Slides 4 - One-Dimensional Steady-State Conduction without...

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One One - - Dimensional, Steady Dimensional, Steady - - State State Conduction without Conduction without Thermal Energy Generation Thermal Energy Generation Chapter Three Chapter Three Sections 3.1 through 3.4 Sections 3.1 through 3.4
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Methodology Specify appropriate form of the heat equation . Solve for the temperature distribution . Apply Fourier’s law to determine the heat flux . Simplest Case: One-Dimensional , Steady-State Conduction with No Thermal Energy Generation . Common Geometries: – The Plane Wall : Described in rectangular ( x ) coordinate. Area perpendicular to direction of heat transfer is constant (independent of x ). – The Tube Wall : Radial conduction through tube wall. – The Spherical Shell : Radial conduction through shell wall. Methodology of a Conduction Analysis
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Plane Wall Consider a plane wall between two fluids of different temperature: The Plane Wall Implications: 0 dd T k dx dx ⎛⎞ = ⎜⎟ ⎝⎠ (3.1) Heat Equation: () Heat flux is independent of . x qx ′′ Heat rate is independent of . x Boundary Conditions: ( ) ( ) ,1 ,2 0, s s TT T L T = = Temperature Distribution for Constant : ,2 ss s x Tx T T T L =+ (3.3) k
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Plane Wall (cont.) Heat Flux and Heat Rate : () ,1 ,2 x ss dT k qk T T dx L ′′ =− = (3.5) ,2 x dT kA A T T dx L = (3.4) Thermal Resistances and Thermal Circuits: t T R q ⎛⎞ Δ = ⎜⎟ ⎝⎠ Conduction in a plane wall: , tcond L R kA = (3.6) Convection: , 1 t conv R hA = (3.9) Thermal circuit for plane wall with adjoining fluids: 12 11 tot L R hA kA h A =+ + (3.12) ,2 x tot TT q R = (3.11)
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Plane Wall (cont.) Thermal Resistance for Unit Surface Area : , tcond L R k ′′ = , 1 tconv R h = Units: K/W t R 2 mK / W t R ↔⋅ Radiation Resistance : , 1 trad r R hA = , 1 r R h = () ( ) 22 r s sur s sur hT T T T εσ =+ + (1.9) Contact Resistance : , AB tc x TT R q
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This note was uploaded on 04/02/2008 for the course MAE 310 taught by Professor Kuznetsov during the Spring '08 term at N.C. State.

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Slides 4 - One-Dimensional Steady-State Conduction without...

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