Page 400 - Introduction to Continuum Mechanics
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384 Energy Equation For a Nowtonian Fluid
where
is the dissipation function for a compressible fluid.We leave it as an exercise [see Prob. 6.39]
to show that the dissipation function <I> can be written
Example 6.17.1
For the simple shearing flow with
Find the rate at which work is converted into heat if the liquid inside of the plates is water with
5
1
2
/* = 2x 10~ lb.s. /ft (0.958 mPa.s), and k = I s" .
Solution Since the only nonzero component of the rate of deformation tensor is
Thus, from Eq. (6.17.4),
_S
Thus, in one second, per cubic feet of water, the heat generated by viscosities is 2.5 x 10
_-J
B.T.U. [or, 0.958x10 joule per cubic meter per second ].
6.18 Energy Equation For a Newtonian Fluid
In Section 4.14 of chapter 4, we derived the energy equation for a continuum to be
where u is the intern al energy per unit mass, p is density, #/ is the component of heat flux
vector, q s is the heat supply due to external sources.
