Question

3. In a heat treatment process, a metal cube of side 2 cm, density 6000 kg/m², and specific heat 300 J/kg.K is heated by convection from a hot fluid at temperature T, = 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: t (min) 0 0.5 1.0 2.0 3.0 6.0 T-T, 1.0 0.85 0.72 T-T 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.

Answer 1

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Dala given Tmin 2 3 6 I- It' Hi-Tf ) 0.85 072 03 Oly IndT-T 0 -0.16252-03283 -0693 -0.9143 -196 IT-TA In/T-Tf) T-18116 Highet from egn Inj I Tf Ti-Tf 11 0.9163 XC PVP 0.6934 0-3286 0.16252 - 0.162525 PxVxCp 0 30 120 1 8 0.4252 px VX D.1852 x 6000 x 6.0233 X800 Bo 60-02)2 32.504 W/m²K 1

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