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UCSD PHYS 121 - Thermal Design

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Thermal DesignWhy Care about Thermal?Chief Thermal PropertiesThermal Conductivity of MaterialsConduction: Heated BoxA Cold FingerR-value of insulationWikipedia on R-values:Convective Heat ExchangeConvection ExamplesRadiative Heat ExchangeRadiative ExamplesCombined ProblemsTwo-Layer insulationConduction plus ConvectionConvection plus RadiationThe whole enchiladaThe enchilada calculationTimescalesHeating a lump by conductionLab ExperimentLab Experiment, cont.Lab Experimental SuiteTemperature measurementRandom NotesRandom Notes, continuedSlide 27Example SeriesTemperature differencesReferences and AssignmentThermal Building DesignHandling External Flow as R-valuePutting TogetherA model houseDealing with the CeilingAll Together NowThermal DesignThermal DesignHeat TransferHeat TransferTemperature MeasurementTemperature MeasurementThe prevalence of the number 5.7The prevalence of the number 5.7Winter 2011UCSD: Physics 121; 20112Why Care about Thermal?Why Care about Thermal?•Scientific equipment often needs temperature controlScientific equipment often needs temperature control–especially in precision measurement•Want to calculate thermal energy requirementsWant to calculate thermal energy requirements–how much energy to change temperature?–how much power to maintain temperature?•Want to calculate thermal time constantsWant to calculate thermal time constants–how long will it take to change the temperature?•Want to understand relative importance of radiation, Want to understand relative importance of radiation, convection, conductionconvection, conduction–which dominates?–how much can we limit/exaggerate a particular process?Winter 2011UCSD: Physics 121; 20113Chief Thermal PropertiesChief Thermal Properties•Thermal ConductivityThermal Conductivity measured in W/m/K–heat flow (in W) isP = ·T·A/t–note that heat flow increases with increasing T, increasing surface area, and decreasing thickness (very intuitive)•Specific Heat CapacitySpecific Heat Capacity–cp measured in J/kg/K–energy locked up in heat is:E = cp·T·m–energy stored proportional to T, and mass (intuitive)•Emisivity, Emisivity, –power radiated is P = AT4Winter 2011UCSD: Physics 121; 20114Thermal Conductivity of MaterialsThermal Conductivity of Materials•(copied from materials lecture)(copied from materials lecture)Material (W m-1 K-1)commentsSilver 422 room T metals feel coldCopper 391 great for pulling away heatGold 295Aluminum 205Stainless Steel 10–25 why cookware uses S.S.Glass, Concrete,Wood 0.5–3 buildingsMany Plastics ~0.4 room T plastics feel warmG-10 fiberglass 0.29 strongest insulator choiceStagnant Air 0.024 but usually moving…Styrofoam 0.01–0.03 can be better than air!Winter 2011UCSD: Physics 121; 20115Conduction: Heated BoxConduction: Heated Box•A 1 m A 1 m  1 m 1 m  2.5 m 2.5 m ice-fishing hutice-fishing hut stands in the stands in the 1010 C cold with 2.5 cm walls of woodC cold with 2.5 cm walls of wood–A = 12 m2–t = 0.025 m  1 W/m/K•To keep this hut at 20To keep this hut at 20 C would require C would requireP = ·T·A/t = (1.0)(30)(12)/(0.025) = 14,400 W–Outrageous!–Replace wood with insulation:  = 0.02; t = 0.025P = ·T·A/t = (0.02)(30)(12)/(0.025) = 288 W–This, we can do for less than $40 at Target•First example unfairFirst example unfair–air won’t carry heat away this fast: more on this laterWinter 2011UCSD: Physics 121; 20116A Cold FingerA Cold Finger•Imagine a plug of aluminum connecting the inside to Imagine a plug of aluminum connecting the inside to the outsidethe outside–how much will it change the story?–cylindrical shape, length t, radius R = 205 W/m/K–just based on conduction alone, since difference in thermal conductivity is a factor of 10,000, the cold finger is as important as the whole box if it’s area is as big as 1/10,000 the area of the box.•this corresponds to a radius of 2 mm !!!•So a cold finger can “short-circuit” the deliberate So a cold finger can “short-circuit” the deliberate attempts at insulationattempts at insulation–provided that heat can couple to it effectively enough: this will often limit the damageWinter 2011UCSD: Physics 121; 20117R-value of insulationR-value of insulation•In a hardware store, you’ll find insulation tagged with In a hardware store, you’ll find insulation tagged with an “R-value”an “R-value”–thermal resistance R-value is t/ –R-value is usually seen in imperial units: ft2·F·hr/Btu–Conversion factor is 5.67:•R-value of 0.025-thick insulation of  = 0.02 W/m/K is:R = 5.67t/ = 5.670.025/0.02 = 7.1–Can insert Home-Depot R=5 insulation into formula:P = 5.67A·T/R–so for our hut with R = 5: P  5.67 (12)(30)/5 = 408 W–note our earlier insulation example had R = 7.1 instead of 5, in which case P = 288 W (check for yourself!)Winter 2011UCSD: Physics 121; 20118Wikipedia on R-values:Wikipedia on R-values:•Note that these examples use the non-SI definition and are per inch. Vacuum insulated panel has the highest R-value of (approximately 45 in English units) for flat, Aerogel has the next highest R-value 10, followed by isocyanurate and phenolic foam insulations with, 8.3 and 7, respectively. They are followed closely by polyurethane and polystyrene insulation at roughly R–6 and R–5. Loose cellulose, fiberglass both blown and in batts, and rock wool both blown and in batts all possess an R-value of roughly 3. Straw bales perform at about R–1.45. Snow is roughly R–1.•Absolutely still air has an R-value of about 5 but this has little practical use: Spaces of one centimeter or greater will allow air to circulate, convecting heat and greatly reducing the insulating value to roughly R–1Winter 2011UCSD: Physics 121; 20119Convective Heat ExchangeConvective Heat Exchange•Air (or any fluid) can pull away heat by physically Air (or any fluid) can pull away heat by physically transporting ittransporting it–really conduction into fluid accompanied by motion of fluid–full, rigorous, treatment beyond scope of this class•General behavior:General behavior:power convected = P = h·T·A–A is area, T is temperature difference between surface and bath–h is the convection coefficient, units: W/K/m2–still air has h  2–5 W/K/m2•higher when T is higher: self-driven convective cells•note that h = 5.67


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UCSD PHYS 121 - Thermal Design

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