BF1-Ch03

# BF1-Ch03 - CHAPTER THREE STEADY-STATE ONE DIMENSIONAL HEAT...

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CHAPTER THREE STEADY-STATE ONE DIMENSIONAL HEAT CONDUCTION 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.

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One-Dimensional, Steady-State Conduction No heat generation. The Plane Wall Recall: Steady-state condition with no distributed source or sink of energy: ( ) p T T k q c x x t ρ + = &
If k is a constant, then the above equation reduces to Example: Steady-state heat conduction in the slab (with no heat generation) is modeled by Eqn (1) Integrating Eqn (1) twice: ( ) 0

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BF1-Ch03 - CHAPTER THREE STEADY-STATE ONE DIMENSIONAL HEAT...

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