A copper sphere of 10-mm diameter, initially at a prescribed elevated temperature T;, is quenched in a

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A copper sphere of 10-mm diameter, initially at a prescribed elevated temperature T;, is quenched in a saturated (1 atm) water bath. Using the lumped capacitance method, estimate the time for the sphere to cool

(a) From T_i = 130°C to 110°C and

(b) From Ti = 550°C to 220°C. Plot the temperature history for each quenching process.

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KNOWN Copper sphere 10 mm diameter initially at a prescribed elevated temperature is quenched in a saturated 1 atm water bath FIND The time for the sphere to cool a from T 130 to 110C and b from T 550C to 220C SCHEMATIC Water 100 C Tsat 3 Sphere D 10 mm copper Quenching processes a T 130 to 110 C b T 550 to 220 C 9 ASSUMPTIONS 1 Sphere approximates lumped capacitance 2 Water saturated at 1 atm PROPERTIES Table A1 Copper p 8933 kgm Table A11 Copper polished 004 typical value Table A4 Water as required for the pool boiling correlations ANALYSIS Treating the sphere as a lumped capacitance and performing an energy balance see Eq 514 dT dt in out st Asp For the sphere VD 6 and A MD Using the IHT Lumped Capacitance Model to solve this differential equation we need to specify 1 the specific heat of the copper sphere as a function sphere temperature use IHT Properties Tool Copper and 2 the heat flux qs associated with the pool boiling processes use IHT Correlations Tool Boiling 12 a Cooling from T 130 to 110 Nucleate pool boiling Rohsenhow correlation Eq 105 b Cooling from T 550 ...View the full answer

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