Prediction of batch heat transfer coefficients for pseudoplastic fluids ...
Prediction of batch heat transfer coefficients for pseudoplastic fluids ... Prediction of batch heat transfer coefficients for pseudoplastic fluids ...
6D and e directions and constant density, the equation becomes I A J(eA i£)_ 0 eJft - (3-7 In the system being considered the mechanical energy input is negligible compared to the heat transferred through the 1..Jal1s. The energy equation for this case is (21) d T 0tdT J/p (-'c;; ( d-c -;- J~ ";-;t ) 7 -f liz dT ) = J& oiL! J [; (3-8 The temperature gradients in the e direction are zero, and the temperature gradients in the z direction are also assumed zero.. Therefore equation 3-8 reduces to Equations 3-5, 3-7 and 3-9 thus describe the model (3-9 discussed above. These equations cannot be solved since the velocity and temperature gradients cannot be expressed analytically. However, the system can be characterized by solving the equations dimensionally. The follo-vring dimensionless variables are defined by Bird, et al. (21) as r-lH~ = ( riDs. ) (3-10 Z~:- = z/Ds. 0-11
61 Vr;> Jt.- ,,"Ii'\... ..", ::: (Vr/V) (3-12 Vz .. ~~ = Vz/V (3-13 p -li- p-p = Ie f/ Z 0 (3-14 t~=- -- tV/Da (3-15 T~~ T = - Too (3-16 Ts - %0 where V is a characteristic velocity which can be quantitatively evaluated. For an agitated vessel, NDa is such a velocity. Da is the diameter of the impeller and N is its rate of revolution .. Solving equations 3-10, 3-11, 3-12, 3-13 and 3-14 for the variables in equation 3-5 r = r~~~:"D a (3-17 z ... J~ z"Da (3-18 Vr :: V ~~-!~V r (3-19 V z = Vz·:"'V (3-20 p :: p~:. (e V2 ) + po (3-21 Equation 3-5 also has differential terms. Equation 3-22 is valid since it is an identity .. (3-22
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- Page 85 and 86: 73 Semi-Empirical Correlation i ..,
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- Page 97 and 98: 85 MATERIAL 7:0 STAIIJLESS STEEL /
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61<br />
Vr;> Jt.- ,,"Ii'\...<br />
..", ::: (Vr/V) (3-12<br />
Vz .. ~~<br />
= Vz/V (3-13<br />
p<br />
-li-<br />
p-p<br />
= Ie f/ Z<br />
0<br />
(3-14<br />
t~=-<br />
-- tV/Da (3-15<br />
T~~ T<br />
=<br />
- Too (3-16<br />
Ts - %0<br />
where V is a characteristic velocity which can be quantitatively<br />
evaluated.<br />
For an agitated vessel, NDa is such a velocity.<br />
Da is the diameter <strong>of</strong> the impeller and N is its rate <strong>of</strong><br />
revolution ..<br />
Solving equations 3-10, 3-11, 3-12, 3-13 and 3-14 <strong>for</strong><br />
the variables in equation 3-5<br />
r = r~~~:"D a (3-17<br />
z ...<br />
J~<br />
z"Da (3-18<br />
Vr :: V ~~-!~V<br />
r (3-19<br />
V z = Vz·:"'V (3-20<br />
p :: p~:. (e V2 ) + po (3-21<br />
Equation 3-5 also has differential terms. Equation 3-22<br />
is valid since it is an identity ..<br />
(3-22
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