Question #223914

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

First, we solve the given equation by substituting as the values:

Then we understand that:

Property of all metal ball,unit ___________ value= 1620 units

Density, kg/m³_______7800= , kg/m³ 6987, kg/m³

Thermal conductivity,W(m-°C) ____35 += 35.17 W(m-°C)

Heat capacity, (J/kg-°C) 460= 0.4604 J/kg-°C

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