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In respect to free convection over a vertical flat plate, the Nusselt number for laminar and turbulent flows varies respectively with Grashoff number G r as
- a)G r and G r1/4
- b)G r1/2 and G r1/3
- c)G r1/4 and G r1/3
- d)G r1/3 and G r1/4
Correct answer is option 'C'. Can you explain this answer?
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In respect to free convection over a vertical flat plate, the Nusselt ...
Explanation: It varies as G r1/4 and G r1/3.
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In respect to free convection over a vertical flat plate, the Nusselt ...
Free Convection over a Vertical Flat Plate
Free convection occurs when fluid motion is induced by buoyancy forces that result from density variations due to temperature gradients. In the context of a vertical flat plate, the Nusselt number (Nu) characterizes the convective heat transfer.
Nusselt Number in Laminar Flow
- For laminar flow (Grashoff number, Gr < 10^9),="" the="" nusselt="" number="" is="" determined="" by="" the="" grashoff="" number="" and="" is="" given="" />
- Nu ∝ Gr^1/4
- This relationship indicates that as the buoyancy effect increases (higher Gr), the heat transfer efficiency improves, but at a slower rate due to the laminar nature of the flow.
Nusselt Number in Turbulent Flow
- For turbulent flow (Gr > 10^9), the relationship changes:
- Nu ∝ Gr^1/3
- In turbulent conditions, the mixing is more vigorous, leading to enhanced heat transfer. Thus, the Nusselt number increases with the Grashoff number at a faster rate than in laminar flow.
Conclusion
- Therefore, the Nusselt number for laminar flow varies with the Grashoff number as Gr^1/4, while for turbulent flow, it varies as Gr^1/3.
- This distinction explains why option 'C' (Gr^1/4 for laminar flow and Gr^1/3 for turbulent flow) is the correct answer.
Understanding these relationships is crucial for designing heat exchangers and other thermal systems where convection plays a significant role.
Free convection occurs when fluid motion is induced by buoyancy forces that result from density variations due to temperature gradients. In the context of a vertical flat plate, the Nusselt number (Nu) characterizes the convective heat transfer.
Nusselt Number in Laminar Flow
- For laminar flow (Grashoff number, Gr < 10^9),="" the="" nusselt="" number="" is="" determined="" by="" the="" grashoff="" number="" and="" is="" given="" />
- Nu ∝ Gr^1/4
- This relationship indicates that as the buoyancy effect increases (higher Gr), the heat transfer efficiency improves, but at a slower rate due to the laminar nature of the flow.
Nusselt Number in Turbulent Flow
- For turbulent flow (Gr > 10^9), the relationship changes:
- Nu ∝ Gr^1/3
- In turbulent conditions, the mixing is more vigorous, leading to enhanced heat transfer. Thus, the Nusselt number increases with the Grashoff number at a faster rate than in laminar flow.
Conclusion
- Therefore, the Nusselt number for laminar flow varies with the Grashoff number as Gr^1/4, while for turbulent flow, it varies as Gr^1/3.
- This distinction explains why option 'C' (Gr^1/4 for laminar flow and Gr^1/3 for turbulent flow) is the correct answer.
Understanding these relationships is crucial for designing heat exchangers and other thermal systems where convection plays a significant role.
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