Explanation Given: The density of milk ( ρ ) is 1 kg / L . The volumetric flow of milk ( V ˙ m i l k ) is 12 L / s . The inlet temperature of the milk ( T 1 ) is 72 ° C . The outlet temperature of the milk ( T 2 ) is 4 ° C . The pasteurized milk temperature ( T 3 ) is 18 ° C . The effectiveness of regenerator ( ε ) is 82 percent. The cost of natural gas is $1.30/therm. The duration is 24 hrs. a day and 365 days year. Calculation: Refer TableA-3, “Properties of common liquids, solids, and foods”, select the specific heat at constant pressure ( c p ) for milk substance as 3.79 kJ / kg ⋅ K . Calculate the mass flow rate of milk ( m ˙ m i l k ) . m ˙ m i l k = ρ V ˙ m i l k m ˙ m i l k = ( 1 kg / L ) ( 12 L / s ) = 12 kg / s Write the expression for the energy balance equation for closed system. E ˙ i n − E ˙ o u t = Δ E ˙ s y s t e m (I) Here, rate of net energy transfer in to the control volume is E ˙ i n , rate of net energy transfer exit from the control volume is E ˙ o u t and rate of change in internal energy of system is Δ E ˙ s y s t e m . The rate of change in internal energy of the system is zero for the steady flow system. Substitute Δ E ˙ s y s t e m = 0 in Equation (I). E ˙ i n − E ˙ o u t = 0 m ˙ h 1 + Q ˙ i n = m ˙ h 2 Q ˙ i n = m ˙ ( h 2 − h 1 ) = m ˙ c p ( T 2 − T 1 ) (II) Here, mass flow rate is m ˙ , enthalpy at initial state is h 1 , enthalpy at final state is h 2 , rate of heat transfer input is Q ˙ i n , specific heat at constant pressure is c p , entry temperature is T 1 and exit temperature is T 2 . Calculate the rate of heat transfer to the milk from the current using equation (II). Q ˙ c u r r e n t = m ˙ m i l k c p ( T 1 − T 2 ) Q ˙ c u r r e n t = ( 12 kg / s ) ( 3.79 kJ / kg ⋅ K ) ( 72 ° C − 4 ° C ) = ( 12 kg / s ) ( 3.79 kJ / kg ⋅ K ) ( ( 72 + 273 ) K − ( 4 + 273 ) K ) = 3093 kJ / s Calculate the rate of heat transfer saved ( Q ˙ s a v e d ) . Q ˙ s a v e d = ε Q ˙ c u r r e n t Q ˙ s a v e d = ( 0

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ISBN: 9781259151323

Author: CENGEL

Publisher: MCGRAW HILL BOOK COMPANY

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Chapter 8, Problem 140P

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Chapter 8, Problem 139P

Chapter 8, Problem 141P

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