Project ForgeHeat Transfer
Conduction
GATE 2012
Medium
A solid sphere with an initial temperature Ti is immersed in a large thermal reservoir of temperature To. The sphere reaches a steady temperature after a certain time t1. If the radius of the sphere is doubled, the time required to reach steady-state will be
- At1/4
- Bt1/2
- C2t1
- 4t1
Explanation
The characteristic time for transient conduction scales as t∝L²/α, where L is a characteristic length (∝ radius for a sphere). Doubling the radius quadruples the required time.
Source: GATE CH 2012 (2012)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.