# Transmission Heat Loss through Building Elements

## Heat loss through common building elements due to transmission, R-values and U-values - imperial and SI units

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The heat transmission through a building wall or similar construction can be expressed as:

H_{t}= U A dt(1)

where

H_{t}= heat flow (Btu/hr, W, J/s)

U= overall heat transfer coefficient, "U-value" (Btu/hr ft^{2}^{o}F, W/m^{2}K)

A = wall area (ft^{2}, m^{2})

dt= temperature difference (^{o}F, K)

The overall heat transfer coefficient - the U-value - describes how well a building element conducts heat or the rate of transfer of heat (in watts or Btu/hr) through one unit area (m^{2} or ft^{2}) of a structure divided by the difference in temperature across the structure.

### Online Heat Loss Calculator

U-value (Btu/hr ft^{2}^{o}F, W/m^{2}K)

Wall Area (ft^{2}, m^{2})

Temperature Difference (^{o}F,^{o}C, K)

### Common Heat Transfer Coefficients of some common Building Elements

Building Element | Heat-Transfer Coefficient U-value | ||
---|---|---|---|

(Btu/(hr ft^{2} ^{o}F)) | (W/(m^{2}K)) | ||

Doors | Single sheet - metal | 1.2 | 6.8 |

1 inch - wood | 0.65 | 3.7 | |

2 inches - wood | 0.45 | 2.6 | |

Roofing | Corrugated metal - uninsulated | 1.5 | 8.5 |

1 inch wood - uninsulated | 0.5 | 2.8 | |

2 inches wood - un-insulated | 0.3 | 1.7 | |

1 inch wood - 1 inch insulation | 0.2 | 1.1 | |

2 inch wood - 1 inch insulation | 0.15 | 0.9 | |

2 inches - concrete slab | 0.3 | 1.7 | |

2 inches - concrete slab - 1 inch insulation | 0.15 | 0.9 | |

Windows | Vertical single glazed window in metal frame | 5.8 | |

Vertical single glazed window in wooden frame | 4.7 | ||

Vertical double glazed window, distance between glasses 30 - 60 mm | 2.8 | ||

Vertical triple glazed window, distance between glasses 30 - 60 mm | 1.85 | ||

Vertical sealed double glazed window, distance between glasses 20 mm | 3.0 | ||

Vertical sealed triple glazed window, distance between glasses 20 mm | 1.9 | ||

Vertical sealed double glazed window with "Low-E" coatings | 0.32 | 1.8 | |

Vertical double glazed window with "Low-E" coatings and heavy gas filling | 0.27 | 1.5 | |

Vertical double glazed window with 3 plastic films ("Low-E" coated) and heavy gas filling | 0.06 | 0.35 | |

Horizontal single glass | 1.4 | 7.9 | |

Walls | 6 inches (150 mm) - poured concrete 80 lb/ft^{3} | 0.7 | 3.9 |

10 inches (250 mm) - brick | 0.36 | 2.0 |

### U and R-values

U-value (or U-factor) is a measure of the rate of heat loss or gain through a construction of materials. The lower the U-factor, the greater the material's resistance to heat flow and the better is the insulating value. U-value is the inverse of R-value.

The overall U-value of a construction consisting of several layers can be expressed as

U = 1 / ∑ R(2)

where

U = heat transfer coefficient (Btu/hr ft^{2}^{o}F, W/m^{2}K)

R= "R-value" - the resistance to heat flow in each layer (hr ft^{2}^{o}F/Btu, m^{2}K/W)

The R-value of the single layer can be expressed as:

R = 1 / C = s/ k(3)

where

C= layer conductance (Btu/hr ft^{2}^{o}F, W/m^{2}K)

k= thermal conductivity of layer material (Btu in/hr ft^{2}^{o}F, W/mK)

s= thickness of layer (inches, m)

Note! - in addition to resistance in each construction layer - there is a resistance from the inner and outer surface to the surroundings. If you want to add the surface resistance to the *U* calculator below - use one - *1*- for thickness - *l*_{t} - and the surface resistance for the conductivity - *K*.

### Online *U value* Calculator

This calculator can be used to calculate the overall U-value for a construction with four layers. Add the thickness - *l _{t}* - and the layer conductivity -

*K*- for each layer. For fewer than four layers, replace the thickness of one or more layers with zero.

1. s (in, m) k (Btu in/hr ft^{2}^{o}F, W/mK)

2. s (in, m) k (Btu in/hr ft^{2}^{o}F, W/mK)

3. s (in, m) k (Btu in/hr ft^{2}^{o}F, W/mK)

4. s (in, m) k (Btu in/hr ft^{2}^{o}F, W/mK)

### Example - U value Concrete Wall

A concrete wall with thickness* 0.25 (m)* and conductivity *1.7 (W/mK)* is used for the default values in the calculator above. The inside and outside surface resistance is estimated to *5.8 (m ^{2 }K/W)*.

The U value can be calculated as

*U = 1 / (1 / (5.8 m ^{2}K/W) + (0.25 m) / (1.7 W/mK)) *

* = 3.13 W/m ^{2}K*

### R-values of Some Common Building Materials

Material | Resistance R-value | |
---|---|---|

(hr ft^{2} ^{o}F/Btu) | (m^{2}K/W) | |

Wood bevel siding 1/2" x 8", lapped | 0.81 | 0.14 |

Wood bevel siding 3/4" x 10", lapped | 1.05 | 0.18 |

Stucco (per inch) | 0.20 | 0.035 |

Building paper | 0.06 | 0.01 |

Plywood 1/4" | 0.31 | 0.05 |

Plywood 3/8" | 0.47 | 0.08 |

Plywood 1/2" | 0.62 | 0.11 |

Hardboard 1/4" | 0.18 | 0.03 |

Softboard, pine or similar 3/4" | 0.94 | 0.17 |

Softboard, pine or similar 1 1/2" | 1.89 | 0.33 |

Softboard, pine or similar 2 1/2" | 3.12 | 0.55 |

Gypsum board 1/2" | 0.45 | 0.08 |

Gypsum board 5/8" | 0.56 | 0.1 |

Fiberglass 2" | 7 | 1.2 |

Fiberglass 6" | 19 | 3.3 |

Common brick per inch | 0.20 | 0.04 |

### R-values of Some Common Wall Constructions

Material | Resistance R-value | |
---|---|---|

(hr ft^{2} ^{o}F/Btu) | (m^{2}K/W) | |

2 x 4 stud wall, uninsulated | 5 | 0.88 |

2 x 4 stud wall with 3 1/2" batt insulation | 15 | 2.6 |

2 x 4 stud wall with 1" polystyrene rigid board, 3 1/2" insulation blanket | 18 | 3.2 |

2 x 4 stud wall with 3/4" insulation board, 3 1/2" batt insulation, 5/8" polyurethane insulation | 22 | 3.9 |

2 x 6 stud wall with 5 1/2" insulation blanket | 23 | 4 |

2 x 6 stud wall with 3/4" insulation board, 5 1/2" batt insulation, 5/8" polyurethane insulation | 28 | 4.9 |

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