- wall temperature
The momentum equation become Gr
Multiplying by Re2 number Re=UL/n

11. Grashof number Characteristic Number for Natural Convection
Buoyancy forces
Viscous forces
The Grashof number has a similar significance for natural convection
as the Reynolds number has for forced convection, i.e. it represents a
ratio of buoyancy to viscous forces.
General equation

12. Natural convection simplified equations
For laminar flow:
For turbulent flow:
For air: Pr ≈ 0.7, n = constant, k= constant, b= constant, g=constant
Simplified equation:
Even more simple
Or:
T∞ - air temperature outside of boundary layer, Ts - surface temperature

13. Forced and/or natural convection
In general, Nu = f(Re, Pr, Gr)
natural and forced convection
forced convection
natural convection

14. Combined forced and natural convention
Churchill and Usagi approach :
This equation favors a dominant term (h1 or h2), and exponent coefficient ‘n’ determines
the value for hcombined when both terms have the same order of value

15. Example of general forced and natural convection
Equation for convection at cooled ceiling surfaces n

16. External convective heat flux Presented model is based on experimental data, Ito (1972)
Primarily forced convection (wind):
Velocity at surfaces that are windward:
Velocity at surfaces that are leeward :
U -wind velocity
Convection coefficient : u
surface u
windward
leeward

17. Boundary Conditions at External Surfaces
1. External convective heat flux
Required parameters:
- wind velocity
wind direction
surface orientation N
leeward
Consequence: U
Energy Simulation (ES) program treats every surface with different orientation as separate object.
windward

18. Wind Direction Wind direction: ~225o
Wind direction is defined in TMY database:
“Value: 0 – 360o Wind direction in degrees at the hou
indicated. ( N = 0 or 360, E = 90,   S = 180,W = 270 ). For calm winds, wind direction equals zero.” N
leeward U
windward
Wind direction: ~225o

19. Conduction

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

21. Boundary conditions
Biot number
convention
conduction

22. Importance of analytical solution

23. What will be the daily temperature distribution profile on internal surface for styrofoam wall?
External temperature profile A. B. T
time

24. What will be the daily temperature distribution profile on internal surface for tin glass?
External temperature profile A. B. T
time

25. Conduction equation describes accumulation

26. Important numbers Convection Nusselt number Conduction Inertial force
Reynolds number
Viscous force
Momentum diffusivity
Prandtl number
Thermal diffusivity
Grashof number
Buoyancy forces
Viscous forces
thermal internal resistance
Biot number
surface film resistance
Reference book: Fundamentals of Heat and Mass Transfer, Incropera & DeWitt

27. HW2
Writhe Energy Balance Equations for the 3 elements of your room from HW1
Conduction
Convection
Radiation
Solar and
Long vawe

28. HW2 Problem East South Steady State Energy Model 2.5 m
Internal surfaces
East
South
Steady State Energy Model

29. You already defined External Boundaries

30. Internal Boundaries Window Internal sources Transmitted
Solar radiation

31. Surface Energy Balance
Energy coming in = Energy going out
Direction does not matter except for the Solar energy

32. Air balance - Convection on internal surfaces + Ventilation + Infiltration
Uniform temperature Assumption
Affect the air temperature
- h, and Q as many as surfaces
- maircp.air DTair= Qconvective+ Qventilation
Tsupply
Qconvective= ΣAihi(TSi-Tair)
Ts1 mi
Qventilation= Σmicp,i(Tsupply-Tair) Q1 Q2
Tair h1 h2