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# testnotes - NCSU-MAE310 TEST NOTES FOR CONDUCTIVE HEAT...

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NCSU-MAE310 08/26/04 T EST N OTES FOR C ONDUCTIVE H EAT T RANSFER Definitions E = heat transfer (J) q = rate of heat transfer (W) q"=q/A = rate of heat transfer per unit area, flux (W/m 2 ) q'=q/L = rate of heat transfer per unit length (W/m) q = heat generated per unit volume (W/m 3 ) α =k/( ρ c) = thermal diffusivity (m 2 /s) ν = μ / ρ = kinematic viscosity (m 2 /s) Rate Equations Conservation of Energy: E in + E generated - E out = E stored = ρ c p 2200 T t Fourier's Law: q x = - k A T x Newton's Law of Cooling: q = h A (T-T ) Thermal Resistances R= T / q Convection: R = 1 h A Planar Conduction: R = L k A Radial Cylindrical Conduction: R = ln (r o /r i ) 2 π k L Radial Spherical Conduction: R = 1 4 π k ( 1 r i - 1 r o ) Conduction Shape Factor S= q / k T Dimensionless Quantities Bi = h L c k , Fo = α t L c 2 , L c = 2200 A s Extended Surfaces Fin Efficiency: η f = q fin h A f (T b - T ) Fin Effectiveness: ε f = q fin h A c,b (T b - T ) Overall Surface Efficiency: η o = q total h A total (T b - T ) = 1 - A fin A total (1 - η f )

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NCSU-MAE310 08/26/04 Temperature Distribution and Heat Loss for Fins of Uniform Cross Section CASE Tip Condition Temperature Distribution θ / θ b Fin Heat Transfer Rate q fin A Convection h θ L = - k d θ dx (L) cosh [m (L-x)] + (h/mk) sinh [m (L-x)] cosh (mL) + (h/mk) sinh (mL) M sinh (mL) + (h/mk) cosh (mL) cosh (mL) + (h/mk) sinh (mL) B Adiabatic d θ dx (L) = 0 cosh [m (L-x)] cosh (mL) M tanh (mL) C Prescribed Temp θ (L) = θ L ( θ L / θ b
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testnotes - NCSU-MAE310 TEST NOTES FOR CONDUCTIVE HEAT...

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