04_thermal

# 67 is equivalent to r 1 our hut from before h 5 wkm2

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Unformatted text preview: ween 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 is equivalent to R = 1 • Our hut from before: – h 5 W/K/m2 – T = 30° C (if the skin is at the hot temperature) – A 12 m 2 – P (5)(30)(12) = 1800 W – gentle breeze may have h 5 – 10 W/K/m2 – forced air may be several times larger (h 1 0–50) Winter 2008 9 Winter 2008 10 UCSD: Physics 121; 2008 UCSD: Physics 121; 2008 Radiative Heat Exchange Radiative Examples • Standing unclothed in room with 273° C walls 273 walls • The Stephan-Boltzmann law tells us: – P = A ( Th 4 Tc 4 ) – The Stephan-Boltzmann constant, = 5.67 10-8 W/m2/K4 – in thermal equilibrium (Th = Tc), there is radiative balance, and P = 0 – the emissivity ranges from 0 (shiny) to 1 (black) – “black” in the thermal infrared band ( 10 µm) might not be intuitive • • • • your skin is nearly black ( 0.8) 0.8–1.0) plastics/organic stuff is nearly black ( even white paint is black in the thermal infrared metals are almost the only exception – for small T around T, P 4 A T3 T = ( 4 T3) ·A· T – which looks like convection, with h = 4 T3 – for room temperature, h 5.7 W/K/m2, so similar in magnitude to convection Winter 2008 Lecture 4 11 – and assume emissivity is 0.8 for skin – A 1 m2 – T = 310 K – P (0.8)(1)(5.67 10-8)(3104) = 419 W (burr) • Now bring walls to 20° C – T = 17 ° C – P (0.8)(1)(5.67 10-8)(3104 2934) = 84 W – pretty similar to convection example – note that we brought our cold surface to 94.5% the absolute temperature of the warm surface, and only reduced the radiation by a factor of 5 (not a factor of 18): the fourth power makes this highly nonlinear Winter 2008 12 3 Thermal Considerations 01/17/2008 UCSD: Physics 121; 2008 UCSD: Physics 121; 2008 Combined Problems Two-Layer insulation • Let’s take our ice-fishing hut and add insulation Le...
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