GATE 2025 CH – Question 52

Heat Transfer · Convection, boundary layers and heat transfer coefficients · 2 marks · Numerical answer

Consider laminar flow of water over a wide flat plate maintained at a uniform temperature of 50 °C as shown in the figure. The freestream velocity and temperature of water are 1.0 m/s (parallel to the plate) and 20 °C, respectively. The distance $x$ from the leading edge, at which the thermal boundary layer thickness $\delta_T = 0.01$ m, is ____ m (rounded off to 1 decimal place).

GIVEN: kinematic viscosity $\nu = 1.0 \times 10^{-6}$ m$^2$/s; Prandtl number $Pr = 7.01$; velocity boundary layer thickness $\delta_H = \frac{4.91x}{\sqrt{Vx/\nu}}$

water at 20 °C flowing at $V = 1.0$ m/s along a flat plate at 50 °C, with the distance $x$ measured from the leading edge.

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Correct answer: 15.12 to 15.28

Explanation

For laminar flow with $Pr > 1$ the thermal boundary layer is thinner than the velocity one: $\frac{\delta_T}{\delta_H} = Pr^{-1/3}$. So $\delta_H = 0.01 \times 7.01^{1/3} = 0.01 \times 1.914 = 0.01914$ m. Also $\delta_H = 4.91\sqrt{\frac{\nu x}{V}} = 4.91 \times 10^{-3}\sqrt{x}$, so $\sqrt{x} = \frac{0.01914}{4.91 \times 10^{-3}} = 3.898$ and $x = 15.2$ m.