22. Develop an algorithm, along with the program (preferably in python), to find the temperature distribution in the example below NOTE: Use the explicit finite differences method EXAMPLE 5.9 A fuel element of a nuclear reactor is in the shape of a plane wall of thickness 2L = 20 mm and is convectively cooled at both surfaces, with h = 1100 W/m². K and T=250°C. At normal operating power, heat is generated uniformly within the element at a volumetric rate of q₁ = 107 W/m³. A departure from the steady-state conditions associated with normal operation will occur if there is a change in the generation rate. Consider a sudden change to q₂ = 2 × 107 W/m³, and use the explicit finite-difference method to determine the fuel element temperature distribu- tion after 1.5 s. The fuel element thermal properties are k = 30 W/m . K and a = 5 × 10-6 m²/s.

Figure Q2 shows discrete locations of sampled soil electrical conductivity (dS/m). Estimate the magnitude of electrical conductivity at points P, R and T using inverse distance weighting 24 24 Estimate the accuracy of the estimation based on R² if the actual values at P is 5.2 dS/m, at 11 dS/m, and 6.9 dS/m at R 21 12 18 15 12 11 9 6 3 3 1.5 23 R 0 3 6 9 50 17 T 12 12 15 18 Figure Q2 24 21 24

1. Suppose you have a 4-foot metal rod, made out of steel which has a thermal conductive factor of a = 4 Assume the temperature on the ends of the rod is always 0 degrees. a) Filling in the numerical parameters mentioned above in the problem, write down the general solution to this heat equation, which should include some unknown coefficients (c,'s), in addition to t's and x's.

One-dimensional, steady-state conduction with uniform internal energy generation occurs in a plane wall which is subject to convection on the left side at x = 0 and being well-insulated on the other.a) Specify the mathematical model defining T(x): provide a governing differential equation and appropriate boundary conditions. Express your answer in terms of defined variables rather than numerical values with units. b) Solve for the temperature profile T(x) referencing the x-origin as shown on the left surface (again expressing your answer in terms of defined variables rather than numericalvalues.) c) Find the maximum temperature in the wall and the wall surface temperature if the volumetric generation is qdot = 1 MW/m^3 with the remaining parameters as specified in the figure.

The steady-state distribution of temperature on a heated plate can be modeled by the Laplace equation, a²T ²T + a²x a²y If the plate is represented by a series of nodes as illustrated in Figure, centered finite-divided differences can be substituted for the second derivatives, which results in a system of linear algebraic equations. Use the Gauss-Seidel method to solve for the temperatures of the nodes in Figure. 0= Submission date: 09/01/2024 25°C T12 T₂2 250°C # T₁1 T₂1 250 CO 75°C 25°C 75°C 0°C 0°C