This section presents the numerical analyses used to evaluate the thermal behavior of the system. The model uses nodal energy balances and matrix methods to compute temperatures at each node of the simplified grid.

Include:

  • description of Example 4.2

  • description of Example 5.11

  • node diagrams

  • MATLAB solution method

The project requires solving these using matrix methods in MATLAB

Example 4.3

Description: The temperature distribution in the turbine blades exposed to hot gas flow. The turbine blades are thereby divided into equally spaced nodes, where the nods represent specific locations of the blade material. The energy equations are applied for each node taking into account the conduction effects with the neighboring nodes, and the convection effects from the surrounding gases. This allows the logical calculation to estimate the temperature distribution within the turbine blades.

Nodal temperatures for Example 4.3 (K):
T1 = 1650.15 K
T2 = 1650.82 K
T3 = 1653.52 K
T4 = 1660.44 K
T5 = 1674.78 K
T6 = 1708.13 K
T7 = 1647.49 K
T8 = 1647.83 K
T9 = 1649.55 K
T10 = 1655.15 K
T11 = 1664.27 K
T12 = 1673.80 K
T13 = 1644.16 K
T14 = 1643.47 K
T15 = 1641.69 K
T16 = 1646.35 K
T17 = 1653.34 K
T18 = 1658.54 K
T19 = 1642.19 K
T20 = 1640.22 K
T21 = 1637.60 K

Corner, outer

Example 5.11

Description: A fuel element of a nuclear reactor is in the shape of a plane wall with a thickness 2L = 20mm that is convectively cooled on both surfaces. To find the solution, a space increment of 2 mm was used. The nodal network yields 6 unknown nodal temperatures that are solved for using the energy balance method.

Nodal Temperatures for Example 5.11 (Celsius):

2D Steady-State Analysis

Include:

  1. object diagram with nodes

  2. boundary conditions

  3. explanation of method

  4. contour plot of temperature field

  5. discussion of results

The contour plot should come from MATLAB

Transient Analysis – Explicit

Include:

  • explanation of explicit method

  • temperature evolution

  • embedded video of temperature contour animation

Transient Analysis – Implicit

Same structure but with implicit solver results.

Both transient analyses must include videos generated from MATLAB