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Heat Transfer from Extended Surfaces

Heat Transfer from Extended Surfaces

(OP)
Need help solving this Heat Transfer course problem, I've been stuck in it for a while now.

Steel balls 12 mm in heating to 1100 K and then slowly cooling to 350 K in an air environment for which Tinf=315 K and h=20 W/m2 K.

a). Assuming the properties of the steel to be k=40 W/m K, p=7800 kg/m and c=600J/kg K, is it reasonable to regard the temperature of steel balls as uniform process?

b). Starting from the balance equation, derive the governing equation with the appropriate initial condition.

c) Find an expression for temperature of steel balls in terms of time t and other relevant parameters, such as initial temperature Ti, air temperature Tinf, convection transfer coefficient h.

d). Estimate the time required for the cooling process.

e) If the air temperature increases with time as Tinf(t)=315K+b*t, where b=0.2K/s. Find an expression for the ball temperature T(t) as a function of time.

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