Transient ResponseTransient Response

Paul Black, Mark Eilertsen, Evan JonesPaul Black, Mark Eilertsen, Evan Jones

How long will it take for How long will it take for ice cold water to reach ice cold water to reach room room temperaturetemperature??

Measured

Transient Response

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285

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300

0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00

Time (hrs)

Tem

pera

ture

(K)

T∞

T (measured)

KKeq eq

Prediction

Lumped CapacitanceLumped Capacitance

Approximate SolutionApproximate Solution

Transient Responce

270

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280

285

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300

0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00

Time (hrs)

Te

mp

era

ture

(K

) T∞

T (measured)

T (Lumped C)

T (4 term aprox.)

Lumped Capacitance Lumped Capacitance Bi < .1Bi < .1

Approximate Approximate

SolutionSolution Fo > .2 Fo > .2

sTransient Response

Comparison of Multiple Terms in the Approximate Method

270.00

275.00

280.00

285.00

290.00

295.00

300.00

0 10 20 30 40 50 60 70 80 90 100

Time (hrs)

Te

mp

era

ture

(K

) Temp (aprox 1 term)

Temp (aprox 2 term)

Temp (aprox 3 term)

Temp (aprox 4 term)

No Difference

ConclusionConclusionCooler kept food cool for Cooler kept food cool for 146 hrs146 hrs

Lumped capacitance Lumped capacitance –Initial response (Bi<.1)Initial response (Bi<.1)

Approximate solutionApproximate solution–Response after some time (Fo>.2)Response after some time (Fo>.2)–One term is good enoughOne term is good enough