An H-section copper conductor carries an overload current of 54000 A. Under steady state conditions, the surface temperature is 60°C.

The dimensions of the bar are given in Figure 1 overleaf, and you are asked to use a numerical method to produce a mesh plot of the temperature distribution and a graph of the temperature distribution along the line y = 0.

The electrical resistivity, ρ, of copper is 2 × 10-8 Ω m, and the thermal conductivity, κ, is 0.311 kW m-1 K-1.

The governing differential equation is ∂2T + ∂2T + g = 0 (1)
∂x2 ∂y2 κ where g is the (constant) generation rate of heat per unit volume:

g = i2ρ (2) and i is the current density.

Using an appropriate Numerical Technique:

Determine the temperature distribution to an accuracy of 4 significant figures

You are expected to hand in the following by the submission date:

Hints

The Gauss-Seidel technique used in Tutorial 9 can be adapted to the present problem by including the additional term g/κ in the finite difference equation. You can generate a mask array as in Tutorial 9 to specify the region of the array covered by the H cross- section.

Try calculating the solution over a square mesh for a range of step lengths h = 5 mm, 2.5 mm, 1.25 mm…
You can if you wish make use of the symmetry of the problem and model just one quarter of the conductor. However, the boundary conditions then become more difficult to apply.

The H section is of width 40mm, depth 30mm and cut outs on top and bottom of depth 10x width 20 mm

Any help would be most appreciated

Cheers

SamAn H-section copper conductor carries an overload current of 54000 A. Under steady state conditions, the surface temperature is 60°C.

The dimensions of the bar are given in Figure 1 overleaf, and you are asked to use a numerical method to produce a mesh plot of the temperature distribution and a graph of the temperature distribution along the line y = 0.

The electrical resistivity, ρ, of copper is 2 × 10-8 Ω m, and the thermal conductivity, κ, is 0.311 kW m-1 K-1.

The governing differential equation is ∂2T + ∂2T + g = 0 (1)
∂x2 ∂y2 κ where g is the (constant) generation rate of heat per unit volume:

g = i2ρ (2) and i is the current density.

Using an appropriate Numerical Technique:

Determine the temperature distribution to an accuracy of 4 significant figures

You are expected to hand in the following by the submission date:

Hints

The Gauss-Seidel technique used in Tutorial 9 can be adapted to the present problem by including the additional term g/κ in the finite difference equation. You can generate a mask array as in Tutorial 9 to specify the region of the array covered by the H cross- section.

Try calculating the solution over a square mesh for a range of step lengths h = 5 mm, 2.5 mm, 1.25 mm…
You can if you wish make use of the symmetry of the problem and model just one quarter of the conductor. However, the boundary conditions then become more difficult to apply.

The H section is of width 40mm, depth 30mm and cut outs on top and bottom of depth 10x width 20 mm

Any help would be most appreciated

Cheers

Sam An H-section copper conductor carries an overload current of 54000 A. Under steady state conditions, the surface temperature is 60°C.

The dimensions of the bar are given in Figure 1 overleaf, and you are asked to use a numerical method to produce a mesh plot of the temperature distribution and a graph of the temperature distribution along the line y = 0.

The electrical resistivity, ρ, of copper is 2 × 10-8 Ω m, and the thermal conductivity, κ, is 0.311 kW m-1 K-1.

The governing differential equation is ∂2T + ∂2T + g = 0 (1)
∂x2 ∂y2 κ where g is the (constant) generation rate of heat per unit volume:

g = i2ρ (2) and i is the current density.

Using an appropriate Numerical Technique:

Determine the temperature distribution to an accuracy of 4 significant figures

You are expected to hand in the following by the submission date:

Hints

The Gauss-Seidel technique used in Tutorial 9 can be adapted to the present problem by including the additional term g/κ in the finite difference equation. You can generate a mask array as in Tutorial 9 to specify the region of the array covered by the H cross- section.

Try calculating the solution over a square mesh for a range of step lengths h = 5 mm, 2.5 mm, 1.25 mm…
You can if you wish make use of the symmetry of the problem and model just one quarter of the conductor. However, the boundary conditions then become more difficult to apply.

The H section is of width 40mm, depth 30mm and cut outs on top and bottom of depth 10x width 20 mm

Any help would be most appreciated

Cheers

Sam differential equations, conductivity, homework, doit4me MATLAB Answers — New Questions

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