Question

A simple counter flow heat exchanger consists of two co-axial tubes with hot process water passing through the inner tube and clean water through the annular space between the inner and outer tubes. The clean water enters at 20°C and leaves at 50°C. The process water enters at 90°C and leaves at 40°C. The mass flowrate of the process water is 3 kgs-1. The inner tube diameter is 30 mm and the outer tube diameter is 50 mm. Take the properties of the fluids at the mean temperatures of the fluids. Film heat transfer coefficient for the outside surface of the inner tube is 14.5 kWm-2K-1 Calculate the mass flowrate of the clean water; the overall heat transfer coefficient; the area required for heat transfer and the film heat transfer coefficient on the inside surface of the inner tube using the expression below Nu 0.023 Re0.8 Pro.4 =

Answer 1

kw/ m2K h=1415 IF Clean water & Hot pocey waloy Isomm Somm =D2 30mm :DI -clean water go'c Oi (90-50) SUO 5008 40°c O2= (40-20) : 20°c 120°c 23 m (Process water) 3 kg/s ho (outer surface) = 14.5 kw park By using heat balance relationship : mpx (px (90-40) E mexCpX(50-20) where Cp is same for both clean water and process water Mc = man flow rate of clean water 3x (50) = M(x 30 me=5kg/ -Ang

Film heat transfer coefficient on the inside surface of the inner tube By using this expression Nu = 0.023 (Re)" (Bogy where Re= PVP, M Mp= PV 20,2 PUDI 4 mp TDI So, Rec ump 'Mean temp of hot process water i.e Rez 4x3 2X0.03 0.000434 4 from the property of Re=293373.167 Fluid table = 0.000439 Pars Pr= MCp = 6.6 w w/mick ПD, щ got40=65°c 2 [(M) at 65cl esater K Kwater = 0.000434X4,18%/03 0.6 Pr= 3.02 0.8 oig 0,4 NU= 0.023 x (Re) °Clyje hipi = 0.023x(2933 73.167)*(3.024 K 0.8 hi 0. 619 [0-0238(293373-1673"&(3.02 304] 0.03 16.93 KW / Ans

over all heat transfer coefficient 1 1 1 ho + H/ hi U 1 1 1 z + 14.5 1693 u= 7.81 KW/m²K Ary LMTD (logarithmic mean temperature difference) LMTD = 01-02 40 20 'yo = 28.85°C In Col In(40 Area required for heat transfer 9= UA CMTD mpxcx (90–40) = 7.81%AX 28.85 X103 3 x 4,18 x103 x 50 = 7.81*703x AX28.85 Area = Any 2078 m² water Specification value may flow rate of 5kg/ Clean overall heat transfer coefficient → 7-81 kW/m2K Area required for heat transfer → 2.78 m² Film heat transfer coefficient (inside) → 16.93 → 16-93 KW/mrk 110 IV Ang
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