The Lumped Capacitance Method
The Lumped Capacitance Method
The Lumped Capacitance Method
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‣ Variation of temperature with location (x * ) and time ( Fo)<br />
:<br />
( x )<br />
θ * = θ<br />
o<br />
* cos ζ<br />
1<br />
*<br />
(5.40b)<br />
‣ Change in thermal energy storage with time:<br />
∆ E<br />
st<br />
=− Q<br />
(5.43a)<br />
⎛ sinζ ⎞<br />
1<br />
Q = Q 1<br />
*<br />
o ⎜ − θ o ⎟<br />
⎝ ζ<br />
1 ⎠<br />
o<br />
( )<br />
Q = ρcV T −T<br />
i<br />
∞<br />
(5.46)<br />
(5.44)<br />
Can the foregoing results be used for a plane wall that is well insulated on one<br />
side and convectively heated or cooled on the other?<br />
( )<br />
Can the foregoing results be used if an isothermal condition T is<br />
s<br />
≠ Ti<br />
instantaneously imposed on both surfaces of a plane wall or on one surface of<br />
a wall whose other surface is well insulated?
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