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Question: problem 2 transdermal heat diffusion multinational pharmaceutical company hires you...

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Problem 2. Transdermal heat diffusion multinational pharmaceutical company hires you and assigns you to a group that deals with sports medicine. For the first assignment, you are asked to check if a heat patch designed by a competitor performs as advertised. You read the label that says: provides temporary relief of minor muscular and joint aches and pains associated with overexertion, strains, sprains and arthritis. In fine print, it says, provides heat for up to eight hours, and also says, takes 30 minutes to reach the maximum temperature. Let us say that the heat patch covers an area S - 10 cm2 on your wrist, thermal conductivity of skin is k- 0.1 W/m.K, the thickness of your skin is h I cm, density of skin is 1000 kg/m, heat capacity is 4000 J/kg.K, and temperature of the heat patch in contact with your the wrists skin surface is maintained at T- 67 °C, which is 30 °C higher than your body temperature. (a) Estimate the penetration depth into the skin in thirty minutes. (15)
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