Question:
A quiescent fluid at temperature T3 is confined between two vertical parallel plates. While plate 1 is kept at temperature T1 and plate 2 is maintained at temperature T2, a velocity profile between the plates, as shown in the figure below, is generated due to heat transfer.
Which one of the following options shows the correct relations among T1, T2, and T3?
A quiescent fluid at temperature T3 is confined between two vertical parallel plates. While plate 1 is kept at temperature T1 and plate 2 is maintained at temperature T2, a velocity profile between the plates, as shown in the figure below, is generated due to heat transfer.
Which one of the following options shows the correct relations among T1, T2, and T3?
Which one of the following options shows the correct relations among T1, T2, and T3?
Show Hint
Match the rising and sinking flow directions shown in the figure to which plate is hotter or colder than the fluid.
Updated On: Aug 14, 2026
- T1 > T3 and T3 > T2
- T1 > T3 and T3 < T2
- T1 < T3 and T3 < T2
- T1 < T3 and T3 > T2
Show Solution
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The Correct Option is A
Solution and Explanation
Step 1: Read the flow direction next to each plate.
The figure shows fluid moving upward next to plate 1 and downward next to plate 2, with the two branches meeting near the middle of the gap.
An up-one-side, down-the-other pattern is the standard natural convection loop that forms inside a vertical enclosure.
Step 2: Link the direction of motion to buoyancy.
Fluid rises where it gets heated and becomes lighter than its surroundings, and it sinks where it gets cooled and becomes heavier.
Since fluid rises next to plate 1, plate 1 must be hotter than the bulk fluid, so \( T_1 > T_3 \).
Since fluid sinks next to plate 2, plate 2 must be cooler than the bulk fluid, so \( T_3 > T_2 \).
Final Answer:
Combining both relations gives \( T_1 > T_3 \) and \( T_3 > T_2 \), which is option (A). \[ \boxed{T_1 > T_3 > T_2} \]
The figure shows fluid moving upward next to plate 1 and downward next to plate 2, with the two branches meeting near the middle of the gap.
An up-one-side, down-the-other pattern is the standard natural convection loop that forms inside a vertical enclosure.
Step 2: Link the direction of motion to buoyancy.
Fluid rises where it gets heated and becomes lighter than its surroundings, and it sinks where it gets cooled and becomes heavier.
Since fluid rises next to plate 1, plate 1 must be hotter than the bulk fluid, so \( T_1 > T_3 \).
Since fluid sinks next to plate 2, plate 2 must be cooler than the bulk fluid, so \( T_3 > T_2 \).
Final Answer:
Combining both relations gives \( T_1 > T_3 \) and \( T_3 > T_2 \), which is option (A). \[ \boxed{T_1 > T_3 > T_2} \]
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