A stainless steel spoon with thermal conductivity k-15 W/(mK) is partially immer

Question

A stainless steel spoon with thermal conductivity k-15 W/(mK) is partially immersed in boiling water at 100degreeC as shown in the figure. 15 cm long section of the handle is exposed to the air. The cross sectional area of spoon handle will be approximated as a rectangle with sides 2 mm and 12 mm. Since boiling water has a very high heat transfer coefficient it will be assumed that the part of the spoon in the water is at constant 100degreeC. If the air is at 27degreeC and heat transfer coefficient between the air and the exposed sides and the tip of the spoon is 6 W/(m.2K), calculate the highest temperature our fingers will be exposed to if we hold the spoon at a 3 cm long region at the tip of the handle.

Explanation / Answer

Q=KAdeltaT/L

here, at the point were our finger will fill max. heat is

K*A*(T2-T)/L1= K*A*(T21-T1)/L2

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