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A quiescent fluid at temperature \(T_{3}\) is confined between two vertical parallel plates. While plate 1 is kept at temperature \(T_{1}\) and plate 2 is maintained at temperature \(T_{2}\), 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 \(T_{1}, T_{2}\), and \(T_{3}\)?

Two vertical plates, plate 1 at T1 on the left and plate 2 at T2 on the right; the velocity profile between them points upward near plate 1 and downward near plate 2; gravity acts downward

  • A.\(T_{1} \gt T_{3}\) and \(T_{3} \gt T_{2}\)
  • B.\(T_{1} \gt T_{3}\) and \(T_{3} \lt T_{2}\)
  • C.\(T_{1} \lt T_{3}\) and \(T_{3} \lt T_{2}\)
  • D.\(T_{1} \lt T_{3}\) and \(T_{3} \gt T_{2}\)

Answer: A

The relations are \(T_{1} \gt T_{3}\) and \(T_{3} \gt T_{2}\).

The flow is natural convection. Fluid moves upward next to plate 1, so it is lighter there, which means it has been heated: plate 1 is hotter than the fluid, \(T_{1} \gt T_{3}\). Fluid moves downward next to plate 2, so it is heavier there and has been cooled: plate 2 is colder than the fluid, \(T_{3} \gt T_{2}\).

Each of the other options reverses at least one of these, which would reverse the direction of flow at that plate.

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