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

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

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

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

Transient Conduction & Biot Number Calculator

Example Problem 1 (from example problem 5.3) Plane Wall Conduction Plane Wall Conduction h = 40 W/m 2 * K h = 40 W/m 2 * K k = 177 W/m * K k = 177 W/m * K l =.003 m l =.003 m Use Program

Example Problem 2 (from Quiz #6) Egg (Approximated to be a sphere with the properties of water) Egg (Approximated to be a sphere with the properties of water) r o =.025 m r o =.025 m h = 400 W/m 2 * K h = 400 W/m 2 * K k =.628 W/m * K k =.628 W/m * K T 0 = 40 F = K T 0 = 40 F = K T done = 160 F = 344 K T done = 160 F = 344 K T s = 95 C = 368 K T s = 95 C = 368 K Use Program  =  = C 1 = 1.95 C 1 = 1.95   = 2.9   = 2.9 T = 1014 s T = 1014 s

Further information for Example Problem 2  =  = C 1 = 1.95 C 1 = 1.95   = 2.9   = 2.9 T = 1014 s T = 1014 s

Conclusions & Recommendations Calculator will calculate the Biot number and recommend either Lumped Capacitance Method, the first-order approximation, or another Exact Solution Method. 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. 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! We recommend that you use it! It may be helpful!

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

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