Questions

1. A nuclear fuel element of thickness 2L is covered with a steel cladding of thickness b. Heat generated within the nuclear fuel at a rate, , is removed by a fluid T∞, which adjoins one surface and is characterized by a convection coefficient h. The other surface is well insulated and the fuel and the steel have a thermal conductivity of ks and kf respectively

(a) Obtain an equation for temperature distribution T(x) in the nuclear fuel(b) For kf = 60W/mK, L = 15 mm, b=3mm, ks=15 W/mK, h=10000W/m2K and T∞=200oC,

what are the largest and the smallest temperature in the fuel element. If the heat is generated uniformly at a volumetric rate of q=2x107W/m3. What are the corresponding locations?

2. Determine the temperature distribution in a solid plate having uniform heat generation q ' ' '

,and variable thermal conductivityk=k o(1+ βT ), ; where β is a constant (K-1). The left

and right side of the plate are maintained at the same constant temperature, Tw.

3. A bar of square cross-section connects two metallic structures; both structures are maintained at a temperature 200°C. The bar, 20mm x 20 mm, is 100mm long and is made of mild steel (k = 0.06 kW/m K). The surroundings are at 20°C and the heat transfer coefficient between the bar and the surroundings is 0.01 kW/mK. Derive an equation for the temperature distribution along the bar and hence calculate the total heat flow rate from the bar to the surroundings. Write down the assumptions

T = 200° C

k = 0.06 kW/m L = 100 mm h = 0.001 kW/mK

T =200°C

Ts = 20° C

LL

bb

Steel

Steel

\

Insulation

Nuclear Fuel

h, T∞

x

4. Derive the steady state temperature distribution in the rectangular plate as shown in the figure and evaluate the temperature at point A, B, C respectively if T = 50 K, q =100 W/m2, l =1m, b=2m. Point B is located at the center of the rectangle, black strips in the figure shows the insulation

.

5. A two-dimensional rectangular plate is subjected to the boundary conditions shown. Derive an expression for the steady-state temperature distribution T(x, y)

T

q

T = 0

T = 0

T = 0

T = Ay2

a

b

A

C Bl

b/4

b/4

l/4

b