Question

5.005 Study A spherical Pyrex glass shell has inside and outside diameters of D1 = 0.1 m and D2 = 0.2 m, respectively. The inner surface is at Ts,1 = 100°C while the outer surface is at Ts2 = 45°C. (a) Determine the temperature at the midpoint of the shell thickness, Trm = 0.075 m). (b) For the same surface temperatures and dimensions as in part (a), show how the midpoint temperature would change if the shell material were aluminum. (a) T(m)glass= (b) T(m)aluminium =

Answer 1

Sol. Given, d, = 0.1m = = d = 0.05m dez 0.2m + ſ = do = 0.1 m. Mid pant (mm) = 0.075 m Grien, Tsy = 105c, T5,2 = 45°c. Ein = Cout Ti-To Tm - T2 Tornio - Tim - Tz re-rm To - Im km-r 41 Krium 4ТК Г, Үm T-Tm TM-T2 rm-r -rm 12. 100 - Im Tm - 45 0.075-0.05 0.1-0.075 0.05 01 2 (100-Tm) - uC Tm-45) 100 - Tm = 2Tm- 90. - 31m = 190 | Tm = 63.33°C

☺ from equation for The Same surface temperature of dimensions as in part @, we can say the mid pant temperature is independent of the shell material (since kis not there) luminium = 6333°C