Transient Conduction & Biot Number Calculator

1. Transient Conduction & Biot Number Calculator By: Matthew Hunter and Jared Oehring

2. 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)

3. 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.

4. 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

5. Transient Conduction & Biot Number Calculator

6. 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

7. 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

8. Further information for Example Problem 2 • a = 0.000015 • C1 = 1.95 • z1 = 2.9 • T = 1014 s

9. 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!

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

11. Any Questions?