Question

A cylindrical nuclear reactor fuel rod with a diameter of 60 mm generates uniform internal heat at a rate (q) of 2 x 107 W/m3, and in steady-state conditions, the temperature distribution takes the form T(r) = a + br2, where T is degrees Celsius and r is in metres, and a is 800 °C and b is -4.167 * 105 °C/m2, respectively. The parameters of the fuel rod are k=35 W/m. K, rho=1100 kg/m3, and Cp=800 J/kg. K. Calculate the initial time rate of temperature change at r = 0 (the centreline) and at r = 30 mm (the surface) and the rate of heat transfer per unit length of the rod. (a) What is the convection coefficient when a cold surface is in contact with a fluid that is 100 °C?

Answer 1

The rate of temperature increase in a nuclear reactor core is calculated using the specific heat formula, factoring in the heat transfer rate, the mass of the reactor core, and the specific heat of the core. Additionally, the time to reach a specified temperature increase can be determined using the calculated rate of temperature increase.

Step-by-step explanation:

Rate of Temperature Increase in a Nuclear Reactor

The rate of temperature increase in the reactor core can be calculated using the specific heat formula: Q = mcΔT, where Q is the heat added, m is the mass, c is the specific heat, and ΔT is the change in temperature. Given the heat transfer rate (Q/t) of 150 MW and converting it to watts (1 MW = 1×106 W), we have Q/t = 150×106 W. The mass of the reactor core m is 1.60×105 kg, and the specific heat c is 0.3349 kJ/kg°C, which needs to be converted to J/kg°C by multiplying by 1000.

The formula for the rate of temperature increase (ΔT/t) is then (ΔT/t) = Q/(mc), plugging the values in gives us ΔT/t = (150×106 W) / (1.60×105 kg × 0.3349×103 J/kg°C). Simplifying this results in the rate of temperature increase in °C/s.

For part (b), to calculate the time needed for a 2000°C increase, we use the formula t = ΔT / (ΔT/t), where ΔT is 2000°C, and (ΔT/t) is the rate of temperature increase calculated in the previous step. This gives us the time in seconds to reach a 2000°C temperature increase.