Tutorial_6

Tutorial_6 - ¾ is nearly constant across the width of the...

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Tutorial 6 Question 1 Derive the 1-D wave equation with gravitational and air drag forces included. The guitar string has fixed ends, length, g , diameter, G , material density, ± , cross-sectional area, ² = ³G ´ 4 u , and is under a tensile force, µ . The string is pulled up vertically and, at time, · = 0 , is released from rest. Derive the PDE which describes the vertical displacement of the string, ¸¹º, ·» , for 0 ≤ º ≤ g . Assume: i) ¸ ≪ g ii) dra¼ ∝ ¹Projected Area»¹Velocity» , and acts opposite to the velocity Question 2 A large cooling fin is attached to an engine block. Consider the central portion of the fin where temperature does not change in the ½ direction – i.e. we consider a section far away from the ½ -edges, where the temperature will be the same at any ½ . Assume that the fin is thin, and thus,
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Unformatted text preview: ¾ is nearly constant across the width of the fin, i.e. ¾ = ¾¹º, ·» only. Heat is conducted outwards, down the fin and into the surrounding air. The fin temperature is initially, ¾ = ¾ ¿ at · = 0 . The engine starts and the block heats up to a temperature, ¾ = ¾ À (assume this temperature is reached instantly). (a) Derive equations to predict the fin temperature, ¾¹º, ·» , and the rate of heat transfer out of the engine block. (b) Derive equations which give the steady state situation for the engine block/ fin combination. º = 0 Side View Hot Engine Block air, ¾ ÁÂà º = g º ½ Engine Block g Unit width Section Very large in the ½ direction. Top View º ½ º = g º = 0 · = 0 Ä Å º ½ µ ¶ µ ¶ Thickness, Æ...
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Tutorial_6 - ¾ is nearly constant across the width of the...

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