Lecture Objectives: Discus HW 1 Finish with Solar Radiation Components Solar angles Solar components calculation process Learn about Internal and External Surface Convection

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.

Solar radiation Direct Diffuse Reflected (diffuse)

Solar Angles qz - Solar altitude angle – Angle of incidence

Solar Angles

Calculation of Solar Angles g – surface azimuth (from 0 to ±180°, east negative and west positive) f - Latitude d - Declination (function of a day in a year) - Hour angle (function of Longitude defined distance from local meridian Austin’s Latitude = 30.2672° N Austin’s Longitude 97.7431° W What is v ? HW1a Part 3) Calculate q for two surfaces in your HW1a for each hour: Use equation 1.6.2 from the handouts. NOTE: When you use excel be careful about degree and radian mode. Default is radian ! 1 1 radian = 180/ degrees.

Direct and Diffuse Components of Solar Radiation

Solar components Global horizontal radiation IGHR Direct normal radiation IDNR Direct component of solar radiation on considered surface: Diffuse components of solar radiation on considered surface: qz Total diffuse solar radiation on considered surface:

Global horizontal radiation IGHR and Diffuse horizontal radiation measurements qz

Measurement of Direct Solar Radiation

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

Laminar and Turbulent Flow forced convection

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

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

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:

Natural convection

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

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

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

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

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

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

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

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

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

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 http://rredc.nrel.gov/solar/pubs/tmy2/ http://rredc.nrel.gov/solar/pubs/tmy2/tab3-2.html leeward U windward Wind direction: ~225o