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A sugar solution (? = 1,080 kg/m3, cp = 3,601 J/kg ? K, kf = 0.5764...

A sugar solution (? = 1,080 kg/m3, cp = 3,601 J/kg ? K, kf = 0.5764 W/m ? K, ? = 1.3 × 10-3N ? s/m2) flows at rate of 2 kg/s and is to be heated from 25°C to 50°C. Water at 95°C is available at a flow rate of 1.5 kg/s (cp = 4,004 J/kg ? K). Sugar solution flows through the annulus. Designing a double-pipe heat exchanger for this process is proposed. The following geometrical parameters are assumed: Length of the hairpin = 3m. Do (annulus) = 6 cm Di (annulus) = 5.25 cm do (Inner tube) = 2.6 cm di (Inner tube) = 2.09 cm Number of tubes inside the annulus = 1 Number of fins = 20 Fin height = 0.0127 m Fin thickness = 0.0009 m Thermal conductivity of the material, k = 52 W/m ? K. a. Calculate the hydraulic diameter of the annulus for pressure drop analysis. b. Calculate the equivalent diameter for heat transfer analysis. c. Calculate the heat transfer surface area of this heat exchanger and the number of hairpins.

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Write the given data. Sugar Solution Py = 1080 kg/m2 (C), = 3601 J/kg ky=0.5764 W/m-K u =1.3x10-2 N-s/m² mg = 2 kg/s Tg = 25°Find the hydraulic diameter. D D. _ 4x1.40522x10-5 =- 0.7546 = 7.4486x10 m The hydraulic diameter of annulus is 7.4486x 10 m4. = 2N; ( nd, L-N,L5) = 2x1(ax0.026x3-20x3x0.0009) =0.3820 m2 The total area of hairpin is: Agri = 2.94 +0.3820 = 3.322 m2 .1727.3455 Nu = (1/2 Re, Pr, 1.07 +12.7( (Pr,23-1) 2.9137 = 592.825 h == L =16349.48 W/m²K Calculations for the water (outer).

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