Transient Conduction

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Transient Conduction Biot Number Calculator

• By Matthew Hunter and Jared Oehring

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Transient Conduction

• Unsteady, time-dependent, problems often arise
  when boundary conditions change.
• There are two main approaches to solve these
  problems
• Lumped Capacitance Method (useable if the
  temperature gradients within the solid may be
  neglected
• Exact Solution (when temperature gradients are
  not negligible)

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Lumped Capacitance

• Assume that the temperature of the solid is
  spatially uniform at any instant during the
  transient process.
• The temperature gradients within the solid are
  negligible.
• Calculate the Biot number to determine if it is
  negligible.

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Need for Exact Solution

• If
• Then temperature gradients are not negligible,
  and we must look for an exact solution.
• We will need to calculate a new Biot number, and
  attempt to use a first-order approximation of the
  exact solution, where
• or

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Transient Conduction Biot Number Calculator
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Example Problem 1(from example problem 5.3)

• Plane Wall Conduction
• h 40 W/m2 K
• k 177 W/m K
• l .003 m

Use Program
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Example Problem 2(from Quiz 6)

• Egg (Approximated to be a sphere with the
  properties of water)
• ro .025 m
• h 400 W/m2 K
• k .628 W/m K
• T0 40 F 277.4 K
• Tdone 160 F 344 K
• Ts 95 C 368 K

• a 0.00000015
• C1 1.95
• z1 2.9
• T 1014 s

Use Program
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Further information for Example Problem 2

• a 0.000015
• C1 1.95
• z1 2.9
• T 1014 s

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Conclusions Recommendations

• Calculator will calculate the Biot number and
  recommend either Lumped Capacitance Method, the
  first-order approximation, or another Exact
  Solution Method.
• It will also give you the Biot number needed to
  solve the first-order approximation problem.
• We recommend that you use it! It may be helpful!

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Appendix

• Equations and examples taken from Fundamentals
  of Heat and Mass Transfer 5th ed. by Frank P.
  Incropera and David P. Dewitt

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Any Questions?