Heat Loss

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Heat Loss Gain Calculations
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How Heat Moves in Homes

• Conduction is the transfer of heat through solid
  objects, such as the ceilings, walls, and floors
  of a home. Insulation (and multiple layers of
  glass in windows) reduces conduction losses. The
  direction of heat flow is from hot to cold, so
  this illustration shows conduction from a warm
  interior to a cooler outdoors.

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Conduction Heat Loss
High Temperature
Low Temperature
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Conduction Heat Loss
Low Temperature
High Temperature
As Temperature Differences Increase, Heat Loss
Increases
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Conduction Heat Loss
Low Temperature
High Temperature
Resistance
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Conduction Heat Loss
High Temperature
Low Temperature
As Resistance Increases, Heat Loss Decreases
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Conduction Heat Loss
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How Heat Moves in Homes

• Convection is the flow of heat by currents of
  air. Air currents are caused by pressure
  differences, stirring fans, and air density
  changes as it heats and cools. As air becomes
  heated, it becomes less dense and rises as air
  cools, it becomes more dense and sinks.

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Convective Heat Loss
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Convective Heat Loss - Air Leakage
High Pressure
Low Pressure
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Convective Heat Loss - Air Leakage
High Pressure
Low Pressure
As Pressure Differences Increase, Heat Loss
Increases
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Convective Heat Loss - Air Leakage
High Pressure
Low Pressure
As Leakage Area Decreases, Heat Loss Decreases
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What Causes Pressure? Natural
High Pressure
Low Pressure
Windward Side of House
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What Causes Pressure? Natural
High Pressure
Low Pressure
Leeward Side of House
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What Causes Pressure? Mechanical
High Pressure
Low Pressure
Tight Supply Duct
No Return Duct
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What Causes Pressure? Mechanical
High Pressure
Low Pressure
Tight Supply Duct
Return Duct Leaks
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What Causes Pressure? Mechanical
High Pressure
Low Pressure
Supply Duct Leaks
Tight Return Ducts
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What Causes Pressure? Stack Effect
Higher Pressure
Hot Air Rises
Lower Pressure
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What Causes Pressure? Stack Effect
Higher Pressure
Effected by Height and Temperature Gradient
Hot Air Rises
Lower Pressure
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What Causes Pressure? Stack Effect
Higher Pressure
Hot Air Rises
Neutral Pressure Plane
Lower Pressure
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How Heat Moves in Homes

• Radiation is the movement of energy in waves from
  warm to cooler objects across empty spaces, such
  as radiant heat traveling from the inner panes of
  glass to outer panes in double-glazed windows in
  winter.

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Equations - Conduction

• q A ?T
• R
• where
• q heat flow, Btu/hr
• A area, ft2
• R resistance, ft2-hr-F/Btu
• ?T temperature differential, F
• Higher temperature Lower temperature

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Where Do You Get R?

• Table of R-values for various materials
• Some values are for entire thickness
• Brick
• Plywood
• Gypsum Board
• Some values are per inch of thickness
• Wood (framing)
• Insulation

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How do R-values Add?
RT R1 R2 R3
R1 R2 R3
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How do R-values Add? - Example
RT for a Structurally Insulated Panel (SIP)
½ inch
plywood 1.25 4 inch Rigid Foam Center 4
per inch 16.00
½ inch plywood 1.25

RT 18.50
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Equations - Conduction

• q U A ?T
• where
• q heat flow, Btu/hr
• A area, ft2
• U conductance, Btu/ft2-hr-F
• ?T temperature differential, F

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Equations - Conduction

• Where does U come from?
• Table values
• How do they add?
• 1 1 1
• UT U1 U2
• Commonly provided for the entire assembly

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U-factor

• A U-factor is used to describe an area that is
  composed of several materials.
• Example
• Window U-factor includes the glass, frame, and
  sash.

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Relationship Between R and U

• q U A ?T
• q A ?T
• R
• U A ?T A ?T
• R
• U A ?T A ?T
• R
• U 1
• R

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Air Leakage - General Equation

• q m Cp ?T
• where
• q heat flow, Btu/hr
• m mass flow of air, lbs/hr
• Cp specific heat of air, 0.24 Btu/lbs -F
• ?T temperature differential, F

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Air Leakage - General Equation

• q m Cp ?T
• where does m come from?
• m mass flow of air, lbs/hr
• Under normal conditions in a home
• Density of Air 13.5 ft3 per lb air
• Cubic Feet of Air m
• 13.5

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Air Leakage For Ducts

• q 1.08 cfm ?T (ducts)
• where
• cfm duct leakage rate to the outside
• where does the 1.08 come from?
• cfm 0.24 60 min/hr cfm 1.08
• 13.5 ft³/lb air

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Air Leakage for an Entire House

• q 0.018 ft³/hr ?T
• where
• ft³/hr air leakage rate for the entire house
• Where does the 0.018 come from?
• ft³/hr 0.24 ft³/hr 0.018
• 13.5 ft³/lb air
• ft3/hr ACHnat Volume (ft3)
• where
• ACHnat Natural Air Changes per hour
• Volume volume of the conditioned space
• q 0.018 ACHnat Volume (ft3) ?T

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Simple Heat Flow, q, Calculation

• Assume 10x10 wall A 100 ft2
• Cavity Insulation R value 13
• ?T 1 degree
• q 100 1 7.69 Btuh
• 13
• What is missing?

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Simple Heat Flow, q, Calculation

• What about the wood framing?
• 2x4 R-value 4.38 (1.25 per inch)

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Simple Heat Flow, q, Calculation

• Typical Wood Framing

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Simple Heat Flow, q, Calculation

• Minimum Wood Framing

• Approximately 10 2x4s, 10 ft long
• Each stud
• 1.5 inches wide
• 10 ft 12 inches/ft 120 inches long
• 10 studs 1.5 in 120 in 1800 square inches
• 1800 in2 / 144 in2 per ft2 12.5 ft2

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Simple Heat Flow, q, Calculation w/Framing

• Total Area 100 ft2 10x10 wall
• Cavity Insulation R-value 13
• Framing R 4.38
• Framing Area 12.5 ft2
• Cavity Insulation Area 100 12.5 87.5 ft2
• ?T 1 degree

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Simple Heat Flow, q, Calculation w/Framing

• qinsulation 87.5 1 6.73 Btuh
• 13
• qframing 12.5 1 2.85 Btuh
• 4.38
• qtotal qinsulation qframing 6.73 2.85
  9.58 Btuh

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Calculating R when q is Known

• q A ?T
• R
• multiply both sides by R
• R q R A ?T
• R
• R q A ?T

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Calculating R when q is Known

• R q A ?T
• Divide both sides by q
• R q A ?T
• q q
• R A ?T
• q

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R-Value of the Entire Wall w/Framing

• qtotal 9.58 Btuh/F
• R A ?T 100 1 10.44
• q 9.58
• TOTAL WALL R

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R-Value of the Entire Wall w/Framing

• Another Equation to Calculate Total Wall R
• RT _______AT________
• _A1_ _A2_
• R1 R2

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Simple Heat Flow, q, Calculation

• What if there is a window in the wall?
• Window
• Size 3 ft x 5 ft 15 ft2
• U-factor 0.40

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Framing Window
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Simple Heat Flow, q, CalculationWith Framing
Window

• Windows Require Extra Framing Materials
• 4 extra studs for kings and jacks
• 2x12 36 inch long for the header
• Approximately 7.8 ft2 of extra framing
• Total framing 12.5 7.8 20.3 ft2

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Simple Heat Flow, q, CalculationWith Framing
Window

• Total Area 100 ft2 10x10 wall
• Cavity Insulation R-value 13
• Framing R-value 4.38
• Framing Area 20.3 ft2
• Window U-factor 0.40
• Window Area 15 ft2
• Cavity Insulation Area 100 20.3 - 15 64.7
  ft2
• ?T 1 degree

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Simple Heat Flow, q, CalculationWith Framing
Window

• qinsulation 64.7 1 4.98 Btuh
• 13
• qframing 20.3 1 4.63 Btuh
• 4.38
• qwindow 0.40 15 1 6 Btuh
• qtotal 4.98 4.63 6 15.61 Btuh

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R-Value of the WallWith Framing Window

• qtotal 15.61 Btuh/F
• q A ?T
• R
• R A ?T 100 1 6.41
• q 15.61

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R-Value Comparison

• Cavity Insulation Only
• R 13
• Cavity Insulation Framing
• R 10.44
• Cavity Insulation Framing Window
• R 6.41

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Your Turn

• Total Area 1000 ft²
• Ceiling
• R 38
• Pull Down Stairs
• Area 15 ft²
• R 2
• What is the R value of the total ceiling?

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Your Turn

• Ceiling
• q (1000 15) 25.92
• 38
• Pull Down Stairs
• q 15 7.5
• 2
• Total q 25.92 7.5 33.42
• R _1000_ 29.92
• 33.42

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HERS Rating Software Examples

• Must know
• Areas
• R / U values
• Temperature Differential
• Indirectly by knowing what is on the other side
  of the surface

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Above Grade Wall Properties
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Conduction Heat Loss
Typical Resistances in a Wall
Cavity Insulation
Exterior Finish
Gypsum Board
Outside Air Film
Inside Air Film
High Temperature
Low Temperature
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Exterior Finish
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R of Cavity Wall Section

Inside Air 0.68
5/8 Gypsum Board 0.56
3 ½ Cavity Insulation 13.00
Exterior Finish 0.94
Outside Air 0.17
Cavity Wall Section R 15.35
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Conduction Heat Loss
Typical Resistances in a Wall
Framing
Exterior Finish
Gypsum Board
Outside Air Film
Inside Air Film
High Temperature
Low Temperature
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R of Framing Wall Section

Inside Air 0.68
5/8 Gypsum Board 0.56
3 ½ Framing 4.37
Exterior Finish 0.94
Outside Air 0.17
Framing Wall Section R 6.72
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Framing Factor
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Framing Factor
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Your Turn - Total Wall R
Cavity Wall Section R 15.35 Framing Wall
Section R 6.72 Framing Factor 0.23 (23 of
the wall is framing) Remember - the objective is
to calculate q correctly
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Your Turn - Total Wall R
Assume the Total Wall Area 100 ft2 Framing Wall
Area 0.23 100 23 ft2 Cavity Wall Area 100
23 77 ft2 Framing q A ?T 23 1
3.42 Btuh R
6.72 Cavity q A ?T 77 1 5.02
Btuh R 15.35 Total
q 3.42 5.02 8.44 Btuh Total Wall R A
100 11.85 q 8.44
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Your Turn - Total Wall R
Assume the Total Wall Area 100 ft2 Framing Wall
Area 0.23 100 23 ft2 Cavity Wall Area 100
23 77 ft2 Framing 23 Area but 3.42/8.44
41 of Flow
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Total Wall U
Total Wall R 11.85 Total Wall U 1
1 0.0843 R
11.85
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Total Wall U
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Total UA for a House

• 2006 IECC Compliance
• (2006 IRC, Chapter 11, Energy Efficiency)
• Prescriptive
• Overall Building UA
• Annual Energy Cost

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REM/Rate Overall Building UA
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REM/Rate Annual Energy Cost
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HVAC Design Peak Loads

• Heating
• What is ?T?
• Winter Design Temperature
• Lexington 6F
• Inside Temperature? Typical 68F
• ?T 68 6 62F

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HVAC Design Peak Loads

• Heating
• Losses (qs)
• Shell (UA for House)
• Infiltration (ACHnat)
• Duct Loss (cfm)
• Gains
• ?? (People are not considered)

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HVAC Design Peak Loads

• Cooling
• What is ?T?
• Summer Design Temperature
• Lexington 91F
• Inside Temperature? Typical 76F
• ?T 91 76 15F

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HVAC Design Peak Loads

• Cooling
• Gains (qs) - Complex
• Shell (UA for House)
• Infiltration (ACHnat)
• Adds Moisture
• Duct Gain
• Solar (Radiation - Windows)
• People

• Losses
• ??

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HVAC Design Peak Loads
Is ?T the same for all surfaces?
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HVAC Design Peak Loads
Is ?T the same for all surfaces? Basement Walls
to the Ground Ceiling to the Attic Wall to the
Garage Floor to the Crawl Space
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REM/Rate Peak Component Loads
0.57 ACHn 15 Duct Loss to Outside
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HVAC Annual Loads

• Heating
• What is an annual ?T?
• Heating Degree Days
• 65F - Average daily temperature
• Add them for one year
• Lexington 4683 HDD
• q U A ?T
• ?T Heating Degree Days 24
• Close but More Complex

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HVAC Annual Loads

• Cooling
• What is an annual ?T?
• Cooling Degree Days
• Average daily temperature 65F
• Add them for one year
• Lexington 1175 CDD
• More Complex Calculation
• Solar Radiation
• Dehumidification

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REM/Rate Annual Component Loads
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HVAC Annual Consumption

• Heating Equipment Efficiency
• Heat Pump
• Heating Season Performance Factor (HSPF)
• Btu/Watt-hr
• Geothermal Heat Pump
• Coefficient of Performance (COP)
• Watt-hr output / Watt-hr input
• Gas (Combustion)
• Annual Fuel Utilization Efficiency (AFUE)
• Btu output / Btu input

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HVAC Annual Consumption

• Cooling Equipment Efficiency
• Heat Pump / Air Conditioner
• Seasonal Energy Efficiency Ratio (SEER)
• Btuh/Watt
• Geothermal Heat Pump
• Energy Efficiency Ratio (EER)
• Btuh/Watt

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HVAC Annual Consumption

• Equipment Efficiency Adjustment in REM/Rate
• Formula Created by Florida Solar Center
• Cooling
• Reduced for Hotter Climates
• Lexington Label SEER 13, Reduced SEER 12.2
• Heating Heat Pump
• Reduced for Cooler Climates
• Lexington Label HSPF 7.7, Reduced HSPF 5.7

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REM/Rate Annual Component Consumption