Question

Solve the following problem using Finite Difference Method An aluminum bar is of a trapezoidal cross section as shown in the schematic. The upper and lower faces are adiabatic. The upper face length is 20 mm, lower face is 40 mm, and the height is 20 mm. The left and right faces are at temperatures Th = 100°C and Tc = 0°C, respectively. Assume the heat conduction is steady state. 1) Determine the temperature distribution using a finite difference approach with ?x = ?y = 10 mm. 2) Determine the heat transfer rate per unit bar length. 3) Compare the heat rate to that of a bar of a 20 mm × 30 mm rectangular cross section where the height of the domain is 20 mm (for rectangular cross section, you may use theoretical calculations based on 1D assumption). 4) Repeat steps 1, 2 and 3 using a finer mesh with spacing of ?x = ?y = 5 mm. 5) Compare the temperature distributions and total heat transfer rates of the coarse and finer meshes.

          Solve the following problem using Finite Difference Method

An aluminum bar is of a trapezoidal cross section as shown in the schematic. The upper and lower faces are adiabatic. The upper face length is 20 mm, lower face is 40 mm, and the height is 20 mm. The left and right faces are at temperatures Th = 100°C and Tc = 0°C, respectively. Assume the heat conduction is steady state.

1) Determine the temperature distribution using a finite difference approach with ?x = ?y = 10 mm.
2) Determine the heat transfer rate per unit bar length.
3) Compare the heat rate to that of a bar of a 20 mm × 30 mm rectangular cross section where the height of the domain is 20 mm (for rectangular cross section, you may use theoretical calculations based on 1D assumption).
4) Repeat steps 1, 2 and 3 using a finer mesh with spacing of ?x = ?y = 5 mm.
5) Compare the temperature distributions and total heat transfer rates of the coarse and finer meshes.

Solve the following problem using Finite Difference Method

An aluminum bar is of a trapezoidal cross section as shown in the schematic. The upper and lower faces are adiabatic. The upper face length is 20 mm, lower face is 40 mm, and the height is 20 mm. The left and right faces are at temperatures Th = 100°C and Tc = 0°C, respectively. Assume the heat conduction is steady state.

1) Determine the temperature distribution using a finite difference approach with ?x = ?y = 10 mm.
2) Determine the heat transfer rate per unit bar length.
3) Compare the heat rate to that of a bar of a 20 mm × 30 mm rectangular cross section where the height of the domain is 20 mm (for rectangular cross section, you may use theoretical calculations based on 1D assumption).
4) Repeat steps 1, 2 and 3 using a finer mesh with spacing of ?x = ?y = 5 mm.
5) Compare the temperature distributions and total heat transfer rates of the coarse and finer meshes.

Added by Stacy Y.

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