Question

Example 5 • A cube (k=204W/mK, đ=8.4x10-5m-/s) of 11 cm on each side is initially at a temperature of 400° C. It is suddenly immersed in a tank of oil maintained at 85°C. The convection coefficient is 1100 W/m2 K. Determine the temperature at the center of one face after a time of 1 min by Heisler chart.

Answer 1

y K nicm k llom allem sie Creun dulu Ti= 400€ The may conductivity of me tube K= 204 w/mk The may diffusiuity 2= 8.4x108 m/s ceach sides of my cube Lallem Contechim Caufficiuut h=11ody/ mich Ta=85a find: Tumpersefere at the Centre face ce obtier linne of minuta (2=0 =0 mid plane) charestic of conca T= 1x 60 Second cm = 5.5cm hc.o.ossm 유 fourier's No. fo = です。 8-4x105X1X60 La (coss) fo=1.666 = 11ooxioss Biot Number bis hic K 5.996 204 I. 3.37 Bi for 10666 At Bi7o.) the intemcy Tumperceleno gradicul are not small, therefore intemcy resistance Cannot he negerected. Thusanne plata can nut be Conside as a lumped systemi the Billoo Pesicher charts can be used to find the solution apma problem I fo = 1.666 3.37 and 200 (mid plane Bi ( from the teiseler tirta tm-tar 2:36 chant ). fm-85 = 136 400-05 tma 198.9°C