Introduction to Heat Transfer Outline 1.Heat Transfer Mechanisms 1.1. Conduction 1.2. Convection 1.3. Radiation 2. Conduction Heat Transfer 2.1. Series/Parallel Resistances 2.2. Geometric Considerations Heat Transfer Mechanisms Conduction Transfer of energy of motion between adjacent molecules May occur across solids, liquids, and gases. Heat Transfer Mechanisms Conduction Molecular Vibration Free Electron Diffusion (for solids) *This is why metals are good conductors. Heat Transfer Mechanisms Convection Transfer by bulk transport and mixing of macroscopic elements of warmer portions with cooler portions of a gas or a liquid. Heat Transfer Mechanisms Convection Forced Convection Free/Natural Convection Heat Transfer Mechanisms Radiation Transfer achieved by electromagnetic waves and requires no physical medium to propagate. Heat Transfer Mechanisms Identify the mechanisms: Conduction Heat Transfer Recall: Fourier’s Law of Heat Conduction Where: Q = heat flow rate A = heat transfer area k = thermal conductivity T = temperature 𝑑𝑇 = temperature gradient 𝑑𝑦 ONE-DIMENSIONAL ONLY 𝑄 𝑑𝑇 = −𝑘 𝐴 𝑑𝑦 Conduction Heat Transfer Recall: Fourier’s Law of Heat Conduction Where: q = heat flux k = thermal conductivity T = temperature THREE-DIMENSIONAL 𝒒 = −𝑘𝛻𝑇 𝜕𝑇 𝜕𝑇 𝜕𝑇 𝛻𝑇 = , , 𝜕𝑥 𝜕𝑦 𝜕𝑧 Conduction Heat Transfer Recall: Fourier’s Law of Heat Conduction 𝑄 𝑑𝑇 = −𝑘 𝐴 𝑑𝑦 Quantity Q A k T SI Units W m2 W/m·K K or °C English Units Btu/hr ft2 Btu/hr·ft·°F °F or °R Conduction Heat Transfer Useful Conversion Factors: 𝐵𝑡𝑢 𝑐𝑎𝑙 −3 1 = 4.1365 × 10 ℎ𝑟 𝑓𝑡 °𝐹 𝑠 𝑐𝑚 °𝐶 𝐵𝑡𝑢 W 1 = 1.73073 ℎ𝑟 𝑓𝑡 °𝐹 𝑚𝐾 𝐵𝑡𝑢 𝑊 1 = 3.1546 2 2 ℎ𝑟 𝑓𝑡 𝑚 𝐵𝑡𝑢 1 = 0.29307 𝑊 ℎ𝑟 Quantity SI Units English Units Q W Btu/hr A m2 ft2 k W/m·K Btu/hr·ft·°F T K or °C °F or °R Conduction Heat Transfer Thermal Conductivity, k A measure of a material’s ability to transfer thermal energy by conduction. Thermal Diffusivity, 𝜶 A measure of a material’s ability to respond to changes in its thermal environment. 𝑘 𝛼= 𝜌𝑐𝑃 Conduction Heat Transfer Thermal Conductivity Conduction Heat Transfer Thermal Conductivity For most liquids, thermal conductivity varies moderately linear with temperature: 𝑘 = 𝑎 + 𝑏𝑇 Conduction Heat Transfer Thermal Conductivity For most liquids, thermal conductivity varies moderately linear with temperature: Conduction Heat Transfer Thermal Conductivity For most liquids, thermal conductivity varies moderately linear with temperature: Conduction Heat Transfer Common Insulators: 1. Cellular glass 2. Polyurethane 3. Polyisocyanurate 4. Polystyrene 5. Glass fiber 6. Calcium silicate 7. Mineral wool Conduction Heat Transfer Exercise: 1. Calculate the heat loss per m2 of surface area for an insulating wall composed of 25.4-mm thick fiber insulating board (k = 0.048 W/mK), where the inside temperature is 352.7 K and the outside temperature is 297.1 K. Conduction Heat Transfer Exercise: 2. A furnace wall is insulated by a material with thermal conductivity expressed as 𝑘 = 0.08(1 + 0.003 𝑇) where k is in Btu/hr-ft-°F and T is in °F. During operation, the temperature inside the furnace reaches 1800°F, releasing heat at 3500 Btu/hr-ft2. Determine the insulation thickness sufficient to bring the temperature outside the wall to 300 °F.