A nickel sphere weighing 1.5 kg, initially at 290 \deg C, is suddenly immersed in a fluid at 15\deg C, with a convective heat transfer coefficient of 58( W)/(m^(2))K. For nickel, k = 90( W)/(m).K, cp = 446( J)/(k)g.K and \rho = 8,906( g)/(c)m^(3.) Justify any approximation made.
(a) Determine the time to cool the piece to 90 \deg C.
(b) Find an expression for the heat transfer rate from the sphere to the fluid as a function of time.