Question

4. Hardening of ball bearings made from Type 440C stainless steel, one of the hardest stainless steels, is accomplished by heating the bearings to 1010 to 1065 °C then quenching (rapidly cooling) them in oil Consider bearings 24 mm in diameter at an initial uniform temperature of 1050 °C, cooled in an oil bath at 50 °C in which the convective heat transfer coefficient is 600 W/(m2 K). Properties of Type 440C Stainless Steel:t Density, 7800 kg/m3 Thermal conductivity, 24 W/(m K) Specific heat capacity, 460 J/(kg K) a. Evaluate the Biot number for a bearing in the oil bath, to verify that the lumped capacitance model would not be expected to give highly accurate results under the specified b. -Verify that the Fourier number, Fo at3 minutes, is large enough for the c. Determine the temperature on the surface of a bearing after cooling in the oil bath d. Determine the temperature at the center of a bearing after cooling in the oil bath for conditions. first term of the series solution to be a good approximation. for 3 minutes. 3 minutes

Answer 1

Biot No ТАЗ 9H -600 xo.oo4 Can b Blet No

只4 800 x 니 60 ec NT ㅋ If, No : 1.254 tc] 6oo x 3 l050- 5o 1853.96 IT- 50] tooo ,853·96T-92,698-41 1000
c(C). As we considered lumped heat analysis is valid in the above problem the temperature of the center of the bearing after 3 mins is the same as the temperature of surface...it is because according to lumped heat analysis temperature of the body is uniform throughout its mass at any instant of time ..ie internal temperature gradients within the body is neglected...