关键词 > MATS3006/6110
MATS3006/6110 – Theoretical Part
发布时间：2022-06-27
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Sample EXAMINATION
MATS3006/6110 – Theoretical Part
1. Answer the following four questions: (15 marks)
(i) What are the main advantages and disadvantages of discretization of the governing equations through the FDM?
(ii) Define the under-relaxation factor. State its advantages and disadvantages when using a small value.
(iii) For the unsteady convection-diffusion process, what is the difference between explicit and implicit time-marching approaches?
2. Consider a 1D convective-type equation
∂φ ∂φ
∂t ∂x
where u is the flow velocity. Use FVM and Crank-Nicolson scheme to approximate the equation. (15 marks)
3. Considering the cooling process of a circular fin by means of convective heat transfer along its length (see figure below), governed by
− a(T − T∞ ) = 0
where a is a parameter and T∝ is the ambient temperature. The fin has a uniform temperature at the cross sectional area (in the radial direction). The base (left side) of the fin is at a constant temperature TB of 100° and the top (right side) of the fine is fully insulated.
Data: L = 1.0 m, a = 25, T∝=20°
Divide the fin into 5 equally spaced cells and use FVM to calculate the temperature distribution of the fin.
Your answer should include:
• A schematic drawing of FVM discretisation of the system
• A general algebraic equation converted from the governing equation
• A set of equations expressing the temperature T of 5 cells
• The value of T at each cell (20 marks)
