GATE ME 2016 Set 2 — Question 53
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0HardBiot & Fourier NumbersConductionHeat TransferHeisler Charts
Heat Transfer → Conduction → Biot & Fourier Numbers
Last updated
Question
Two cylindrical shafts A and B at the same initial temperature are simultaneously placed in a furnace. The surfaces of the shafts remain at the furnace gas temperature at all times after they are introduced into the furnace. The temperature variation in the axial direction of the shafts can be assumed to be negligible. The data related to shafts A and B is given in the following Table.
The temperature at the centerline of the shaft A reaches 400 C after two hours. The time required (in hours) for the centerline of the shaft B to attain the temperature of 400 C is _______
| Quantity | Shaft A | Shaft B |
|---|---|---|
| Diameter (m) | 0.4 | 0.1 |
| Thermal conductivity (W/m-K) | 40 | 20 |
| Volumetric heat capacity (J/m-K) |
Correct answer
2.4 to 2.6
Solution
For transient heat conduction in a cylinder where the surface temperature is suddenly changed and maintained constant, the temperature at any point is a function of the Fourier number () and the Biot number (). Since the furnace gas temperature is the same for both and the centerline temperature target is the same, the temperature ratio is identical for both shafts.Assuming the surface resistance is negligible (), the temperature ratio depends only on the Fourier number: , where is the thermal diffusivity.For Shaft A:
For Shaft B:
Equating the Fourier numbers ():The time required for shaft B is 2.5 hours.
For Shaft B:
Equating the Fourier numbers ():The time required for shaft B is 2.5 hours.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE ME question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Conduction
2026 Set 1 Q27A quiescent fluid at temperature is confined between two vertical parallel plates. While…2026 Set 1 Q35A sphere of radius 5 mm is initially in equilibrium at 400 in a furnace. It is…2026 Set 1 Q43A very long fin of a uniform square cross-section is replaced by another very long fin of a uniform…2026 Set 1 Q54Two rectangular surfaces both having area are placed perpendicular to each other…2026 Set 1 Q55Convective heat transfer coefficients for Fluid 1 and Fluid 2 in a heat exchanger, as shown in the…