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Ch2-Intro to Conduction - Chapter 2 Introduction to...

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Chapter 2 Introduction to Conduction
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A rate equation that allows determination of the conduction heat flux from knowledge of the temperature distribution in a medium Fourier’s Law Its most general (vector) form for multidimensional conduction is: ′′ = - q k T Implications: Heat transfer is in the direction of decreasing temperature (basis for minus sign). Direction of heat transfer is perpendicular to lines of constant temperature (isotherms). Heat flux vector may be resolved into orthogonal components
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(2.22) φ ′′ = - - - T T T q k i k j k k r r z ′′ r q φ ′′ q ′′ z q Cylindrical Coordinates: ( 29 , , T r z φ sin θ θ φ ′′ = - - - T T T q k i k j k k r r r (2.25) ′′ r q θ ′′ q φ ′′ q Spherical Coordinates: ( 29 , , T r φ θ Cartesian Coordinates: ( 29 , , T x y z ′′ = - - - T T T q k i k j k k x y z ′′ x q ′′ y q ′′ z q (2.3) 2 π ′′
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