GATE ME 2021 Set 1 — Question 24
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+1 / -0.33MediumHeat Transfer Through FinsConductionHeat Transfer
Heat Transfer → Conduction → Heat Transfer Through Fins
Last updated
Question
An infinitely long pin fin, attached to an isothermal hot surface, transfers heat at a steady rate of to the ambient air. If the thermal conductivity of the fin material is doubled, while keeping everything else constant, the rate of steady-state heat transfer from the fin becomes . The ratio is
Correct answer
(A) √(2)
Solution
For an infinitely long fin, the rate of heat transfer () is given by the formula:
where:
Now, the thermal conductivity of the fin material is doubled, so the new thermal conductivity is . All other parameters () remain constant. Let the new heat transfer rate be .
Substitute the expression for into the equation for :
We need to find the ratio :
The final answer is
where:
- is the convective heat transfer coefficient
- is the perimeter of the fin
- is the thermal conductivity of the fin material
- is the cross-sectional area of the fin
- is the base temperature of the fin
- is the ambient air temperature
Now, the thermal conductivity of the fin material is doubled, so the new thermal conductivity is . All other parameters () remain constant. Let the new heat transfer rate be .
Substitute the expression for into the equation for :
We need to find the ratio :
The final answer is
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…