Question

3. In a heat treatment process, a metal cube of side 2 cm, density 6000 kg/m', and specific heat 300 J/kg.K is heated by convection from a hot fluid at temperature TE = 220 °C. The initial temperature of the cube is T; = 20 °C. If the temperature T within the cube may be taken as uniform, write down the equation that governs the temperature as a function of time t. Obtain the general form of the solution. If the measured temperature values at different time intervals are given as: 0 0.5 1.0 2.0 3.0 6.0 + (min) T-T 7.-T, 1.0 0.85 0.72 0.5 0.4 0.14 obtain a best fit to these data using information from the analytical solution for T(T). Sketch the resulting curve and plot the original data to indicate how good a representation of the data is obtained by this curve. From the results obtained, compute the heat transfer coefficient h.

please help, thermal design aubject

Answer 1

0.5 I min 2.0 3.0 6.0 0.5 0.4 0.14 0.72 0.85 1.0 We know according humped heat analysis T-TE - Int e Ti - Tt 1 Imin = 60sec case 1 hx30x6 G000x300x 0.02) e 0.85 - t=30sec 32.50 he as wlm²k 60 come 2. hxo x 6 160 x 30 x002 0.72 = С. t = Gosed h = 32.85 wlmek Case 3. x 120x 0.5 = C 6000 x 300 x 0.02 t = 120 sec 34.67 w/mk