Explanation Consider the water flows at steady state through one inlet and one exit system (pipe and duct flow). Hence, the inlet and exit mass flow rates are equal. m ˙ 1 = m ˙ 2 = m ˙ Write the energy rate balance equation for one inlet and one outlet system. [ Q ˙ 1 + W ˙ 1 + m ˙ ( h 1 + V 1 2 2 + g z 1 ) ] − [ Q ˙ 2 + W ˙ 2 + m ˙ ( h 2 + V 2 2 2 + g z 2 ) ] = Δ E ˙ system (I) Here, the rate of heat transfer is Q ˙ , the rate of work transfer is W ˙ , the enthalpy is h and the velocity is V , the gravitational acceleration is g , the elevation from the datum is z and the rate of change in net energy of the system is Δ E ˙ system ; the suffixes 1 and 2 indicates the inlet and outlet of the system. The system is at steady state. Hence, the rate of change in net energy of the system becomes zero. Δ E ˙ system = 0 The heat is added to the cooling water. Neglect the heat transfer at the outlet, work transfer, kinetic and potential energies. The Equations (I) reduced as follows. [ 0 + Q ˙ 1 + m ˙ ( h 1 + 0 + 0 ) ] − [ 0 + 0 + m ˙ ( h 2 + 0 + 0 ) ] = 0 Q ˙ 1 + m ˙ h 1 − m ˙ h 2 = 0 Q ˙ 1 = m ˙ h 2 − m ˙ h 1 Q ˙ 1 = m ˙ ( h 2 − h 1 ) (II) The change in enthalpy is expresses as follow. h 2 − h 1 = c p ( T 2 − T 1 ) Here, the specific heat is c p , the exit temperature is T 2 and the inlet temperature is T 1 . Substitute c p ( T 2 − T 1 ) for h 2 − h 1 in Equation (II). Q ˙ 1 = m ˙ [ c p ( T 2 − T 1 ) ] = m ˙ c p ( T 2 − T 1 ) (III) Write the formula for mass flow rate of water ( m ˙ ) . m ˙ = ρ A V = ρ ( π D 2 4 ) V (IV) Here, the density is ρ , the cross sectional area is A , the diameter is D and the velocity is V

9th Edition

ISBN: 9781259822674

Author: Yunus A. Cengel Dr., Michael A. Boles

Publisher: McGraw-Hill Education

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Work and Heat Transfer

It is generally related to thermal engineering which tells about the use, creation, conversion and transfer of heat energy between the systems. It is also considered that to transfer heat from one source to another, transfer of masses is also required. T…

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Chapter 5.5, Problem 151RP

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Chapter 5.5, Problem 150RP

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The rate of condensation of the steam.

Solution Summary: The author analyzes the rate of condensation of steam at the outside of the pipe and the energy rate balance equation for one inlet and one outlet system.

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