ASRAE Student Branch meeting Speaker: Kenneth Simpson USGBC – LEED rating system

1. ASRAE Student Branch meeting Speaker: Kenneth Simpson USGBC – LEED rating system Today at 5 pm ECJ 5.410

2. Lecture Objectives: • Review - Heat transfer • Convection • Conduction • Radiation

3. 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:

4. Natural convection

5. GOVERNING EQUATIONSNatural 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

6. 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

7. 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

8. Natural convectionsimplified 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

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

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

11. Conduction

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

13. Importance of analytical solution

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

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

16. Conduction equation describes accumulation

17. Radiation

18. Radiation wavelength

19. Short-wave & long-wave radiation • Short-wave – solar radiation • <3mm • Glass is transparent • Does not depend on surface temperature • Long-wave – surface or temperature radiation • >3mm • Glass is not transparent • Depends on surface temperature

20. Radiation emission The total energy emitted by a body, regardless of the wavelengths, is given by: Temperature always in K ! - absolute temperatures • – emissivity of surface • – Stefan-Boltzmann constant A - area

21. Surface properties • Emission ( e ) is same as Absorption ( a ) for gray surfaces • Gray surface: properties do not depend on wavelength • Black surface: e = a = 1 • Diffuse surface: emits and reflects in each directionequally absorbed (α), transmitted (τ), and reflected (ρ) radiation

22. View (shape) factors http://www.me.utexas.edu/~howell/ For closed envelope – such as room

23. Example: View factor relations F11=0, F12=1/2 F22=0, F12=F21 F31=1/3, F13=1/3 A2 A3 A1=A2=A3 A1

24. Radiative heat flux between two surfaces Simplified equation for non-closed envelope Exact equations for closed envelope ψi,j - Radiative heat exchange factor

25. Summary • Convection • Boundary layer • Laminar transient and turbulent flow • Large number of equation for h for specific airflows • Conduction • Unsteady-state heat transfer • Partial difference equation + boundary conditions • Numerical methods for solving • Radiation • Short-wave and long-wave • View factors • Simplified equation for external surfaces • System of equation for internal surfaces

26. Building components