Heat Lectures 0- CM30 /5/06 CM30 ransport I Part II: Heat ransfer Radiation Heat ransfer In Unit Operations Heat Shields Professor Faith Morrison Department of Chemical Engineering Michigan echnological University CM30 ransport Processes and Unit Operations I Part : Heat ransfer Summary (Part thus far) Within homogeneous phases: Microscopic Energy Balances D Steady solutions rectangular: conduction cylindrical: ln emperature and Newton s law of cooling boundary conditions (if is supplied) Unsteady solutions (from literature) Carslaw and Jeager Heisler charts
Heat Lectures 0- CM30 /5/06 CM30 ransport Processes and Unit Operations I Part : Heat ransfer Summary (Part thus far) cross phase boundaries: Microscopic Energy, Momentum, and Mass Balances Micro momentum: Micro energy: convection Simultaneous effects (complex) Solutions are difficult to obtain (and often not really necessary) use and expts to obtain Data correlations for: forced convection natural convection phase evaporation/condensation change radiation 3 One more type of heat transfer Radiation versus Conduction and Convection Continuum view Conduction is caused by macroscopic temperature gradients Convection is caused by macroscopic flow Radiation? NO CONINUUM EXPLNION
Heat Lectures 0- CM30 /5/06 Continuum versus Molecular description of matter Real matter is not a continuum; at small enough length scales, molecules are discrete. continuum is infinitely divisible 5 Radiation versus Conduction and Convection Continuum view Conduction is caused by macroscopic temperature gradients Convection is caused by macroscopic flow Radiation? NO CONINUUM EXPLNION Molecular view Conduction Brownian motion Convection flow here is also, of course, a molecular explanation of these effects, since we know that matter is made of atoms and molecules Radiation is caused by changes in electron energy states in molecules and atoms Molecular view 6 3
Heat Lectures 0- CM30 /5/06 Molecular view Individual molecules carry: chemical identity macroscopic velocity (speed and direction) internal energy (Brownian velocity) When they undergo Brownian motion within an inhomogeneous mixture, they cause: diffusion (mass transport) exchange of momentum (viscous transport) conduction (energy transport) 7 Kinetic heory J. C. Maxwell, L. Boltzmann, 860 Molecules are in constant motion (Brownian motion) emperature is related to, of the molecules Molecular view Simplest model no particle volume no intermolecular forces More realistic model finite particle volume intermolecular forces s Intermolecular potential function 0.5 0 0 3-0.5 r - 8
Heat Lectures 0- CM30 /5/06 But, there is more to molecular energy than just Brownian motion Molecular view In atoms and molecules, electrons can exist in multiple, discrete energy states ransfers between energy states are accompanied by an emission of radiation Energy discrete energy levels Sienko and Plane, Chemistry: Principles and pplications, McGraw Hill, 979 Quantum Mechanics Radiation Heat ransfer is related to these non- Brownian mechanisms. 9 Kinetic heory Molecular view Is based on Brownian motion (molecules in constant motion proportional to their temperature) Predicts that properties that are carried by individual molecules (chemical identity, momentum, average kinetic energy) will be transported DOWN gradients in these uantities. Gradient transport laws are due to Brownian motion Heat ransfer by Radiation Energy discrete energy levels Is due to the release of energy stored in molecules that is NO related to average kinetic energy (temperature), but rather to changing populations of excited states. Radiation is NO a Brownian effect 0 5
Heat Lectures 0- CM30 /5/06 How does this relate to chemical engineering? Consider a furnace with an internal blower: here is heat transfer due to convection: surface temp (Use correlations) Bulk temp here is also heat transfer due to radiation. Where do we get? Where do we get? nswer: Heat transfer due to radiation hot surface We need to look into the physics of this mode of heat transfer. 6
Heat Lectures 0- CM30 /5/06 Radiation does not reuire a medium to transfer energy (works in a vacuum) travels at the speed of light, 3 00 / travels as a wave; differs from x-rays, light, only by wavelength, l radiation is important when temperatures are high hot surface examples: the sun home radiator hot walls in vacuum oven heat exchanger walls when Δ is high and a vapor film has formed Note: absolute temperature units 3 hot surface Why is radiation flux related to temperature and not to something else? (From kinetic theory, temperature is related to average kinetic energy) nswer: s a molecule gains energy, it both speeds up (increases average kinetic energy) and increases its population of excited states. he increase in average kinetic energy is reflected in temperature (directly proportional), and heat transfer through conduction. he increase in number of electrons in excited states is reflected in increased radiation heat flux. Electrons enter excited states in proportion to absolute. 7
Heat Lectures 0- CM30 /5/06 Electromagnetic Spectrum visible from P.. ipler, Physics, Worth, 976 Gamma rays X rays Ultraviolet Infrared Short radio waves 0-0 -3 0-0 - 0-0 0-9 0-8 0-7 0-6 0-5 0-0 -3 0-0 - 0 0 0 =nm =mm =mm Wavelength l, m thermal radiation 0.m 0m FM radio, V 0 M radio 5 What causes energy transfer by radiation? energy hits surface pushes some molecules into an excited state when the molecules/atoms relax from the excited state, they emit radiation incident emits radiation hot body reflects emits absorptivity absorbed incident absorbs, increases 6 8
Heat Lectures 0- CM30 /5/06 absorptivity absorbed incident bsorption In general, absorptivity is a function of wavelength incident reflected absorbs, increases emitted absorbed gray body: a body for which a is constant (does not depend on ) black body: a body for which, i.e. absorbs all incident radiation 7 emissivity emitted emitted, black body Emission gray body: a body for which a is constant black body: a body for which absorptivity absorbed incident true for black and non-black solid surfaces Kirchhoff s Law: emissivity euals absorptivity at the same temperature the fraction of energy absorbed by a material = the relative amount of energy emitted from that material compared to a black body 8 9
Heat Lectures 0- CM30 /5/06 emissivity emitted emitted, black body Black Bodies Stefan-Boltzmann Law: the amount of energy emitted by a black body is proportional to emitted emitted, black body 0.7 0 5.676 0 NOE: absolute temperature 9 Non-Black Bodies emissivity emitted emitted, black body emitted emitted, nonblack body emitted, black body emitted, black body Stefan-Boltzmann: Energy emitted by a non-black body emitted, nonblack body 0 0
Heat Lectures 0- CM30 /5/06 Radiation Summary: bsorptivity, α gray body: constant black body: Emissivity,, Kirchoff s law: ε Stefan-Boltzman law, 0.7 0 5.676 0 How does this relate to chemical engineering? Consider a furnace with an internal blower: here is heat transfer due to convection: surface temp (Use correlations) Bulk temp here is also heat transfer due to radiation: Because these two types of physics do not interact, we can just add the effects.
Heat Lectures 0- CM30 /5/06 How does this relate to chemical engineering? Consider a furnace with an internal blower: here is heat transfer due to convection: surface temp (Use correlations) Bulk temp here is also heat transfer due to radiation: Where do we get? Because these two types of physics do not interact, we can just add the effects. 3 Where do we get?, b, black body, net flux to object: Net flux to the body = Heat/area absorbed - Heat/area emitted
Heat Lectures 0- CM30 /5/06 Where do we get? net flux to object: Heat/area absorbed,,, fraction absorbed b Incident energy,, energy emitted by walls, which are acting as a black body, using Kirchhoff s law black body, 5 Where do we get?, b, net flux to object: Heat/area emitted,, Object is a gray body, assuming: 6 3
Heat Lectures 0- CM30 /5/06 Where do we get?, b, net flux to object: Net flux to the body = Heat/area absorbed - Heat/area emitted assuming: 7 Finally, calculate net energy absorbed: assuming: euating with expression for : Geankoplis th ed., en.0-0 p30 8
Heat Lectures 0- CM30 /5/06 Example: Geankoplis.0-3 horizontal oxidized steel pipe carrying steam and having an OD of 0.683m has a surface temperature of 37.9 K and is exposed to air at 97. K in a large enclosure. Calculate the heat loss for 0.305 m of pipe. 0.79 9 Example: Geankoplis.0-3 horizontal oxidized steel pipe carrying steam and having an OD of 0.683m has a surface temperature of 37.9 K and is exposed to air at 97. K in a large enclosure. Calculate the heat loss for 0.305 m of pipe. nswers: 6.9/ 6./ 63 0.79 30 5
Heat Lectures 0- CM30 /5/06 One final topic: Radiation Heat ransfer Between wo Infinite Plates Consider a uantity of radiation energy that is emitted from surface. Reflected= not absorbed See: Geankoplis, section.b lso: Bird, Stewart, and Lightfoot, ransport Phenomena 960 Wiley PP6-8 Left plate at Right plate at emit reflect 3 absorb emit 6 absorb 5 reflect 7 emit 3 First round surface Quantity of energy incident at surface : Quantity of energy absorbed at surface : Quantity of energy reflected from surface : Radiation Heat ransfer Between wo Infinite Plates his energy goes back to surface. fraction reflected (not absorbed) incident energy 3 6
Heat Lectures 0- CM30 /5/06 Second round surface Quantity of energy absorbed at surface (second round): Radiation Heat ransfer Between wo Infinite Plates fraction absorbed incident energy Quantity of energy reflected from surface (second round): fraction reflected (not absorbed) incident energy 33 hird round surface Radiation Heat ransfer Between wo Infinite Plates Quantity of energy absorbed at surface (third round): fraction absorbed incident energy Quantity of energy reflected from surface (third round): fraction reflected (not absorbed) incident energy here is a pattern. 3 7
Heat Lectures 0- CM30 /5/06 Radiation Heat ransfer Between wo Infinite Plates Now, calculate the radiation energy going from surface to surface : Later, calculate energy from to ; then subtract to obtain net energy transferred. energy absorbed at surface n n energy from 35 Radiation Heat ransfer Between wo Infinite Plates Radiation energy going from surface to surface : n n0 n How can we calculate? nswer: / 36 8
Heat Lectures 0- CM30 /5/06 9 Radiation Heat ransfer Between wo Infinite Plates Radiation energy going from surface to surface : Final Result 37 Faith. Morrison, Michigan Radiation Heat ransfer Between wo Infinite Plates Radiation energy going from surface to surface : Radiation energy going from surface to surface : NE Radiation energy going from surface to surface : 38
Heat Lectures 0- CM30 /5/06 Radiation Shields Radiation Shield Left plate at Right plate at 3 Purpose of Heat Shields: o reduce the amount of energy transfer from (hotter) plate at to second (cooler) plate at 3. Note: net, net,3 39 nalysis of Radiation Shields Radiation Shield We will assume that the emissivity is the same for all surfaces. net, net,3 3 Now we eliminate between these euations. Note: net, net,3 3 0 0
Heat Lectures 0- CM30 /5/06 nalysis of Radiation Shields Radiation Shield 3 3 3 3 3 3 nalysis of Radiation Shields Radiation Shield 3 With one heat shield present, falls by half compared to no heat shield. Heat Shield N Heat Shields With N heat shields present, falls by a factor of /N compared to no heat shield. by the same analysis,
Heat Lectures 0- CM30 /5/06 Radiation Summary: General properties: bsorptivity, α gray body: constant black body: Emissivity,, Kirchoff s law: ε Stefan-Boltzman law, 0.7 0 5.676 0 Heat transfer coefficient: Geankoplis th ed., en.0-0 p30 Heat shields: lways use absolute temperature (Kelvin) in radiation calculations. 3 CM30 ransport Processes and Unit Operations I Part : Professor Faith Morrison Department of Chemical Engineering Michigan echnological University CM30 - Momentum and Heat ransport CM30 Heat and Mass ransport www.chem.mtu.edu/~fmorriso/cm30/cm30.html
Heat Lectures 0- CM30 /5/06 CM30 ransport Processes and Unit Operations I Part : Heat ransfer Summary Within homogeneous phases: Microscopic Energy Balances D Steady solutions rectangular: cylindrical: ln emperature and Newton s law of cooling boundary conditions (if is supplied) Unsteady solutions (from literature) Carslaw and Jeager Heisler charts 5 CM30 ransport Processes and Unit Operations I Part : Heat ransfer Summary cross phase boundaries: Microscopic Energy, Momentum, and Mass Balances Micro momentum: Micro energy: Simultaneous effects (complex) Solutions are difficult to obtain (and often not really necessary) use to obtain Data correlations for: forced convection, natural convection (use in design) evaporation/condensation radiation 6 3
Heat Lectures 0- CM30 /5/06 CM30 ransport Processes and Unit Operations I Part : Heat ransfer Summary Heat ransfer Unit Operations Macroscopic energy balances Heat Exchangers double pipe (Δ Shell-and-tube Heat exchanger effectiveness Evaporators/ Condensers Ovens Heat Shields 7 CM30 ransport Processes and Unit Operations I Professor Faith Morrison Department of Chemical Engineering Michigan echnological University CM30 - Momentum and Heat ransport CM30 Heat and Mass ransport www.chem.mtu.edu/~fmorriso/cm30/cm30.html 8