(a) Explanation Given: Hot fluid is ethylene glycol and cold fluid is water Hot and cold fluid inlet temperature T h , i = 333 K and T c , i = 283 K Mass flow rate of the hot and cold fluid are m ⋅ h = 2 k g / s and m ⋅ c = 5 k g / s Overall heat transfer coefficient = U = 800 W / m 2 ⋅ K Total heat transfer area of the shell and tube heat exchanger is A=15 m 2 Explaination: No. of transfer unit = N T U = U A C min Heat loss by heat fluid is equal to heat gained by the cold fluid by performing an energy balance. Accordingly we have q = C h ( T h , i − T h , o ) = C c ( T c , o − T c , i ) ........ ( 2 ) Where heat capacity of the cold fluid is C c = m ⋅ c c p , c And, heat capacity of hot fluid C h = m ⋅ h c p , h For cold fluid = (at T ¯ ≈ 288 K ): Specific heat of cold fluid is C p , c = 4186 k J / k g ⋅ K By putting the values of parameter into C c , C c = 5 k g / s × 4.186 k J / k g ⋅ K Or C c = 20930 W/K For hot fluid = (at T ¯ ≈ 313 K ): Specific heat of cold fluid is C p , h = 2.474 k J / k g ⋅ K By putting the values of parameter into C h , 2 k g / s × 2.474 k J / k g ⋅ K Or C h = 4948 W / K By putting C c , C h and the operating temperatures into (2) 4948 W / K ( 333 − T h , o , ) K = 20930 W / K ( T c , o − 283 ) K T c , o − 361.723 = 0.2364 T h , o T c , o + 0.2364 T h , o = 361.723....... ( 3 ) By observing C min = C h a n d C max = C c Heat capacity ratio = C r = C min C max Accordingly, C r = 4948 W / K 20930 W / K = 0.2364 By putting the values of parameter into 1 N T U = 800 W / m 2 ⋅ K × 15 m 2 4948 W / K = 12000 4948 W / K o r N T U = 2.425 For a shell and tube heat exchanger with one shell pass and (2,4…. Tube passes) effectiveness from the effectiveness relatons is ε = 2 { 1 + C r + ( 1 + C r 2 } 0 (b) To determine The fluid outlet temperatures

7th Edition

ISBN: 9780470917855

Author: Bergman, Theodore L./

Publisher: John Wiley & Sons Inc

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Chapter 11, Problem 11.84P

(a)

To determine

Rate of heat transfer

(b)

To determine

The fluid outlet temperatures

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2-b Hot exhaust gases, which enter a finned-tube, cross-flow heat exchanger at 300 °C and leave at 100 °C. are used to heat pressurized water at a flow rate of 1 kg/s from 35 °C to 125 °C. The specific heat of water at the average water temperature is 4197 J/kg. K. The overall heat transfers coefficient based on the gas-side surface area is Un = 100 W/m².K. Determine the required gas-side surface area A, using the LMTD and E-NTU method.

a one shell and two tube pass heat exchanger, coolant enters the tube at 4.81 kg/s (spread over 72 tubes with each tube being 0.01 m in diameter and 1.95 m length) at an initial temperature of 25 C. Water enters the shell at 2.5 kg/s at an initial temperature of 5 C. The average convection coefficient of the water is known to be 1e4 W/m2.K. What is the overall heat transfer coefficient, assuming no fouling, negligible tube thermal resistance and near-identical inner and outer tube surfaces? What is the actual heat transfer rate? What is the coolant outlet temperature? The coolant properties are Cp = 1040 J/kg.K, μ = 7.65e-4 kg/s.m, k = 0.058 W/m.K and Pr = 14. Assume the water Cp = 4200 J/kg.K.

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Rate of heat transfer

Solution Summary: The author explains that heat loss by heat fluid is equal to heat gained by the cold fluid by performing an energy balance.

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