A metal ball of diameter $$60mm$$ is initially at $${220^ \circ }C.$$ The ball is suddenly cooled by an air jet of $${20^ \circ }C.$$ The heat transfer coefficient is $$200\,W/{m^2}.K.$$ The specific heat, thermal conductivity and density of the metal ball are $$400\,\,J/kg.K,\,\,400\,\,W/m.K$$ and $$\,9000\,\,kg/{m^3},$$ respectively. The ball temperature (in $${}^ \circ C$$) after $$90$$ seconds will be approximately.

A cylindrical steel rod, $$0.01$$ $$m$$ in diameter and $$0.2$$ $$m$$ in length is first heated to $${750^ \circ }C$$ and then immersed in a water bath at $${100^ \circ }C.$$ The heat transfer coefficient is $$250\,W/{m^2}$$-$$K.$$ The density, specific heat and thermal conductivity of steel are $$\rho = 7801\,\,kg/{m^3},$$ $$c = 473$$ $$J/kg$$-$$K,$$ and $$k = 43$$ $$W/m$$-$$K,$$ respectively. The time required for the rod to reach $${300^ \circ }C$$ is ________ seconds.

Two cylindrical shafts $$A$$ and $$B$$ at the same initial temperature are simultaneously placed in a furnace. The surfaces of the shafts remain at the furnace gas temperature at all times after they are introduced into the furnace. The temperature variation in the axial direction of the shafts can be assumed to be negligible. The data related to shafts $$A$$ and $$B$$ is given in the following Table.

The temperature at the center-line of the shaft $$A$$ reaches $${400^ \circ }C$$ after two hours. The time required (in hours) for the center-line of the shaft $$B$$ to attain the temperature of $${400^ \circ }C$$ is ____________

A steel ball of $$10$$ $$mm$$ diameter at $$1000$$ $$K$$ is required to be cooled to $$350$$ $$K$$ by immersing it in a water environment at $$300$$ $$K.$$ The convective heat transfer coefficient is $$1000\,\,W/{m^2}$$-$$K.$$ Thermal conductivity of steel is $$40$$ $$W/m$$-$$K.$$ The time constant for the cooling process $$\tau $$ is $$16s.$$ The time required (in $$s$$) to reach the final temperature is __________________.