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Uniform internal heat generation at  q˙⁢ = 2.00 × 107 W/m3 is occurring in a cylindrical nuclear...

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Mechanical Engineering

Uniform internal heat generation at  q˙⁢ = 2.00 × 107W/m3 is occurring in a cylindrical nuclear reactor fuelrod of 50-mm diameter, and under steady-state conditions thetemperature distribution is of the form T(r)=a+br^2, where T is indegrees Celsius and r is in meters, while a= 800 °C and b=-4.167 × 105 °C/m2. The fuel rod propertiesare k= 30 W/m·K, ρ= 1100 kg/m3, and cp= 800 J/kg·K.

Find the steady state temperature gradient, d⁢T/d⁢r, at theouter surface of the rod, in °C/m.

What is the steady state rate of heat transfer at the outersurface, in W/m?

Immediately after the sudden increase in reactor power level (att= 0 sec), what is the temperature at the centerline?

Immediately after the sudden increase in reactor power level (att= 0 sec), what is the time rate of temperature change, d⁢T/d⁢t, atthe centerline, in °C/s?

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