A heat transfer engineer is working on the better understanding of a chimney with a square-shaped cross-section.
We consider a steady heat conduction problem in 2D. These can be solved analytically, numerically or through a conductance shape factor look-up table. The latter are particularly popular while easy to use. Take ‘Shape factor #5’ from table 3.2 in ‘Mills’: conduction through concentric square cylinders. We investigate how good it is…
· Write a computer program to calculate this shape factor; based on my numerical code as attached: Adapt the grid (to a square and/or #cells), and impose the appropriate BC for outside and for the inner square (by simply overwriting the intended inner block of cells after each Jacobi- step with the intended initial condition). A hint how to do that is already added.
Apply ratios a/b = 2, 3/2, 4/3, 5/4 and 8/7. Take care for yourself that the grid is correctly fitting the values, and also for each be critical on the number of grid points to use.
· Compare your numerical result with the outcome of Shape factor #5. (directly)
· Construct the same geometry from ‘flat plates’ and ‘edges’ (Shape factor #10).
Compare the three methods tabular and in a graph.
b) Application. Assuming the models in a) are appropriate, design a reasonable chimney for a 1 GWe coal-fired power plant of 40% efficiency.
The chimney will be 100 m high, and of (constant over height) inner dimension 12 m.
It will also need to withstand windforce 12.
- What is a realistic wall thickness regarding wind loading?
Brick material has been used as a building material.
Hint: determine compressive and tensional stresses at the foot of the pipe.
- What will be the exhaust temperature of the Chimney, assuming we have an inlet temperature to the Chimney of 100oC, at a throughput of 100 kg of exhaust gas/s?
Will condensation occur?
A small report ~10 pages, containing some relevant pictures and the code for a/b = 1.5.