# U V A L U E

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- 1. University of Balamand ALBAH.V.A.C .Heat Transmission By Eng. Wael Zmerly 2007-2008 University of Balamand - ALBA HEAT TRANSMISSION HVACEng. Wael Zmerly 2007-2008

2. THERMAL CONDUCTIVITY HomogeneousMaterial = constantIsotropic Thermal conductivity of the material (W/m.C)v Transmission by vibrations of atoms or molecules e Transmission by the free electrons WoodBrickCopperGlass IronAir Glass Fiber 0.210.52 386 0.74 850.0240.046(W/m.C) University of Balamand - ALBAHEAT TRANSMISSION HVACEng. Wael Zmerly 2007-2008One will consider the Homognes solids (characteristic physics and identical mechanicsin any point) and Isotropic (even characteristic in all the directions). Thus, some ofthem, will depend only on the temperature, the influence of the pressure beingneglected.There are two mechanisms for conduction in the solids: a heat transfer by thevibrations of the atoms or molecules that one characterizes it by a coefficient anda heat transfer by the free electrons characterized by a coefficient .Thermal conductivity of a body will be such as: = + is the thermal coefficient of conductivity expressed out of W/m.CIt is a function of the temperature, but in the intervals of temperatures of currentuses one will suppose = constant. 3. THERMAL CONDUCTIVITY METALS AND ALLOYS (at the ambient temperature) Insulator Copper 99,9%Aluminum 99,9%386228TinNickel6161Aluminum 99%203 Mild steel (1% of C)46 Conductor ZincAlloy (Al 92% - Mg 8%)111104LeadTitanium3521Brass (Cu 70% - Zn 30%) 99Stainless steel (Cr 18% - Nor 8%) 16Iron85 NONMETAL SOLIDS (at the ambient temperature) Gas < Liquids Electro graphite116 Wood0.21Concrete1.75Polyester 0.209Glass pyrex 1.16Polyvinyls0.162Porcelain 0.928 Asbestos (sheets) 0.162 Liquids< SolidsGlass 0.74Phenoplasts 0.046Asbestos cement 0.70Glass Fiber 0.046Bricks0.52Rock Wool 0.043 LIQUIDSGAS (at 0C and under the normal pressure) Void = oSodium at 200CMercury at 20C81,208,47HydrogenAir0.1740.024Water at 100C0.67Nitrogen0.024 in (W/m.C) Water at 20CBenzene at 30C0.590.162OxygenAcetylene0.0240.019Dowtherm A at 20C0.139 Carbon dioxide0.014 University of Balamand - ALBA HEAT TRANSMISSION HVACEng. Wael Zmerly 2007-2008The table so above contains thermal conductivities out of W/mC of variousmaterials.The smaller the value of is, the more the material will be known as INSULATING.The larger the value of is, the more the material will be known as DRIVER.It is noted that among the solids, metals are much more conductive than thenonmetal compounds except for graphite (used in certain exchangers of heat). Thestainless steel is less conductive than the majority of other metals and alloys.Among the liquids, mercury is detached clearly, the molten metals are good conductivewhat explains for example the use of sodium salts like coolant for the cooling of thenuclear engines.Except for the molten metals: of gases < of the liquids < of the solidsFor the vacuum = O 4. FOURIER EQUATION: T T T T T T( x ) = - (i + j + k) o xi + yj + zk = 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 neglectedgrad T =idx Statement: The density of the thermal flow 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 T2dT (X)n ( x ) = - . dxXdx University of Balamand - ALBA HEAT TRANSMISSION HVACEng. Wael Zmerly 2007-2008GENERALIZATION OF THE EQUATION OF FOURIER:If one considers a solid in space (characterized by its co-ordinates X, y, Z), L equationis written: T T T T T T ( x ) = - ( i +j + k ) o i + j +k = grad T With: grad T x (variation in temperature) represents the variation in thezy z x y temperatureaccording to all the directions. And is the derivative partial of the temperaturecompared 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: dTgrad T =To convention the leaving heat flow is counted negatively.i dx Statement:That is to say a homogeneous material length dx and conductivity , whose externalsurfaces are respectively at temperatures T1 and T2The density flow thermal which runs out in the matter is proportional to thevariation in the temperature and the thermal conductivity of the medium. 5. CONDUCTION THROUGH A HOMOGENEOUS WALL Heat flow through the wall: A = A.= TIsothermal pland Tx = Density of flow [W/m ] = Heat flow [W] : Thermal Conductivity (W/mC)XT1 T2 d : Walls Thickness (m) : Heat flow (W) A: Walls Surfaces (m) dT : Temperature Difference (C) University of Balamand - ALBA 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 analysisThe heat flow , in a tube of flow of section S, will be written:dT = - = cste dT = dxdx T1 - T2T2 e =eT1 dT = dxfrom where 0S = S. = ( T1 - T2 )e 6. THE THERMAL RESISTANCE OF A WALL Equivalent thermal resistanceT2T1 RdR d n din R =R ==Rii=1i i=1 R: Thermal resistance (mC/W)Electric analogy: In series, total resistance isequal to the sum of resistances.University of Balamand - ALBAHEAT TRANSMISSION HVACEng. 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 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 .S(temperature in a point of co-ordinate of an isothermal surface) X ;- . (T (X) T1) = . XEvolution T = F (E) linear. T( x ) x T1 dT= dx 0( T1 - T2 ) ( T(x) - T1 ) = .x. e( T1 - T2 ) T(x ) = T1 - .xe 7. TRANSMISSION THROUGH MULTI-LAYER WALLSWall in seriesWall in ParallelA111 A2 2 1 2 3 A 23 A3 3d1 d2 d3di d d dA A A A R = 1 + 2+ 3 Homogeneous walls = 1 1 + 2 2+ 3 31 2 3 R d1d2 d3AiAi R = RiNon-Homogeneous walls= RRi University of Balamand - ALBA HEAT TRANSMISSION HVAC Eng. Wael Zmerly 2007-20081) Layers perpendicular to flow crossing the wall.Example, floor with insulator, cover and floor covering, concrete wall with brought backinsulation, etcThe thermal resistance of the wall is calculated according to the following formula:2) Layers parallel with flow crossing R wall.R = the iEach section I parallel with the heat flow can be in its turn made up of severalsuperimposed 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: Ai Ai= R Ri 8. GLOBAL HEAT TRANSMISSION COEFFICIENT U External surfaceInternal surfacetransfer transferThermal ResistanceR = Rsi + Ri + RseRs = Rsi + RseConduction Global Heat Transmissionthrough theCoefficientwall1U = R [W/mC]University of Balamand - ALBAHEAT TRANSMISSION HVACEng. Wael Zmerly 2007-2008Elements such as floors, walls, flagstones, roofs, windows and doors are composed ofseveral nonhomogeneous layer. The heat flow which crosses an element is defined bythe thermal coefficient of transmission U.The value U (W/m2C) is the quotient of the density flux thermal which crosses, instationary regime, the structural component considered, by the difference intemperature between two environments contiguous to this element. The thermalcoefficient of transmission of an element is the reverse of its total resistance. U=1/RThe Heat flux through this element will be: = U.A . TThe following phenomena influence the value U of an element:- Heat Transfer enters the interior air and L `element. This process is described bythe coefficient of transfer of surface heat interior hi, or surface resistance Rsi=1interior/hi- Conduction of heat inside an element. The parameter determining is thermalconductivity here L (lambda) of various materials.-Heat transfer enters the element and the surrounding air. This process is describedby the coefficient of surface transfer of heat external He or surface resistanceRse=1 outside/HeIf 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. SURFACE RESISTANCESWALL FlowRsiRse Rs Vertical0,13 0,040,170,10 0,040,14Horizontal0,17 0,040,21Rse = 0.04 mC/WRsi = 0.13 mC/WRse = 0 mC/W Rsi = 0.17 mC/W Air CirculationRsi = 0.10 mC/WUniversity of Balamand - ALBA HEAT TRANSMISSION HVACEng. Wael Zmerly 2007-2008 The surface resistance of walls Rs (m2C/W) is calculated according to the following formula:1RS = 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/m2C: 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. . Tm 3 hro is the coefficient of radiation of a black body: is the constant of Stefan-Bolzmann: = 5,67051 X 10-8 Tm is the average temperature of surface (Tm=273,15+temprature measured) Example for 10C: 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/m2C For the interior faces: - If the heat flow is Ascendant hc = 5 W/m2C - If the heat flow is Descendant hc = 0.7 W/m2C h = 4+4.v - If the heat flow is Horizontalc hc = 2.5 W/m2C For the outsides: v is the speed of the wind in m/s near surface. 11 1 1 One Si =RSe =R definite surface resistances interior Rsi and external RseRof + RSe = RS = Si a wall:+ hihehi heand 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 20C and a temperature with dimensions outside for Rse of 0C 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. THERMAL RESISTANCE Of AIR LAYER thickness of the Thermal resistance Rg mC/W non-ventilatedair layerin mm 1 0.035 0.0350.03550.11 0.110.1170.13 0.130.1310 0.15 0.150.1515 0.16 0.170.1725 0.16 0.170.1950 0.16 0.170.21 100 0.16 0.170.22 300 0.16 0.170.23 Rg: thermal resistance of air layers University of Balamand - ALBA HEAT TRANSMISSION HVACEng. Wael Zmerly 2007-2008Blade 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 per m length counted horizontally for the vertical blades of air. 500 mm per m 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 but 500 mm but