Chapter 2B: BASIC THERMAL SCIENCES: CONDUCTION AND CONVECTION Agami Reddy (rev Dec 2017) Conduction heat transfer - Steady-state1-D equation through walls - Electric resistance analog - Conductivity of materials - Series and parallel heat paths - Conduction through cylinders - Conduction shape factors - Thermal bridging Convection heat transfer - Basic description: Newton’s law of cooling - Classes of convective regimes - Factors influencing convection coefficient - Determination of convective coeff: Dimensionless vs dimensional eqns - Examples of external and internal heat transfer - Combined conduction-convection HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Heat Transfer (HT) The science behind heat flow is called heat transfer There are three ways by which heat can be transferred: conduction, convection, and radiation Heat flow depends on the temperature difference From CPO slides HCB-3 Chap 2B: Conduction & Convection

Steady-State and Unsteady State HT Steady-state HT occurs when the heat flow into wall is equal to heat flow out of the wall. This would occur when thermal mass of the wall is negligible and so no time lags Norbert Lechner, 2015. Heating, Cooling, Lighting, 4th Ed., Wiley HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Water Analogy Thermal heat capacity = Mcp Norbert Lechner, 2015. Heating, Cooling, Lighting, 4th Ed., Wiley HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection

Conduction HT- One Dimensional (1-D) Conduction – The form of heat transfer through a body that occurs without any movement of the body. It is due to molecular or electron vibration or movement  Conductance inverse of resistance   - Watts or Btu/h q = /A W/m2 Btu/(h-ft2) Fig. 2.10 (a) Single layer heat flow   A- area thru which conduction occurs A Steady-state HT can be assumed if temperatures T1 and T2 do not change in time or change very slowly compared to the heat capacity of the body HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Steady state heat transfer rate due to conduction: The commonly used “R value” is the conductive resistance per unit area We define thermal resistance Q T1 Analogy of heat transfer and electricity: Heat flux – Current Temperature difference – Voltage Thermal resistance – Resistance T2 HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Fig 2.13. Thermal conductivity varies with temperature. However, for most HVAC applications, the range of operation in temperature is so narrow that conductivity can be assumed constant HCB-3 Chap 2B: Conduction & Convection

Table 2.5 Representative Magnitudes Material Conductivity, Btu/(h.ft.°F) Conductivity, W/(m.K) Atmospheric-pressure gases 0.004–0.10 0.007–0.17 Insulating materials 0.02–0.12 0.034–0.21 Nonmetallic liquids 0.05–0.40 0.086–0.69 Nonmetallic solids (brick, stone, concrete) 0.02–1.50 0.034–2.6 Metal alloys 8–70 14–120 Pure metals 30–240 52–410 HCB-3 Chap 2B: Conduction & Convection

Table 2.6 Conductivity of Materials k, Btu/(h.ft.°F) T, °F k, W/(m.K) T, °C Construction materials    Asphalt 0.43–0.44 68–132 0.74–0.76 20–55  Cement, cinder 0.44 75 0.76 24  Glass, window 0.45 68 0.78 20  Concrete 1.0 1.73  Marble 1.2–1.7 — 2.08–2.94  Balsa 0.032 86 0.055 30  White pine 0.065 0.112  Oak 0.096 0.166 Insulating materials  Glass fiber 0.021 0.036  Expanded polystyrene 0.017 0.029  Polyisocyanurate 0.012 0.020 Gases at atm. pressure  Air 0.0157 100 0.027 38  Helium 0.0977 200 0.169 93  Refrigerant 12 0.0048 32 0.0083 0.0080 212 0.0038 HCB-3 Chap 2B: Conduction & Convection

Conduction HT Through Composite Walls - Series Path Multi-layer material is treated like a series electrical network: Rtotal = R1 + R2+ R3… Fig. 2.10 (b) Multi-layer series-resistance heat flow HCB-3 Chap 2B: Conduction & Convection

Conduction HT- Example HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Perform calculations with 1 m2 area Note: 96% of total resistance due to insulation layer B oC HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Can you calculate the intermediate temperatures T2 and T3 ? HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Composite Walls Single wooden stud (4” x 6”) construction Double stud walls with spray foam HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Metal studs (about 15 cm thick and spaced about 50 cm apart) Common in commercial building construction- These walls are usually not load bearing by only support lateral loads HCB-3 Chap 2B: Conduction & Convection

Conduction HT Through Composite Walls- Parallel Paths For resistances in parallel, conductance U add up. Average U value Fig. 2.10 (c) Multi-layer parallel-resistance heat flow HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Comments The thermal conductivity of wood is about 2.5 times that of insulation. - The presence of wood studs has caused the heat flux through this wall to increase by 18% (=4.88/4.13=1.18), even though the studs represent only 8% of the wall heat flow area, because. - The stud is a simple example of a thermal bridge, a part of the building envelope with higher than average thermal losses HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Thermal Bridges A thermal bridge is a local area of a building's envelope with relatively lower thermal resistance than exists in its surroundings. The wood stud considered is an example of a thermal bridge. The presence of the stud causes the wall heat flow to increase. Similar or greater increases are caused by structural members that penetrate walls (e.g., balcony supports in a high-rise building) or that support walls (e.g., the steel structure in a high rise) Thermal bridges are unavoidable in conventional building practice and cause at least two significant difficulties: - Heat losses and gains are increased. - Lower temperature can cause condensation, leading to moisture problems in winter (material degradation, paint peeling, mold) HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Thermal breaks (low conductivity material inserted) in overhangs to avoid thermal bridging HCB-3 Chap 2B: Conduction & Convection

Conduction HT Through Cylinders Fig. 2.11 Conduction in cylinders Single layer Multiple layers HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Heat loss through insulated pipe Fig.2.11 Resistance offered by iron pipe negligible compared to that of insulation HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Conduction Shape Factor In 2-D cases, the conduction shape factor (S) approach simplifies the analysis The value of S can be found in tables for a few cases Q Tables HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Conduction Shape Factors For 3-D HT Fig. 2.12 HCB-3 Chap 2B: Conduction & Convection

Convection HT- Basic Description Convection: form of heat transfer that results from bulk movement of liquids or gases Newton’s Law of cooling where h is the convection coefficient, W/m2-°C or Btu/h-ft2-°F h depends on fluid, its moving velocity, shape of the obstacle… (normally obtained experimentally) Define R = 1/h, then Outdoor air Ti Q T1 Room air T2 To Unlike conduction problems where k is easily found in tables, the challenge is to determine h for the particular situation! HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection - Forced convection: one in which fluid motion is caused by external pressure (fan, pump, wind,…) - Free or natural convection: one in which fluid motion is caused by buoyancy effects Velocity profiles adjacent to wall are very much different for forced and free convection flows ! HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Depends on Reynolds number (Re) If viscous force is strong, laminar flow Critical Re number depends on geometry HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Some Important Dimensional Equations SI (2.49) IP Equation 2.49 SI (2.50) IP HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection External Flows Equation 2.53 or 2.54 SI Eq. 2.54 Surface is horizontal- so eq 2.45 is used HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Eq. 2.56 Eq. 2.56 This is 4.5 times larger than that for free convective coefficient determined in Ex. 2.9. Eq. 2.46 and 2.47 HCB-3 Chap 2B: Conduction & Convection

Effect of Wind Speed on Convective HT Factors affecting forced convective coeff. h: Surface roughness Temperature diff. Conversion: 1 Btu/(h.ft2.oF)= 5.7 W/(m2.K) Fig. 2.14 HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Internal Flows Eq. 2.59 SI Note: Convective coefficients for water much higher than those for air HCB-3 Chap 2B: Conduction & Convection

Combined Conduction-Convection HT Overall thermal resistance: with air films on both sides of wall Internal Qw Qi T1 Wall External Cold air Ti Steady-state Qi Qw Qo T1 Where U = Overall thermal loss coeff per unit area: T2 Overall thermal resistance per unit area: To Warm air HCB-3 Chap 2B: Conduction & Convection

Example 2.13 Combined Conduction- Convection Example Repeat Example 2.5 for a stud wall to include the effect of inner and outer surface convection coefficients. Inner surface coefficient = 0.4 Btu/(h.ft2.°F) from Equation 2.50 IP Outer surface coefficient is 3.7 Btu/(h.ft2 .°F) from Equation 2.56 IP). Find the overall wall R value. Fig. 2.16 a Composite wall with all 3 resistances in series HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Two Possible HT Network Configurations Consider a building element such as a stud wall consisting of wooden studs with insulation in-between and which is sandwiched between two layers as in Example 2.4. Flow is really 2-D Isothermal plane representation (N1) Parallel path representation (N2) Fig. 2.16(b) HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Two Possible HT Network Configurations contd… The heat flow is actually 2-D since the heat flow lines would no longer be parallel in the x-direction, but would get distorted and bend so as to preferentially favor flow through the studs which have higher conductivity material (thermal bridge effect) Thus, less heat will flow through the insulation (lower conductivity material) and more through the wooden stud section. Hence, the 1-D network model N1 would underestimate the resistance and predict a higher heat loss than network N2. According to ASHRAE (2013) : Acceptable to use network N2 if all materials involved (the bridge element and all building envelope elements in contact with it) are non-metals (such as wood, drywall, concrete). Recommended that network N1 be used if any portion of the bridge has high conductivity (e.g., structural steel or building skin materials or aluminum frames of windows) compared to the other elements HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Example 2.14: Heat losses in parallel This example illustrates heat flows in parallel occurring from a small building. The walls of a 40 ft × 60 ft office have 8 ft ceilings and the walls contain 2 in. thick doors of total surface area 80 ft2 and single-glazed windows of 200 ft2 area. What fraction of the total heat loss occurs through the windows. Given: Wall: Thermal conductance Uwall = 0.08 Btu/(h.ft2 .°F), Window: Uwindow = 1.13 Btu/(h.ft2 .°F), Awindow = 200 ft2, Wooden door: conductivity kwood = 0.10 Btu/(h.ft .°F), Adoor = 80 ft2, thickness x = 2 in. Assumptions: Inside and outside film resistances are 0.68 (h.ft2.°F)/Btu, 0.17 (h.ft2. °F)/Btu. HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection (h.ft2.0F/Btu) HCB-3 Chap 2B: Conduction & Convection

Summary-Convective Heat Transfer Newton’s Law of cooling: Ts=surface temperature Tf=fluid temperature External flows vs internal flows Free convection vs forced convection- also effect of surface tilt Laminar vs turbulent Table 2.7 HCB-3 Chap 2B: Conduction & Convection

HCB-3 Chap 2B: Conduction & Convection Outcomes Understand difference between the three modes of HT: conduction, convection, and radiation Appreciate distinction between 1-D, 2-D and 3-D conduction HT Familiarity with concepts of conductivity and resistivity of materials Understand analogy of heat transfer and electricity networks Be able to solve problems involving conduction HT through simple and composite walls under series and parallel configurations Understand concept of conduction shape factor and its usefulness Understand concept of thermal bridging, its relevance to heat flows through building envelopes, and ways to mitigate it Understand the usefulness and limitations of Newton’s law of cooling Familiarity with different correlations to estimate convective HT Be able to apply correlations to solve forced and natural convection problems Be able to analyze problems involving combined conduction-convection HT Appreciate the differences and applicability between the two possible network wall network configurations for analyzing HT through a composite wall HCB-3 Chap 2B: Conduction & Convection