### Write a code using the Finite-Volume-Method -

**Assignment Detail:- ** SEM400 Computational Fluid Dynamics - Deakin University
Assignment: Programming Exercise
In your first assignment, you will have to complete a programming task- You can use any programming language you prefer, but we recommend MatLab, as it allows for relatively easy implementation and visualization- You can use programming libraries only for the solution of linear algebraic problems -e-g- linsolve-A,b- or inv-A-- and for plotting data- All other routines need to be programmed in primitive statements -i-e, if statements, loops and assignments-- We can offer support for MatLab, C and Fortran-
Your task is to write a code using the Finite-Volume-Method -FVM- to solve the following 1D equations-
Question 1-: Solve the 1D heat conduction equation without a source term-
The 1D heat conduction equation without a source term can be written as:
d/dx -k-dT/dx- = 0
Where k is the thermal conductivity, T the local temperature and x the spatial coordinate-
Using the Finite Volume Method, use this equation to solve for the temperature T in a rod- The rod has a length of L = 2-0 m, a cross-section area of A = 10·10-2m3, the thermal conductivity is k = 1500 W/Km, and the temperatures at the ends are held constant at 200°C and 600°C, respectively
Question 2-: Solve the 1D heat conduction equation with a source term-
The 1D heat conduction equation with a source term can be written as:
d/dx -k-dT/dx- + q = 0
with k being the thermal conductivity, T the local temperature, x the spatial coordinate and q the source term-
Using the Finite Volume Method, use this equation to solve for the temperature T across the thickness of a flat plate of thickness L = 3 cm- The thermal conductivity is k = 1-25 W/Km, and the temperatures at the two ends are held constant at 150°C and 300°C, respectively- An electric current creates a constant heat source of q = 1100 kW/m3-
Question 3-: Solve the 1D convection-diffusion problem
The 1D convection-diffusion problem can be written as:
d/dx -ρuΦ- = d/dx-ΓdΦ/dx-
With Φ the property that is being transported, u the convection speed, Γ the diffusivity and ρ the density-
The length of the domain is L = 1-0 m, the density is ρ = 1-0 kg/m3, the diffusivity Γ = 0-1 kg/ms- Determine the distribution of Φ for the following cases-
i- u = 0-1 m/s using 5 cells-ii- u = 2-5 m/s using 5 cells-iii- u = 2-5 m/s using 20 cells
For Assignment 1, you need to submit your results for the programming exercise:
1- The MatLab code-s- -eg- myFVM-m-2- A report
This part of the assignment will contribute 20% to your final grade- You will be graded on
• The code -working, easy readable, adaptable, efficient- -5 percentage points-• Verification -compare to analytical results- -5 percentage points-• Project report -10 percentage points-a- Explain approach and code -!--b- Show verification, results andc- Interpretation, especially regarding your results from the convection-diffusion problem-d- Show how the code can be used for other problems -i-e- set your own boundary conditions and solve, 1 example--

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