0. HeatTransfer_web

0. HeatTransfer_web - ENU 4134 Single-Phase Heat Transfer...

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Unformatted text preview: ENU 4134 Single-Phase Heat Transfer Review D. Schubring September 8, 2009 Topics I Conduction I Radiation I Convection I Application to Rod Bundles Conduction General conduction equation: c p ( ~ r , T ) T ( ~ r , t ) t = k ( ~ r , t ) T ( ~ r , t ) + q 000 ( ~ r , t ) (1) Conduction (2) Possible simplifications Steady-state constant power in fuel: 0 = k ( ~ r ) T ( ~ r ) + q 000 ( ~ r ) (2) and constant conductivity can be assumed for fuel behavior under certain conditions: 0 = k 2 T ( ~ r ) + q 000 ( ~ r ) (3) and no heat generation cladding: 0 = 2 T ( ~ r , t ) (4) Radiation q 00 out = T 4 (5) Must use absolute temperature! Emissivity ( ) a value between 0 and 1 indicating how efficiently surface emits thermal radiation I In general, can be a function of wavelength, temperature, position, etc. Well model as a constant. Stefan-Boltzmann constant ( ) = 5 . 67 10- 8 W m 2 K 4 (6) Radiation Examples = 1 Temperature of 300 K (atmosphere): q 00 out = T 4 = 5 . 67 10- 8 300 4 = 460 W m 2 (7) Negligible Temperature of 500 K (LWR): q 00 out = T 4 = 5 . 67 10- 8 500 4 = 3 , 500 W m 2 (8) Minor Temperature of 1200 K (VHTR): q 00 out = T 4 = 5 . 67 10- 8 1200 4 = 118 , 000 W m 2 (9) Significant Convection Combination of conduction in the fluid and mass transfer Usually phrased as a heat transfer coefficient, h (sometimes ): h = q 00 T (10) Often correlated as the dimensionless Nusselt number, Nu Nu = hL k (11) L is a length scale ( e.g. , D for round tubes, D h other geometries), and k , the thermal conductivity, is evaluated in the fluid . Laminar Flow...
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0. HeatTransfer_web - ENU 4134 Single-Phase Heat Transfer...

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