Question

Consider a large uranium plate of thickness L = 4 cm and thermal conductivity k = 28 W/m·K in which heat is generated uniformly at a constant rate of ? = 5 × 10^6 W/m³ as shown in Figure 1. One side of the plate is maintained at 0°C by iced water while the other side is subjected to convection to an environment at T? = 30°C with a heat transfer coefficient h = 45 W/m²·K. Uranium plate 0°C k = 28 W/m·K ? = 5 × 10^6 W/m³ h T? L 0 1 2 3 4 x Figure 1 Considering a total of five equally spaced nodes in the medium as shown in Figure 1, estimate the temperatures under steady conditions using the finite difference (FD) approach and Microsoft Excel and compare your FD solution with the exact solution.

          Consider a large uranium plate of thickness L = 4 cm and thermal conductivity k = 28 W/m·K in which heat is generated uniformly at a constant rate of ? = 5 × 10^6 W/m³ as shown in Figure 1. One side of the plate is maintained at 0°C by iced water while the other side is subjected to convection to an environment at T? = 30°C with a heat transfer coefficient h = 45 W/m²·K.

Uranium plate
0°C
k = 28 W/m·K
? = 5 × 10^6 W/m³
h
T?
L
0
1
2
3
4
x
Figure 1

Considering a total of five equally spaced nodes in the medium as shown in Figure 1, estimate the temperatures under steady conditions using the finite difference (FD) approach and Microsoft Excel and compare your FD solution with the exact solution.

Consider a large uranium plate of thickness L = 4 cm and thermal conductivity k = 28 W/m·K in which heat is generated uniformly at a constant rate of ? = 5 × 10^6 W/m³ as shown in Figure 1. One side of the plate is maintained at 0°C by iced water while the other side is subjected to convection to an environment at T? = 30°C with a heat transfer coefficient h = 45 W/m²·K.

Uranium plate
0°C
k = 28 W/m·K
? = 5 × 10^6 W/m³
h
T?
L
0
1
2
3
4
x
Figure 1

Considering a total of five equally spaced nodes in the medium as shown in Figure 1, estimate the temperatures under steady conditions using the finite difference (FD) approach and Microsoft Excel and compare your FD solution with the exact solution.

Added by Mark V.

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