2 6.1 Definitions Mechanisms of Heat (Thermal Energy) Transfer: Conduction: transmission of heat across matter, due to direct physical contact, e.g. in solids, liquids and gases.Radiation: heat transfer due to electromagnetic radiation across a space, even in a vacuum.Convection: heat transfer by “currents” in a gas or liquid, due to temperature differences or forced flow, an important mechanism of energy transfer between a solid surface and a liquid or a gas.All mechanisms may be involved in practical heat transfer,but the dominant mechanism differs in different cases.(Source of illustrations:heattransfer/heattransfer.html)
3 Kelvin = Degree Celsius (oC) + 273 6.1 DefinitionsConcepts & Terminologies:THERMAL CAPACITY (of a system): Quantity of ENERGY required to heat a whole system by 1 K (Kelvin). Unit: J·K-1SPECIFIC HEAT (or SPECIFIC HEAT CAPACITY): Quantity of ENERGY required to heat a unit mass of a system by 1 K.Unit: J·kg-1·K-1Kelvin = Degree Celsius (oC) + 273J= joule
4 (error in handout “m-3” ) 6.1 DefinitionsT1T2QAdTemperature profileTHERMAL CONDUCTIVITY, k :a measurement of heat flow through a body. It is the heat transmitted in unit time, in a direction normal to a surface of unit area, through a distance, d, across a unit temperature difference over the distance.Q, heat flow per unit time (Js-1) × d, distance (m)A, area (m2) × (T1-T2) temperature difference (K)k =(Eq. 6a)(Eq. 6a)Unit: Wm-1K (or Wm-1 °C-1)(error in handout “m-3” )(analogous to electrical conductivity or hydraulic permeability)( note: 1W = 1 J s-1)
5 (T1-T2) temperature difference (K) 6.1 DefinitionsT1T2QAdTemperature profileAnother way of understanding the THERMAL CONDUCTIVITY, k, is to re-arrange the equation as :Q, heat flow per unit time (Js-1)A, area (m2)(T1-T2) temperature difference (K)d, distance (m)= k(Eq. 6b)The temperature difference per unit distance is called temperature gradientHeat flow per unit time per unit area is proportional to the temperature gradient; this proportionality is called thermal conductivity, k.The higher the thermal conductivity, the faster the heat flows
6 6.1 Definitions Why are diamonds so “cool”? Brick Styrofoam Thermal conductivity of other common materials:6.1 DefinitionsWhy are diamonds so “cool”?MaterialThermal conductivity (298 K), W·m-1·K-1Diamond( the highest k)Carbon Nanotubes1400Silver429Copper386Gold317Aluminium237Iron80.2BrickWoodWoolStyrofoam(for building insulation)0.15 – 0.60.04 (very low k)0.01Why dose wool feel so “warm”?
7 where R is the resistance 6.1 DefinitionsTHERMAL RESISTIVITY, ρ : reciprocal of conductivity, 1/kUnit: m K W-1THERMAL Resistance of a system, R:where R is the resistanced is the thicknessρ is the resistivityR = d = d/k(error in handout, not divided by “A”)Note that the R-value above is a UNIT AREA THERMAL RESISTANCE (or thermal insulance), because the resistivity, ρ, is related to the conductivity, k, which is measured per unit area.Unit for R: m K W-1 m = Km2 W-1(The reason for defining the thermal resistance, R, is that the R values are “additive” in multi-layer insulations and this makes calculations simpler. This will be explained later)
8 6.2 Conduction d Q. How much heat is conducted through a system ? Q A Temperature profileQ. How much heat is conducted through a system ?We know:-the larger the A, the larger the heat flow;-the larger the d, the smaller the heat flow.Therefore; orDirect analogy with electricity:-Current (I) is equivalent to Heat Flow per unit area (Q/A) ; & Potential Difference (V1 - V2) or voltage is equivalent to temperature difference (T1-T2).
9 6.2 Conduction R = R1 + R2 + R3 + ........ i.e. resistances in series In most situations we have composite materials to deal with - e.g. a wall consisting of an outer skin (brick), a cavity, an inner skin and then plaster.Since the thermal resistance of each component has considered the thickness, the Total UNIT AREA THERMAL RESISTANCE is simply given bybrickcavityplasterR = R1 + R2 + Ri.e. resistances in seriesElectrical Analogue
10 6.2 Conduction“Resistance in Parallel”: e.g. conduction through a wall with a window, which is more complicated, as total (average) heat transfer depends on the thermal resistances and the relative areas of both components.Proportion of wall or window area to the total areaThe U - value is defined as 1/R, where R is resistance per unit area
11 R U clear ? 6.2 Conduction Thermal transmittance, the U value: The U value is simply defined as 1/R; Unit: W·K-1·m-2(Remember: R is resistance per unit area, so U is transmittance per unit area as well)Both the R-value and the U-value are used to grade the insulation properties of a material or a system (e.g. a double-glazed assembly).R U clear ?A higher R-Value means the materials are more resistant to heat loss.A lower U-Value means the system will transmit less heat.Both mean the same thing & are desirable, from the insulation point of view.
12 6.2 Conduction Simple Example: Tbp Brick Brick wall 105 mm thick plasterBrick20°C0 °CTbp105mm15mmBrick wall mm thickplaster mm thick on insideInternal temperature = 20°CExternal Temperature= 0 °Ckbrick = W m-1 K -1kplaster = W m-1 K -1What is the U - value of the construction and also the temperature at the interface between the brick and the plaster?
13 6.2 Conduction Brick 20°C 0 °C Tbp 105mm 15mm Simple Example: plasterBrick20°C0 °CTbp105mm15mmSimple Example:Total resistance, R = = m2 ºC W-1and the U-value = 1/R = 1/ = W m-2 ºC-1==============Now heat flow in plaster = heat flow in brick=heat flow through the whole bodySo if Tbp is temperature at interfaceHence Tbp = * = ºC=========