26.1 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)
3Kelvin = 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
66.1 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”?
7where 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)
86.2 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).
96.2 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
106.2 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
11R 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.
126.2 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?
136.2 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=========