A manufacturer of ski equipment wishes to develop headgear that will offer enhanced thermal protection for skiers on cold days at the slopes. Headgear can be made with good thermal insulating characteristics, but it tends to be bulky and cumbersome. Skiers prefer comfortable lighter gear that offers good visibility, but such gear tends to have poor thermal insulating characteristics. The manufacturer decides to take a new approach to headgear design by concentrating the insulation in areas about the head that are prone to the highest heat losses from the skier and minimizing use of insulation in other locations. Hence the manufacturer must determine the local heat transfer coefficients associated with the human head with a velocity of V = 10 m/s directed normal to the face and an air temperature of - 13°C. A young engineer is assigned the task of building the heat transfer experiment but soon finds the experimental challenges to be daunting. She decides to make use of the heat and mass transfer analogy and the naphthalene sublimation technique (see Problem 6.51) and casts head shapes of solid naphthalene with characteristic dimensions that are half-scale (i.e., the models are half as large as the full-scale head).

(a) What wind tunnel velocity (T∞ = 300 K) is needed in order to apply the experimental results to the human head associated with V = 10 m/s?

(b) A wind tunnel experiment is performed for ∆t = 120 min, T∞ = 27°C. The engineer finds that the naphthalene has receded by δ1 = 0.1 mm at the back of the head, δ2 = 0.32 mm in the middle of the forehead, and δ3 = 0.64 mm on the ear. Determine the heat transfer coefficients at these locations for the full-scale head at -13°e. The density of solid naphthalene is P A. sol = 1025 kg/m3.

(c) After the new headgear is designed, the models are fitted with the new gear (half-scale) and the experiments are repeated. Some areas of the model that were found to have extremely small local heat transfer coefficients are left uncovered since insulating these areas would have little overall benefit in reducing heat losses during skiing. Would you expect the local heat transfer coefficients for these exposed areas to remain the same as before fitting the model with the headgear? Explain why.