Question

3.25. 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 T, = 220°C. The initial temperature of the cube is T; = 20°C. If the temperature T within the cube may be taken as uni- form, write down the equation that governs the temperature as a func- tion of time t. Obtain the general form of the solution. If the measured temperature values at different time intervals are given as

Answer 1

The increase in internal (het heat transfer from the body energy of the body ] - HACT-Tp) dt equation -dt T-Tf - SV Cp dT Governing fVCp Crdt ha T IT-TA HA SVCp t lu General form of Solution Ti-TA T(min) 0.5 9 2 3 6 T- Tf 0.85 0172 0.5 0.4 0.14 (T; - If -0.9163-1966 len (T-If 0 -0.16252 -0.3285 Ti-Tf/ -0.693

1.966 In I- If Ti-T (negative) 0.9163 8.693 0-32857 01/62527 120 180 360 og ce Ellecond)

-ha Graph is not a exact straight line. But slope is not changing significantly T-TE Ti-Tf 3 VCp -0.16252 (30 SVCP len -ha 0.16282 HA SUCp 30 0116252 30 X h = 6000 x(0.023x300 6x10.02)2 h= 32.504 W/mk
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