Question

Homework 3 The figure below shows a very simple model of your skin on a very cold day in Wisconsin. The skin is composed of two lavers. The inner laver is the dermis which has a thickness of tha-3 mm and conductivity k- 0.32 W/m-K. The epidermis is the outer layer which has a thickness of thed0.12 mm and conductivity kod 0.14 W/m-K. The inner surface of the dermis is exposed to blood flow and therefore remains at Tiod34°C. The outer surface of the epidermis is exposed to cold air at T.--24°C. The skin both radiates and convects to the surroundings at T The emissivity of the skin is - 1 and the heat transfer coefficient is h -50 W/m2-K T-24°C h-50 W/m2-K th-0.12 mm epidemmis, k-0.14 W/m-K th,-3 mm dermis, k,-0.32 W/m-K T -34°C a.) Determine the temperature of the skin exposed to the air (in C). resistance network that you use for this calculation. b.) Prepare a plot showing your skin temperature as a function of the heat transfer coefficient. c.) You begin to feel cold-related discomfort when your skin temperature reaches approximately Ttn 25°C. Determine the heat transfer coefficient (which is related to the wind speed) at which d.) You are in danger of frost-bite when your skin temperature reaches approximately Tm10°C. Determine the heat transfer coefficient at which time you are in danger of frost-bite. Sketch the you experience cold-related discomfort. The figure below illustrates a very simple model of your skin on a very cold day in Wisconsin after you put gloves on. The thickness of the glove is the 5 mm and the effective conductivity of the filler within the glove is ke 0.14 W/m-K. The outer surface of the glove has an emissivity of a- 1 T--24 C -50 W/m-K th-5 mm glove, k,-0.14 W/m-K th-0.12 mm epidermis, k0.14 Wim-K th,-3 mm dermis, &,-0.32 W/m-K Tod34°C e.) Determine the temperature of the skin within the glove (in C). Sketch the resistance network that you use for this calculation. f.) Rank the thermal resistances in your resistance network in terms of their importance. Explain. g.) Overlay on your plot from (b) the skin temperature with gloves as a function of heat transfer coefficient. At what heat transfer coefficient will you experience discomfort? Will you ever experience frost-bit? Finally, the figure below illustrates a very simple model of your skin on a very cold day in Wisconsin after you put gloves on and insert a hand warmer. The hand warmer is a thin (assume negligibly thin) package filled with a chemical that reacts exothermically with air. The energy given off per unit area by the hand warmer is g-250 W/m The thickness of the glove is the 5 mm and the effective conductivity of the filler within the glove is k,-0.14 W/m - K. The outer surface of the glove has an emissivity ofe-1 T-24-C 50 Wm2-K tk,-5 mm glove, ,-0.14 Win-K hand warmer, e-250 Wim th-0.12 mm epidermis, &-014 Wm-K sh,-3 mm dermis, &,0.32 Wim-K -34'C h) Determine the temperature of the skin within the glove with the hand warmer (in °C). Sketch the resistance network that you use for this calculation. Overlay on your plot from (g) the skin temperature with gloves and hand warmer as a Gpction of heat transfer coefficient. At what heat transfer coefficient will vo experience discomfort? Will you ever experience frost-bit?

Answer 1

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T2. funetio b) Plot can detined by ev ( 3322.80 24h 97.72 at h So T 14,37C at 20. 377 구。 12 h o C C 3. 287 1D So 3 o heat tg1ahsfes The Coe iient 25C (c) at which temperature be comes sRin at 2니 h 3322.86 25 25h + 2443,2sa 332286- 24h h + 97. 73 Ans ent&) Heat Coe o at T2 Frast bite that 3 3 2 2.8- 24h 24h 1아 + 9구구.3 = 3 32286 h 97. 73 68.387 w(n21k 234s.56 3니h