CHE3123 Chap15BW - CHE 3123 Momentum Heat and Mass Transfer...

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CHE 3123 Momentum, Heat and Mass Transfer II “Review Momentum Transport (as in 3113) Newton’s τ μ dv velocity viscosity law dy (eq.7-4) viscosity direction stress of momentum (force/area)
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y fluid moving v along a plate x Fluids that obey this law (water etc. ) are called “Newtonian”
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Besides looking at τ as a stress, or force per unit area, we can also look at τ as, momentum transport per time per area. That is momentum is being transported towards the plate by “fast” particles of fluid rubbing against relatively slow particles Look at units of τ τ force N kg-m area m 2 s 2 .m 2 kg m 1 1 s m 2 s
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(mass) (velocity) momentum area . time area . time HEAT TRANSPORT You will find heat transport easier to understand. Momentum transport involves the transport of a vector quantity, momentum. But heat transport involves only a scalar quantity, thermal energy.
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The relation in heat transfer which is analogous to Newton’s law of viscosity is Fourier’s law heat/time temperature Fourier q x k dT Law A dx area to thermal direction direction of heat conductivity of heat flow transport
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A more general form of this, in vectors notation, is q k T A Observe that q x a flux A energy,momentum,mass stuff (area) (time)
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As this mention of “stuff” suggests, let us write down the third important equation for this course conc. Fick’s first J A,z D A,B dc A law dz (eq 24-15) molar flux diffusivity in z direction (of component A)
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Note that the gradients or driving forces for the three transfer phenomena are dv a velocity gradient dz dT a temperature gradient dz dc A a concentration gradient dz
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