Question

. A disposable coffee cup (including a lid) may be regarded as a polystyrene cylinder, diameter 50mm, height 80mm and thickness 2.5mm. The base and lid may be regarded as 2.5mm thick disks. When being held using finger tips (having a very small area) the heat transfer coefficient from the outside of the cup is 20W/m2K and from the coffee to the inner wall is 100W/m2K. Estimate the rate of heat loss from the cup when the coffee is at 65oC and ambient temperature is 18oC. The conductivity of the polystyrene is 0.04W/mK.

Ans = 6.33W

Answer 1

the thickness of coffee cup film =t= 2.5 mm = 0.0025 m

cylindrical surface area exposed to atmosphere = A1 = 3.14*50*80 = 12560 mm² = 0.0125 m²

Heat transfer coefficient from out side of the cup=h1 = 20 W/m²K

Heat transfer coefficient from the coffe to inner wall = h0 = 100 W/m² K

thermal conductivity of polysterene = K = 0.04 W /m K.

Coffe temp = 65 C

outside temp = 18 C

heat trasfer = Temp differece / thermal resistance

Heat transfer = Q = 65-18 / R_th

Thermal resistance R_th = convection resistance by from coffee to wall (R1)+ wall resistance (R2)+ convection resistance from wall to surroundings(R3).

R1 = 1/h0A = 1/ (100*0.0125) = 0.8

R2 = t/kA = 0.0025/(0.04*0.0125) = 5

R3 = 1/h1A = 1/(200*0.0125) = 0.4

R4 = x/kA =0.8+5+0.4 = 6.2

Total resistance = Rth = 6.2

Heat transfer = Q = (65-18) / 6.2 = 7.5