Heat Transfer Course Notes

Heat Transfer Course Notes - LECTURE NOTES ON INTERMEDIATE...

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Unformatted text preview: LECTURE NOTES ON INTERMEDIATE HEAT TRANSFER Mihir Sen Department of Aerospace and Mechanical Engineering University of Notre Dame Notre Dame, IN 46556 January 16, 2003 2 Contents Preface 9 I Preliminaries 11 1 Mathematical review 13 1.1 Fractals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.1.1 Cantor set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.1.2 Koch curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.1.3 Knopp function . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.1.4 Weierstrass function . . . . . . . . . . . . . . . . . . . . . . . 16 1.1.5 Julia set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.1.6 Mandelbrot set . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.2 Dynamical systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.2.1 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.2.2 Bifurcations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.2.3 One-dimensional systems . . . . . . . . . . . . . . . . . . . . . 18 1.2.4 Examples of bifurcations . . . . . . . . . . . . . . . . . . . . . 20 1.2.5 Unfolding and structural instability . . . . . . . . . . . . . . . 23 1.2.6 Two-dimensional systems . . . . . . . . . . . . . . . . . . . . . 23 1.2.7 Three-dimensional systems . . . . . . . . . . . . . . . . . . . . 26 1.2.8 Nonlinear analysis . . . . . . . . . . . . . . . . . . . . . . . . 29 1.3 Singularity theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 II Conduction 33 2 No spatial dimension 35 3 2.1 Justication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.1.1 Steady state . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.1.2 Transient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.2 Convective cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.2.1 Variable h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.2.2 Radiative cooling . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.2.3 Convective with weak radiation . . . . . . . . . . . . . . . . . 40 2.3 Radiation in an enclosure . . . . . . . . . . . . . . . . . . . . . . . . 41 2.4 Long time behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.4.1 Linear analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.4.2 Nonlinear analysis . . . . . . . . . . . . . . . . . . . . . . . . 42 2.5 Time-dependent T . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.5.1 Linear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.5.2 Oscillatory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.6 Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.6.1 PID control . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
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This note was uploaded on 05/21/2008 for the course AEROSPACE Eng taught by Professor Mihrsen during the Spring '02 term at Notre Dame.

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Heat Transfer Course Notes - LECTURE NOTES ON INTERMEDIATE...

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