testnotes - NCSU-MAE310 08/26/04 T EST N OTES FOR C...

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Unformatted text preview: 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 ) =k/( c) = thermal diffusivity (m 2 /s) = / = kinematic viscosity (m 2 /s) Rate Equations Conservation of Energy: E in + E generated- E out = E stored = 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 k L Radial Spherical Conduction: R = 1 4 k ( 1 r i- 1 r o ) Conduction Shape Factor S= q / k T Dimensionless Quantities Bi = h L c k , Fo = t L c 2 , L c = 2200 A s Extended Surfaces Fin Efficiency: f = q fin h A f (T b- T ) Fin Effectiveness: f = q fin h A c,b (T b- T ) Overall Surface Efficiency: o = q total h A total (T b- T ) = 1 - A fin A total (1 - f ) NCSU-MAE310 08/26/04 Temperature Distribution and Heat Loss for Fins of Uniform Cross Section CASE Tip Condition Temperature Distribution / b Fin Heat Transfer Rate q fin A Convection h L = - k d 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 dx (L) = 0 cosh [m (L-x)] cosh (mL) M tanh (mL)...
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testnotes - NCSU-MAE310 08/26/04 T EST N OTES FOR C...

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