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Microsoft PowerPoint - Introduction To Heat conduction

# Microsoft PowerPoint - Introduction To Heat conduction -...

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Introduction To Heat conduction Course By : Prof. Mohajer prepared by: S.M. rafigh 2011

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Fourier’s Law • 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. – Fourier’s Law serves to define the thermal conductivity of the medium / k q T → → ′′ ≡ -
Heat Flux Components (2.18) T T T q k i k j k k ′′ = - - - • Cylindrical Coordinates: ( 29 , , T r z φ • 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) r r z r q ′′ q ′′ z q ′′ sin T T T q k i k j k k r r r θ θ φ ′′ = - - - (2.21) r q ′′ q ′′ q ′′ • Spherical Coordinates: ( 29 , , T r φ θ

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Heat Flux Components (cont.) • In angular coordinates , the temperature gradient is still based on temperature change over a length scale and hence has units of ° C/m and not ° C/deg. ( 29 or , φ φ θ Heat rate for one-dimensional, radial conduction in a cylinder or sphere: Cylinder 2 r r r r q A q rLq π ′′ ′′ = = or, 2 r r r r q A q rq ′ ′′ = = Sphere 2 4 r r r r q A q r q ′′ ′′ = =
Heat Equation The Heat Equation • A differential equation whose solution provides the temperature distribution in a stationary medium. • Based on applying conservation of energy to a differential control volume

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Microsoft PowerPoint - Introduction To Heat conduction -...

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