U V A L U E

639 views

Published on

Published in: Business, Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
639
On SlideShare
0
From Embeds
0
Number of Embeds
3
Actions
Shares
0
Downloads
37
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

U V A L U E

  1. 1. University of Balamand ALBA H.V.A.C . Heat Transmission By Eng. Wael Zmerly – 2007-2008 University of Balamand - ALBA ١ HEAT TRANSMISSION HVAC Eng. Wael Zmerly – 2007-2008
  2. 2. THERMAL CONDUCTIVITY Homogeneous Material “λ = constant” Isotropic λ λ Thermal conductivity λ of the material (W/m.°C) λv Transmission by vibrations of atoms or molecules λ λe Transmission by the free electrons Wood Brick Copper Glass Iron Air Glass Fiber 0.21 0.52 386 0.74 85 0.024 0.046 (W/m.°C) University of Balamand - ALBA ٢ HEAT TRANSMISSION HVAC Eng. Wael Zmerly – 2007-2008 One will consider the Homogènes solids (characteristic physics and identical mechanics in any point) and Isotropic (even characteristic in all the directions). Thus, some of them, will depend only on the temperature, the influence of the pressure being neglected. There are two mechanisms for conduction in the solids: a heat transfer by the vibrations of the atoms or molecules that one characterizes it by a coefficient λϖ and a heat transfer by the free electrons characterized by a coefficient λε. Thermal conductivity Λ of a body will be such as: λ = λϖ + ιτ λ is the thermal coefficient of conductivity expressed out of W/m.°C It is a function of the temperature, but in the intervals of temperatures of current uses one will suppose “λ = constant”.
  3. 3. THERMAL CONDUCTIVITY METALS AND ALLOYS (at the ambient temperature) λ Insulator Copper 99,9% Aluminum 99,9% 386 228 Tin Nickel 61 61 Aluminum 99% 203 Mild steel (1% of C) 46 λ Conductor Zinc Alloy (Al 92% - Mg 8%) 111 104 Lead Titanium 35 21 Brass (Cu 70% - Zn 30%) 99 Stainless steel (Cr 18% - Nor 8%) 16 Iron 85 NONMETAL SOLIDS (at the ambient temperature) λ Gas < λ Liquids Electro graphite 116 Wood 0.21 Concrete 1.75 Polyester 0.209 Glass pyrex 1.16 Polyvinyls 0.162 Porcelain 0.928 Asbestos (sheets) 0.162 λ Liquids<λ Solids Glass 0.74 Phenoplasts 0.046 Asbestos cement 0.70 Glass Fiber 0.046 Bricks 0.52 Rock Wool 0.043 LIQUIDS GAS (at 0°C and under the normal pressure) λ Void = o Sodium at 200°C Mercury at 20°C 81,20 8,47 Hydrogen Air 0.174 0.024 Water at 100°C 0.67 Nitrogen 0.024 λ in (W/m.°C) Water at 20°C Benzene at 30°C 0.59 0.162 Oxygen Acetylene 0.024 0.019 Dowtherm A at 20°C 0.139 Carbon dioxide 0.014 University of Balamand - ALBA ٣ HEAT TRANSMISSION HVAC Eng. Wael Zmerly – 2007-2008 The table so above contains thermal conductivities λ out of W/m°C of various materials. The smaller the value of λ is, the more the material will be known as INSULATING. The larger the value of λ is, the more the material will be known as DRIVER. It is noted that among the solids, metals are much more conductive than the nonmetal compounds except for graphite (used in certain exchangers of heat). The stainless steel is less conductive than the majority of other metals and alloys. Among the liquids, mercury is detached clearly, the molten metals are good conductive what explains for example the use of sodium salts like coolant for the cooling of the nuclear engines. Except for the molten metals: λ of gases < λ of the liquids < Λ of the solids For the vacuum λ = O
  4. 4. FOURIER EQUATION: ∂ T ∂ T ∂ T ∂ T ∂ T ∂ T ϕ( x ) = - λ × ( i + j + k) où ∂ x i + ∂ y j + ∂ z k = grad T ∂ x ∂ y ∂ z Assumptions: - Isothermal surfaces are consisted of parallel plans. dT - The side losses of heat (according to “y” and “Z”) are neglected grad T = i dx Statement: The density of the thermal flow ϕ which runs out in the material is proportional to the variation of the temperature and the thermal conductivity of the environment . Z Isothermal Isothermal Surface Surface with T1 in T2 dT ϑ (X) n ϕ( x ) = - λ . dx X dx University of Balamand - ALBA ٤ HEAT TRANSMISSION HVAC Eng. Wael Zmerly – 2007-2008 GENERALIZATION OF THE EQUATION OF FOURIER: If one considers a solid in space (characterized by its co-ordinates “X, y, Z), L” equation is written: ∂ T ∂T ∂ T ∂ T ∂ T ∂ T ϕ( x ) = - λ × ( i + j + k ) où i + j + k = grad T With: grad T x ∂ (variation in temperature) represents the variation in thez ∂y ∂ z ∂ x ∂ y ∂ temperature according to all the directions. And is the derivative partial of the temperature compared to the axis “X”. STATEMENT IN THE PLAN: Simplifying assumptions: - Isothermal surfaces are consisted parallel plans between them. - The side losses of heat (according to “y” and “Z”) are neglected. The variation in temperature is reduced to: dT grad T = To convention the leaving heat flow is counted negatively. i dx Statement: That is to say a homogeneous material length “dx” and conductivity “λ”, whose external surfaces are respectively at temperatures T1 and T2 The density flow thermal ϕ which runs out in the matter is proportional to the variation in the temperature and the thermal conductivity of the medium.
  5. 5. CONDUCTION THROUGH A HOMOGENEOUS WALL Heat flow through the wall: A Φ = A.ϕ = λ ΔT Isothermal plan d Tx ϕ ϕ = Density of flow [W/m ²] Φ = Heat flow [W] λ : Thermal Conductivity (W/m°C) X T1 T2 d : Walls Thickness (m) Φ : Heat flow (W) λ A: Walls Surfaces (m²) d ΔT : Temperature Difference (°C) University of Balamand - ALBA ٥ HEAT TRANSMISSION HVAC Eng. Wael Zmerly – 2007-2008 This case makes it possible to solve the majority of the problems encountered in the building. 1-assumptions: - Homogeneous and isotropic Solid - Neglected side Losses. - Low thickness compared to transverse dimensions - 2 it heat flow through the wall: By applicant the Fourier analysis The heat flow “Φ”, in a tube of flow of section “S”, will be written: dT ϕ = -λ = cste − λ dT = ϕ dx dx T1 - T2 T2 e ϕ = e −λ T1 ∫ dT = ϕ ∫ dx from where λ 0 S Φ = S.ϕ = λ ( T1 - T2 ) e
  6. 6. THE THERMAL RESISTANCE OF A WALL Equivalent thermal resistance λ T2 T1 R d R d n di n R = R = ∑λ = ∑R i λ i =1 i i=1 R: Thermal resistance (m²°C/W) Electric analogy: In series, total resistance is equal to the sum of resistances. University of Balamand - ALBA ٦ HEAT TRANSMISSION HVAC Eng. Wael Zmerly – 2007-2008 3 - the thermal resistance of a plane wall: As in electricity, resistance is the report/ratio of a potential difference thus here of temperature and of a flow of energy thus here Φ flow, from where the following expression of thermal resistance. R is total thermal resistance [°C/W] 4 - Law of evolution T (X): = R - T2 ) = (T1 e λ .S (temperature in a point of co-ordinate Φ of an isothermal surface) “X” ; - λ. (T (X) – T1) = ϕ. X Evolution T = F (E) linear. T( x ) x −λ T1 ∫ dT = ϕ ∫ dx 0 ( T1 - T2 ) − λ × ( T(x) - T1 ) = .x.λ e ( T1 - T2 ) T(x ) = T1 - .x e
  7. 7. TRANSMISSION THROUGH MULTI-LAYER WALLS Wall in series Wall in Parallel Φ A1 Φ1 λ1 A2 Φ2 λ1 λ2 λ3 A λ2 λ3 A3 Φ3 d1 d2 d3 di d d d A Aλ A λ A λ R = 1 + 2+ 3 Homogeneous walls = 1 1 + 2 2+ 3 3 λ1 λ2 λ3 R d1 d2 d3 ΣAi Ai R = ΣRi Non-Homogeneous walls = Σ R Ri University of Balamand - ALBA ٧ HEAT TRANSMISSION HVAC Eng. Wael Zmerly – 2007-2008 1) Layers perpendicular to flow crossing the wall. Example, floor with insulator, cover and floor covering, concrete wall with brought back insulation, etc… The thermal resistance of the wall is calculated according to the following formula: 2) Layers parallel with flow crossing ΣR wall. R = the i Each section I parallel with the heat flow can be in its turn made up of several superimposed layers J and perpendicular to flow. Example, blocks full with horizontal and vertical joints. The thermal resistance of the wall is calculated according to the following formula: ΣAi Ai = Σ R Ri
  8. 8. GLOBAL HEAT TRANSMISSION COEFFICIENT U External surface Internal surface transfer transfer Thermal Resistance R = Rsi + ΣRi + Rse Rs = Rsi + Rse Conduction Global Heat Transmission through the Coefficient wall 1 U = R [W/m²°C] University of Balamand - ALBA ٨ HEAT TRANSMISSION HVAC Eng. Wael Zmerly – 2007-2008 Elements such as floors, walls, flagstones, roofs, windows and doors are composed of several nonhomogeneous layer. The heat flow which crosses an element is defined by the thermal coefficient of transmission U. The value U (W/m2°C) is the quotient of the density flux thermal which crosses, in stationary regime, the structural component considered, by the difference in temperature between two environments contiguous to this element. The thermal coefficient of transmission of an element is the reverse of its total resistance. U=1/R The Heat flux through this element will be: Φ = U.A . ΔT The following phenomena influence the value U of an element: - Heat Transfer enters the interior air and L `element. This process is described by the coefficient of transfer of surface heat interior hi, or surface resistance Rsi=1 interior/hi - Conduction of heat inside an element. The parameter determining is thermal conductivity here L (lambda) of various materials. -Heat transfer enters the element and the surrounding air. This process is described by the coefficient of surface transfer of heat external He or surface resistance Rse=1 outside/He If the element is an interior wall one applies Rsi twice. One definite surface resistance Rs total - External wall: Rs = Rse + Rsi - Interior wall: Rs = Rsi + Rsi
  9. 9. SURFACE RESISTANCES WALL Flow Rsi Rse Rs Vertical 0,13 0,04 0,17 0,10 0,04 0,14 Horizontal 0,17 0,04 0,21 Rse = 0.04 m²°C/W Rsi = 0.13 m²°C/W Rse = 0 m²°C/W Rsi = 0.17 m²°C/W Air Circulation Rsi = 0.10 m²°C/W University of Balamand - ALBA ٩ HEAT TRANSMISSION HVAC Eng. Wael Zmerly – 2007-2008 The surface resistance of walls Rs (m2°C/W) is calculated according to the following formula: 1 RS = H and the coefficient of exchanges per radiation and Convection: h = hr + hc h hr is the coefficient of exchanges per radiation out of W/m2°C: hr = Mc . hro Mc = corrected emissivity of surface, by defect of one takes Mc = 0,9 who is an average value for materials used in construction. hro = 4. σ . Tm 3 hro is the coefficient of radiation of a black body: σ is the constant of Stefan-Bolzmann: σ = 5,67051 X 10-8 Tm is the average temperature of surface (Tm=273,15+température measured) Example for 10°C: hro = 4 X (5,67051 X 10-8) X (273,15 + 10) 3 = 5,15 hc is the coefficient of exchange by convection out of W/m2°C For the interior faces: - If the heat flow is Ascendant hc = 5 W/m2°C - If the heat flow is Descendant hc = 0.7 W/m2°C h = 4+4.v - If the heat flow is Horizontalc hc = 2.5 W/m2°C For the outsides: v is the speed of the wind in m/s near surface. 1 1 1 1 One Si = RSe = R definite surface resistances interior Rsi and external RseRof + RSe = RS = Si a wall: + hi he hi he and From where All times and to avoid these calculations, the values of Rsi and Rse of the table below can be used. They one obtained with emissivity a corrected of 0,9 and one temperature with dimensions interior for Rsi of 20°C and a temperature with dimensions outside for Rse of 0°C with a speed of wind of 4 m/s. If the wall gives on a room not heated, a roof, an underfloor space, Rsi applies of the 2 with dimensions ones. * Wall giving on: outside, an open passage or an open room. A room is known as open if the report/ratio of the total surface of its permanent openings on outside, with its volume, is equal or higher than 0,005 m2/m3.
  10. 10. THERMAL RESISTANCE Of AIR LAYER thickness of the Thermal resistance Rg m²°C/W non-ventilated air layer in mm 1 0.035 0.035 0.035 5 0.11 0.11 0.11 7 0.13 0.13 0.13 10 0.15 0.15 0.15 15 0.16 0.17 0.17 25 0.16 0.17 0.19 50 0.16 0.17 0.21 100 0.16 0.17 0.22 300 0.16 0.17 0.23 Rg: thermal resistance of air layers University of Balamand - ALBA ١٠ HEAT TRANSMISSION HVAC Eng. Wael Zmerly – 2007-2008 Blade of air: Is regarded as blade of air, a layer of air of which the thickness in the direction of the heat flow does not exceed 0,30 Mr. Blade of air non-ventilated: if there is no specific provision for a flow of air crossing it (example, a double glazing). A blade of air can be regarded as non-ventilated if the openings do not allow a flow of crossing air and if they do not exceed: 500 mm ² per m length counted horizontally for the vertical blades of air. 500 mm ² per m ² of surface for the horizontal blades of air. Default values are given in the table above for non-ventilated blades of air. The values for a horizontal flow also apply to tilted heat fluxes until more or less 30% compared to the horizontal plane. Blade of air slightly ventilated: when the external air flow is limited because of dimension of the openings, dimensions included/understood in the following ranges: >500 mm ² but <1500 mm ² per m length counted horizontally for the vertical blades of air. >500 mm ² but <1500 mm ² per m ² of surface for the horizontal blades of air. Resistance of a blade of air slightly ventilated The thermal resistance of a blade of air slightly ventilated is equal to half of that corresponding to a non-ventilated blade of air. Nevertheless, if the thermal resistance of the layers located between the blade of air and outside is higher than 0,15 m2°C/W, this resistance must be replaced by the value of 0,15 m2°C/W.
  11. 11. THERMAL RESISTANCE Of AIR LAYER Indoor Outoor Ventilated Air Layer Clading Rsi Rse = Rsi University of Balamand - ALBA ١١ HEAT TRANSMISSION HVAC Eng. Wael Zmerly – 2007-2008 Blade of air strongly ventilated: It is about blade of air of which openings towards outside surplus: 1500 mm ² per m length counted horizontally for the vertical blades of air. 1500 mm ² per m ² of surface for the horizontal blades of air. Resistance of a blade of air strongly ventilated In this case, one neglects the thermal resistance of the blade of air and of all the layers located between the blade of air and outside and one applies not to the wall a surface thermal resistance Rse but Rsi.
  12. 12. CALCULATION OF VALUE U d1...dn : thickness of the layer of the corresponding material, in m Indoor Outoor Rsi, Rse : surface resistances, in W/m²°C λ1 … λ2 : thermal conductivity of the corresponding material, in W/m°C R = Rsi + ΣRi + Rse Rsi Rse d1 d 2 d R = Rsi + + + ... + n + Rse 5 λ1 λ2 λn 1 4 4 U = 5 R University of Balamand - ALBA ١٢ HEAT TRANSMISSION HVAC Eng. Wael Zmerly – 2007-2008 Construction of the Wall Designation of the Wall No Building Material d l R , d/λ (m) (W/m°C) (m²°C/W) 1 Internal Surface Resistance Rsi 2 3 4 5 6 7 8 9 External Surface Resistance Rse 1 Valeur U = = (W/m2 . C) Rtotal =____ Rtotal
  13. 13. EXAMPLE OF CALCULATION OF U VALUE Internal Plaster Brick terra cotta Heat insulation Brick terra cotta External Plaster Rsi Rse R = Rsi + ΣRi + Rse 1 U = R 0.015 0.15 0.16 0.12 0.02 R = 0.13 + + + + + + 0.04 = 5.26 0.7 0.44 0.36 0.44 0.87 University of Balamand - ALBA ١٣ HEAT TRANSMISSION HVAC Eng. Wael Zmerly – 2007-2008 Construction of the Wall Designation of the External Wall. No Building Material d λ R, d/λ (m) (W/m°C) (m²°C/W) 1 Interior Surface Resistance Rsi - - 0.13 2 Interior Plaster 0.015 0.7 0.02 3 Brick terra cotta 0.15 0.44 0.34 4 Insulation 0.16 0.036 4.44 5 Brick terra cotta 0.12 0.44 0.27 6 External Plaster 0.02 0.87 0.02 7 External Surface Resistance Rse - - 0.04 8 9 1 U Value = = 0.19 (W/m2 . C) Rtotal = 5.26 Rtotal
  14. 14. MATERIALS d λ R m W/m°C m²°C/W Béton CONCRETE 1.200 -1.750 Béton caverneux 1.400 Béton de vermex 0.240 Béton cellulaire 0.160 - 0.330 Blolc de Construction Concrete hollow block 2 Layers 10cm 0.1 0.090 Concrete hollow block 2 Layers 12,5cm 0.125 0.100 Concrete hollow block 2 Layers 15cm 0.15 0.120 Concrete hollow block 2 Layers 17,5cm 0.175 0.140 Concrete hollow block 2 Layers 20cm 0.2 0.160 Concrete hollow block 2 Layers 7,5cm 0.075 0.070 Concrete hollow block 3 Layers 15cm 0.15 0.140 Concrete hollow block 3 Layers 17,5cm 0.175 0.160 Concrete hollow block 3 Layers 20cm 0.2 0.190 Concrete hollow block 3 Layers 22,5cm 0.225 0.210 Concrete hollow block 4 Layers 20cm 0.2 0.220 Concrete hollow block 4 Layers 22,5cm 0.225 0.240 Concrete hollow block 4 Layers 25cm 0.25 0.260 Concrete hollow block 4 Layers 27,5cm 0.275 0.280 Concrete hollow block 5 Layers 27,5cm 0.275 0.310 Concrete hollow block 5 Layers 30cm 0.3 0.340 Concrete hollow block 5 Layers 32,5cm 0.325 0.360 Concrete hollow block 6 Layers 32,5cm 0.325 0.400 Bricks Brick 5cm 0.05 0.100 Brick 7,5cm 0.075 0.160 Brick 10cm 0.1 0.200 Brick 12,5cm 0.125 0.270 Brick 15cm 0.15 0.300 Brick 17,5cm 0.175 0.330 Brick 20cm 0.2 0.390 Brick 22,5cm 0.225 0.420 Brick 25cm 0.25 0.450 Brick 27,5cm 0.275 0.520 Brick 30cm 0.3 0.590
  15. 15. Hourdi Hourdi Concrete 8+4 0.12 0.110 Hourdi Concrete 12+4 0.16 0.130 Hourdi Concrete 16+4 0.2 0.150 Hourdi Concrete 20+5 0.25 0.180 Hourdi Concrete 25+5 0.3 0.210 Hourdi Concrete 12+4 0.16 0.130 Hourdi Terra Cotta 5+3 0.08 0.110 Hourdi Terra Cotta 8+4 0.12 0.140 Hourdi Terra Cotta 12+4 0.16 0.230 Hourdi Terra Cotta 16+4 0.2 0.260 Hourdi Terra Cotta 20+5 0.25 0.310 Hourdi Terra Cotta 25+5 0.3 0.400 Insulation Materials Rock Wool 0.038 - 0.047 Fiber Glass 0.031 - 0.055 Liège expansé 0.040 - 0.047 Expanded Polystyrene (EPS) 0.032 - 0.048 Extruded Polystyrene (XPS) 0.028 - 0.036 Polyurethane 0.022 - 0.038 Plaster Placo-plâtre 0.01 0.350 Plâtre d'enduit 0.01 0.300 Carreau de plâtre 0.05 0.350 Cement Plaster 0.01 0.700 Wood Wood (chêne, hêtre, frêne, pichpin) 0.230 Wood (pine) 0.150 Plancher wood (pine) 0.027 0.150 Wood (sapin, peuplier, okoumé) 0.120 Mouchette bois 0.015 0.150 Stones Stone, granite, gneiss, porphyre 3.200 Stone shistes, ardoise 2.200 Basaltes 1.600 Laves, trachytes, andesites 1.100 Lime Stone 2.400
  16. 16. Tiling Ceramic 1.000 Vinyl 0.020 Granite 3.200 Linoleum 0,180 Marble 3.400 Carpets 0.006 - 0.010 0.060-0.150 Parquet 0.200 PVC 0.230 Floor Clay or lime 1.500 Rock 3.500 Sand et Gravel (tout venant) 2.000 Metals Steel 50 Stainless Steel 17 Aluminium Alloy 160 Aluminium 230 Bronze 65 Copper 380 Pure Iron 72 Iron, Cast Iron 50 Brass 120 Plomb 35 Zinc 380 Gas Air 0.025 Argon 0.017 Krypton 0.009 Xenon 0.0054 Other Glass 1.150 Water Profing 0.230 Mortar 1.200
  17. 17. External Walls Ceilling Hollow Block Insulation Air Layer Hollow Block U (W/m².°C) Description U (W/m².°C) 10cm - - - 3.53 Intermediate Floor 2.26 15cm - - - 3.19 Last Floor with attic 2.54 20cm - - - 2.83 Roof 2.99 10cm - 3cm 10cm 0.75 Toilet (Atic) 3.68 10cm 2cm - 10cm 0.94 10cm 2.5cm - 10cm 0.83 Floors 10cm 5cm - 10cm 0.49 Description U (W/m².°C) 10cm 3cm 2cm 10cm 0.65 Ground Floor 2.25 10cm - 5cm 10cm 1.84 Intermediate Floor 1.72 15cm 5cm - 10cm 0.48 15cm 3cm 2cm 10cm 0.64 15cm - 5cm 10cm 1.74 Glass Description U (W/m².°C) Single Glass 6.40 External Walls with Clading Double Glass 3.30 Hollow Block Insulation Air Layer Hollow Block U (W/m².°C) Triple Glass (6-8-6-8-6) en mm 2.20 10cm - - - 3.33 Triple Glass (6-12-6-12-6) en mm 2.01 15cm - - - 3.03 20cm - - - 2.70 10cm 2.5cm - 10cm 0.82 Internal Wall 10cm 5cm - 10cm 0.49 Hollow Block U (W/m².°C) 10cm 3cm 2cm 10cm 0.64 10cm 2.71 10cm - 5cm 10cm 1.78 15cm 2.51 15cm 5cm - 10cm 0.48 20cm 2.28 15cm 3cm 2cm 10cm 0.63 15cm - 5cm 10cm 1.69 External Walls with mechanical Clading Hollow Block Insulation Air Layer Hollow Block U (W/m².°C) 10cm - - - 2.71 15cm - - - 2.51 20cm - - - 2.28 10cm 2.5cm - 10cm 0.77 10cm 5cm - 10cm 0.47 10cm 3cm 2cm 10cm 0.61 10cm - 5cm 10cm 1.59 15cm 5cm - 10cm 0.46 15cm 3cm 2cm 10cm 0.60 15cm - 5cm 10cm 1.52

×