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GATE 2022 ME (ME2) – Question 25

Heat Transfer · Convection: boundary layer, dimensionless parameters and correlations · 1 mark · Multiple choice

Which of the following non-dimensional terms is an estimate of Nusselt number?

  1. Ratio of internal thermal resistance of a solid to the boundary layer thermal resistance
  2. Ratio of the rate at which internal energy is advected to the rate of conduction heat transfer
  3. Non-dimensional temperature gradient
  4. Non-dimensional velocity gradient multiplied by Prandtl number

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Correct answer: (C) Non-dimensional temperature gradient

Explanation

**Definition.** At the wall the heat leaving by conduction into the fluid equals the convective heat transfer:
$$h\,(T_w-T_\infty)=-k\left(\frac{\partial T}{\partial n}\right)_w .$$

Rearranging with a length scale $L$ and a temperature difference $\Delta T$,
$$Nu=\frac{hL}{k}=\frac{-(\partial T/\partial n)_w\,L}{\Delta T}=-\left(\frac{\partial T^*}{\partial n^*}\right)_w ,$$
which is the **non-dimensional temperature gradient** at the wall.

The other options describe different groups:
- A, a ratio of internal solid resistance to boundary-layer resistance, is the **Biot number** ($hL/k_s$).
- B, advection to conduction, is the **Péclet number**.
- D, a velocity gradient times Pr, is not a Nusselt number.

Answer **C**.