GATE 2025 ME – Question 51

Heat Transfer · Convection: boundary layer, dimensionless parameters and correlations · 2 marks · Numerical answer

Water enters a tube of diameter, D = 60 mm with mass flow rate of 0.01 kg s$^{-1}$ as shown in the figure below. The inlet mean temperature is $T_{m,i}$ = 293 K and the uniform heat flux at the surface of the tube is 2000 W m$^{-2}$. For the exit mean temperature of $T_{m,o}$ = 353 K, the length of the tube, $L$ is ________ m (rounded off to 1 decimal place).

Use the specific heat of water as 4181 J kg$^{-1}$ K$^{-1}$.

A tube of diameter D = 60 mm with a uniform heat flux of 2000 W/m$^2$ at its surface. Water at 293 K enters at 0.01 kg/s and leaves at 353 K.

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Correct answer: 6.67 to 6.73

Explanation

The heat gained by the water is $\dot{m}c_p\Delta T = 0.01 \times 4181 \times 60 = 2508.6$ W. The heat supplied by the wall is $q''\pi DL = 2000 \times \pi \times 0.06 \times L = 376.99\,L$. Setting them equal gives $L = \frac{2508.6}{376.99} = 6.7$ m.