Question

The inner surface of a 5 cm diameter, 3 mm thick, and 7 cm high styrofoam cup is at 70 °C. the outer surface is exposed to air at 20 °C. the surface heat transfer coefficient associated with the outer surface is 8 w/m² °C. Determine

The heat transfer rate through the cylindrical surface of the cup.

The outer surface temperature of the cup.

Answer 1

For this we will first assume that only the cylindrical portion of the cup is transferring heat and the bottom circle which will be resting on the ground won't contribute to heat transfer

Thermal conductivity of styrofoam cup, K =0.033 w/mk

Now

Rate of heat transferred by styrofoam cup = Heat absorbed by the surrounding

Hstyrofoam_cup =H_surrounding

Now Tin = 70 ^oC, Tsurr =20 ^oC, H = 8 w/m^2oC, D = 5 cm

Ri = 2.5 cm

Ro =Ri + thickness = 2.5 + 0.3 = 2.8 cm, L = 7 cm = 0.07 m,

substituting all the known data in above heat transfer equation to obtain the value of T_out

Do = Di +2*thickness = 5 cm + 2(0.3) = 5.6 cm = 0.056 m

Tout = 48.26 oC

Hence outer surface of the cup is 48.26 ^oC

Rate of heat transfer

= 2.784 Watts