A steel ball of diameter $$60$$ $$mm$$ is initially in thermal equilibrium at $${1030^ \circ }C$$ in a furnace. It is suddenly removed from the furnace and cooled in ambient air at $${30^ \circ }C$$ with convective heat transfer coefficient $$h = 20\,W/{m^2}K.$$ The thermo-physical properties of steel are: density $$\rho = 7800\,\,kg/{m^3},$$ , conductivity $$k = 40 W/mK$$ and specific heat $$c = 600 J/kgK.$$ The time required in seconds to cool the steel ball in air from $${1030^ \circ }C$$ to $${430^ \circ }C$$ is

A spherical steel ball of $$12mm$$ diameter is initially at $$100K.$$ It is slowly cooled in a surrounding of $$300K.$$ The heat transfer coefficient between the steel ball and the surrounding is $$5W/{m^2}K.$$ The thermal conductivity of steel is $$20$$ $$W/mK.$$ The temperature difference between the centre and the surface of steel ball is

A fin has $$5mm$$ diameter and $$100mm$$ length. The thermal conductivity of fin material is $$400W/m K.$$ One end of the fin is maintained at $${130^ \circ }C$$ and its remaining surface is exposed to ambient air at $${30^ \circ }C.$$ if the convective heat transfer coefficient is $$40W/{m^2}K,$$ the heat loss (in $$W$$) from the fin is

A small copper ball of $$5$$ $$mm$$ diameter at $$500$$ $$K$$ is dropped into an oil bath whose temperature is $$300$$ $$K.$$ the thermal conductivity of copper is $$400$$ $$W/m.$$ $$K,$$ its density $$9000\,\,kg/{m^3}$$ and its specific heat $$385\,J/kg.\,\,K.$$ if the heat transfer coefficient is $$250\,\,W/{m^2}K$$ and lumped analysis is assumed to be valid, the rate of fall of the temperature of the ball at the beginning of cooling will be, in $$K/s.$$