A stainless steel cylindrical billet [k = 14.4 W/(m K), = 3.9 10??6m2/s] is heated to

Question:

A stainless steel cylindrical billet [k = 14.4 W/(m K), α = 3.9 ×10??6m2/s] is heated to 593?C preparatory to a forming process. If the minimum temperature permissible for forming is 482?C, how long may the billet be exposed to air at 38?C if the average heat transfer coefficient is 85W/(m2K)? The shape of the billet is shown in the sketch.GIVENA stainless steel cylindrical billet exposed to airThermal conductivity (k) = 14.4 W/(m K)Thermal diffusivity (α) = 3.9 × 10??6m2/sInitial temperature (To) = 593?CThe minimum temperature permissible for forming is 482?CAir temperature (T??) = 38?CAverage heat transfer coefficient (hc ) = 85 W/(m2 K)ASSUMPTIONSEnd effects are negligibleConstant heat transfer coefficientConduction in the radial direction onlyUniform thermalproperties