GATE 2026 ME – Question 55

Heat Transfer · Heat exchangers: LMTD and NTU methods · 2 marks · Numerical answer

Convective heat transfer coefficients for Fluid 1 and Fluid 2 in a heat exchanger, as shown in the figure below, are 50 W/(m$^2$K) and 80 W/(m$^2$K), respectively. The inner tube is made of a material which has a thermal conductivity 386 W/(mK) for the given range of temperatures in the heat exchanger. The length of the heat exchanging surface, the inside radius of the inner tube, and thickness of the inner tube are 1 m, 10 mm, and 1 mm, respectively. Considering no heat exchange between the outer tube and the surrounding, the heat transfer rate for the heat exchanger is ________ W (*rounded off to 1 decimal place*).

A double-pipe heat exchanger. Fluid 2 enters the inner tube at 20 °C and leaves at 30 °C. Fluid 1 enters the outer annulus at 60 °C from the opposite end and leaves at 40 °C.

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Correct answer: 50.25 to 50.75

Explanation

The flows are in opposite directions (counterflow). The temperature differences at the two ends are $60 - 30 = 30$ K and $40 - 20 = 20$ K, so the log mean temperature difference is $\frac{30 - 20}{\ln 1.5} = 24.66$ K. The resistances are: inside convection $\frac{1}{80 \times 2\pi(0.01)(1)} = 0.1989$ K/W, wall conduction $\frac{\ln(11/10)}{2\pi \times 386 \times 1} = 0.00004$ K/W, and outside convection $\frac{1}{50 \times 2\pi(0.011)(1)} = 0.2894$ K/W. The total is 0.4884 K/W, so $q = \frac{24.66}{0.4884} = 50.5$ W.