Question

The wall of a liquid-to-gas heat exchanger has a surface area on the liquid side of 1.8 m2 (0.6 m 3.0 m) with a heat transfer coefficient of 255 W/m2K. On the other side of the heat exchanger wall a gas flows, and the wall has 96 thin rectangular steel fins 0.5 cm thick and 1.25 cm high (k = 3 W/m K) as shown in the figure below. The fins are 3 m long and the heat transfer coefficient on the gas side is 57 W/m2 K. Assume that the thermal resistance of the wall is negligible, the heat exchanger is at the steady-state conditions, the heat transfer is one-dimensional, the thermal conductivity, k, is constant, and we have convection from the fin tip. Determine the rate of heat transfer if the overall temperature difference between the mainstream gas and liquid is 40.5°C. L=0.0125 m W = 3 m 1 = 0.005 m Liquid Gas A section of the wall About 8000 W About 80,000 W About 80 W About 800 W

Answer 1

Given is an example of heat transfer from a fin with losing heat from tip. Please refer to attached images for solution of given problem, do comment in case of any query. Please upvote this answer if you find my solution to be useful. Good luck!!

Calven is an example of heat dissipation from a Rin losing heat at tip. Data provided Liquid side area (18m2) heig 255 147602.12 Total number of fins na 96. Thicknew of Rina 0.5cm - 0:00 sm Height of Rina 1.25cm o.0125 m Thermal conducksity of Rin (K) = 3 14/mith Length of Rin red a 3 m. Heat transfer coeffigent side, ha 57 H/m2.k on gas Temperature difference beth 40.5°c. & liquid * For fin losing heat aut tip, the amount of heat transfered; V Phka (to-ta). Itanhmet hlikm] Lat hitanume Qpina Km

h (22+2w) V (wth.k (572(6+0.012 (370.005)(3) 87.25 Qrins 1 (26+20).(57):(3) (wt) x 4695 Х ton h (87258 0.0125 + 57 3x8 7.25 It tan 5(8725X0.0125). 57 3x8 7.25 Qfana 159.01 1.0 ly87 17358 latte. / Ran. 137.509. is heat transfer This from fini only. Now heat transfer from bare area Abare Awall - (96 Pins) Carea of Ipin 1.8m2 1962.53 x0'005] 0.36 m² Qbore = hg. Abare AT 57 x 0.36 x 40.5 831.06

Total heat transfer rate Q Q baret 96 QRIA 831.06+ 96 [137.5097 14031.924 ia

Nearest answer is 8000W