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

Lecture Objectives: Review - Heat transfer –Convection –Conduction –Radiation

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

Natural convection

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

Characteristic Number for Natural Convection Non-dimensionless governing equations Using L = characteristic length and U 0 = arbitrary reference velocity T w - wall temperature The momentum equation become Multiplying by R e 2 number R e =U  L/ Gr

Grashof number Characteristic Number for Natural Convection 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. Buoyancy forces Viscous forces General equation

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

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

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

Conduction

Conductive heat transfer Steady-state Unsteady-state Boundary conditions –Dirichlet T surface = T known –Neumann L T air k - conductivity of material T S1 T S2 h

Importance of analytical solution

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

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

Conduction equation describes accumulation

Radiation

Radiation wavelength

Short-wave & long-wave radiation Short-wave – solar radiation – <3  m –Glass is transparent –Does not depend on surface temperature Long-wave – surface or temperature radiation – >3  m –Glass is not transparent –Depends on surface temperature

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

Surface properties Emission (  is same as Absorption (  ) for gray surfaces Gray surface: properties do not depend on wavelength Black surface:   Diffuse surface: emits and reflects in each direction equally absorbed (α), transmitted (τ), and reflected (ρ) radiation

View (shape) factors For closed envelope – such as room

Example: View factor relations F 11 =0, F 12 =1/2 F 22 =0, F 12 =F 21 F 31 =1/3, F 13 =1/3 A1 A2 A3A1=A2=A3

Radiative heat flux between two surfaces ψ i,j - Radiative heat exchange factor Exact equations for closed envelope Simplified equation for non-closed envelope

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

Building components