10-int_lam_flw2-1-1

10-int_lam_flw2-1-1 - Module 10 1 Internal Laminar Flow-II...

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Module 10 ME 6302 1 Internal Laminar Flow-II Professor S.M. Ghiaasiaan G.W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, GA 30332-0405
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Module 10 ME 6302 2 Analytical Solution for Heat Transfer in Circular Tubes • Hydro dynamically-fully developed, thermally-developed flow, uniform heat flux – Energy Equation – Velocity Profile – Thermally-fully developed condition – Resulting equation 1 p TT Cu k r x rr r ρ ∂∂ ⎛⎞ = ⎜⎟ ⎝⎠ 2 2 0 21 avg r uU r =− avg dT T x dx = 2 2 0 avg pa v g dT kT r rC U r r d x
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Module 10 ME 6302 3 Analytical Solution for Heat Transfer in Circular Tubes • Solution • We can now use the above equation in the definition of 42 2 0 00 2 31 1 16 16 4 avg avg s Ur d T rr TT dx r r α ⎛⎞ −= + ⎜⎟ ⎝⎠ 0 r 2 0 0 2 0 1 () ( ) 2 11 48 sa v g s avg avg avg v g u r d r rU Ud T r dx π
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Module 10 ME 6302 4 Analytical Solution for Heat Transfer in Circular Tubes • Combine with overall energy balance : " 0 " 2 48 () 1 1 avg pa v g s s sa v g dT CU q dx r qD hD Nu kT T k ρ = ⇒= = =
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Module 10 ME 6302 5 Hydro dynamically-Fully Developed, Thermally- Developed, Uniform Wall Temperature
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10-int_lam_flw2-1-1 - Module 10 1 Internal Laminar Flow-II...

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