engineering recuitment GATE ME 2023-24 Test Series Heat Transfer Conduction Conduction with Uniform Heat Generation
Uniform internal heat generation at \(\dot q = 5 \times {10^7}\frac{W}{{{m^3}}}\) is occurring in a cylindrical nuclear reactor fuel rod of 50 mm diameter. Under steady state conditions, the temperature varies as T(r) = a + br2, where T is in °C and r is in meters, while a = 800°C and b = -4.167 × 105 °C/m2. The fuel rod properties are K = 30 W/m-K, \(\rho = 1100\;\frac{{kg}}{{{m^3}}}\) and CP = 800 J/kg-K
1
The rate of heat transfer per unit length of the rod at r = 0 (the centreline) is 0
2
The rate of heat transfer per unit length of the rod at r = 25 mm (the surface) is 98 kW/m
3
If the reactor power level is suddenly increases to \({\dot q_2} = {10^8}\frac{W}{{{m^3}}}\) the initial time rate of temperature change at r = 0 and r = 25 mm is 56.82 K/s
4
If the reactor power level is suddenly increases to \({\dot q_2} = {10^8}\frac{W}{{{m^3}}}\) the initial time rate of temperature change at r = 0 and r = 25 mm is 45.56 K/s