Question #223924

A metal ball (radius 2.5 cm) initially at a uniform temperature of 450°C is suddenly placed in a controlled environment in which the temperature is maintained at 100°C. The convective heat transfer coefficient is 10 W/(m² -K). Determine the time taken (in hours) for the metal ball to cool to 150 °C ? Clearly mention the suitable assumptions if necessary?. Property data are given below.

Property of all metal ball,unit ___________ value

Density, kg/m³_______7800

Thermal conductivity,W(m-°C)____35

Heat capacity, (J/kg-°C) 460

Expert's answer

Time Required for Heating/Cooling is given by the formula:

[ M x C p x Log(( T - t1 )/( T- t2 )) ] / (U x A ).

We can substitute the provided data to obtain how long it will take for metl ball to cool to

150 °C

Data:

Density, kg/m³: 7800

Thermal conductivity,W(m-°C): 35

Heat capacity, (J/kg-°C): 460

[ 150 x C 7800 x Log(( T -35)/( T- 2.5 )) ] / (450 x `10 ).

This gives the value of T as 3.2 hours

It implies it will take 3.2 hours for the reaction to cool to 150 °C

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