Question

A hot surface of a plate is cooled by attaching a circular fin (called pin fins) to it. The surface of the plate (left end of the pin) is at 0 °C. The typical fin is 4cm (0.04m) long and a cross-sectional area of A=5x10-6 m2 with a perimeter (P) of 0.006m. The fin is made of cooper with thermal conductivity (K) of 400 W/m°C. The temperature of the surrounding air is T\infty =30 °C with heat transfer coefficient on the surface (including the right end) estimated to be 20 W/m2 °C. a) Use TWO ELEMENTS in your model to estimate the temperature distribution along the fin length (15) marks. b) Find the heat flux in element 1 (5 marks). Note: Please seperately write expression for conductivity matrix and force vectors.

          A hot surface of a plate is cooled by attaching a circular fin (called pin fins) to it. The surface of the plate (left end of the pin) is at 0 °C. The typical fin is 4cm (0.04m) long and a cross-sectional area of A=5x10<sup>-6</sup> m<sup>2</sup> with a perimeter (P) of 0.006m. The fin is made of cooper with thermal conductivity (K) of 400 W/m°C. The temperature of the surrounding air is T<sub>\infty</sub> =30 °C with heat transfer coefficient on the surface (including the right end) estimated to be 20 W/m<sup>2</sup> °C.
a) Use TWO ELEMENTS in your model to estimate the temperature distribution along the fin length (15) marks.
b) Find the heat flux in element 1 (5 marks).
Note: Please seperately write expression for conductivity matrix and force vectors.

A hot surface of a plate is cooled by attaching a circular fin (called pin fins) to it. The surface of the plate (left end of the pin) is at 0 °C. The typical fin is 4cm (0.04m) long and a cross-sectional area of A=5x10<sup>-6</sup> m<sup>2</sup> with a perimeter (P) of 0.006m. The fin is made of cooper with thermal conductivity (K) of 400 W/m°C. The temperature of the surrounding air is T<sub>∞</sub> =30 °C with heat transfer coefficient on the surface (including the right end) estimated to be 20 W/m<sup>2</sup> °C.
a) Use TWO ELEMENTS in your model to estimate the temperature distribution along the fin length (15) marks.
b) Find the heat flux in element 1 (5 marks).
Note: Please seperately write expression for conductivity matrix and force vectors.

Added by Kathleen F.

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