heat - HEAT TRANSFER Mechanisms of Heat Transfer: (1) C...

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HEAT TRANSFER Mechanisms of Heat Transfer: (1) Conduction where Q is the amount of heat, Btu, transferred in time t, h k is the thermal conductivity, Btu/[h ft 2 ( o F/ft)] A is the area of heat transfer normal to heat flow, ft 2 T is the temperature, o F x is the thickness of the conduction path, ft. (2) Convection h is the heat transfer coefficient, Btu/[h ft 2 o F]. dx dT A k dt dQ - = T A h dt dQ = ChE 4253 - Design I
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HEAT TRANSFER Mechanisms of Heat Transfer: (3) Radiation where σ is the Stefan-Boltzmann constant = 0.1713 10 -8 Btu/(h ft 2 o R 4 ) ε is the emissivity of surface A is the exposed area for heat transfer, ft 2 T is absolute temperature, o R. 4 T A dt dQ = ChE 4253 - Design I
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Heat Transfer - Steady State (1) Conduction where q is the rate of heat transfer, Btu/h (2) Convection (3) Radiation (from pipe) where h r is a fictitious heat transfer coefficient based on the rate at which heat leaves the surface of the pipe due as radiation. For this case: x T A k q t Q - = = T A h q = T A h q r = 1 ( 29 ( 29 [ ] 2 1 4 2 4 1 1 100 100 171 . 0 T T T T h r - - = ε ChE 4253 - Design I
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Overall Heat Transfer Coefficient Definition of the overall heat transfer coefficient, U U [=] Btu/(h ft 2 o F) DT tot is the total temperature difference (overall driving force for the process). Important: The overall heat transfer coefficient, U, is an empiricism. It is a very useful engineering concept that “sweeps the details under the rug”. It is defined in combination with the area A (e.g., inside/outside area of a pipe). tot T A U q = ChE 4253 - Design I
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General correlation: Intensity=Potential/Resistance Rate = Driving Force/Resistance Applies for electricity, flow, flux etc. Heat transport: Overall resistance, R=1/UA Overall Heat Transfer Coefficient tot T A U q = r in r out Heat flux ChE 4253 - Design I
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Resistances in series: Overall resistance = Sum of resistances In our case: U o : overall heat transfer coefficient based on the outside area h o , h i : outside/inside film heat transfer coefficient d o , d i : outside/inside pipe diameter k w : wall thermal conductivity h od , h id : outside/inside fouling heat transfer coefficient Overall Heat Transfer Coefficient r in r out Heat flux ( 29 id i o i i o w i o o od o o h d d h d d k d d d h h U 1 1 2 ln 1 1 1 + + + + = ChE 4253 - Design I
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Double-pipe exchanger, used for cooling or heating. Shell and tube heat exchangers, used for all applications. Plate-fin exchangers. Spiral heat exchangers. Air cooled: coolers and condensers. Direct contact: cooling and quenching. Agitated vessels.
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heat - HEAT TRANSFER Mechanisms of Heat Transfer: (1) C...

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