a$)(20$ marks$)$

A $25$ cm diameter stainless steel ball $)=8055\frac{kg}{m^3},c_1=(480\frac{J}{k}gC$ is removed from the oven at a uniform temperature of $300C.$ The ball is then subjected to flow of air at $1$ atm pressure and $25C$ with a velocity of $3\frac{m}{s}.$ The surface temperature of the ball eventually drops $200C.$ Using an illustrative diagram, estimate,

i$)$ The average convection heat transfer coefficient during cooling

ii$)$ The average rate of heat loss from the ball by convection

iii$)$ The cooling time $($using convection method only$).$

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