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 water flows at steady state through the system. Hence, the rate of change in net energy of the system becomes zero. Δ E ˙ system = 0 The heat is added through the electric heater, i.e. work input ( W ˙ e , in ) to the water flowing through the pipe. Neglect the heat transfer, work transfer at exit, kinetic and potential energies. The Equations (I) reduced as follows. [ 0 + W ˙ e , in + m ˙ ( h 1 + 0 + 0 ) ] − [ 0 + 0 + m ˙ ( h 2 + 0 + 0 ) ] = 0 W ˙ e , in + m ˙ h 1 − m ˙ h 2 = 0 W ˙ e , in = m ˙ h 2 − m ˙ h 1 W ˙ e , in = 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). W ˙ e , in = m ˙ [ c p ( T 2 − T 1 ) ] = m ˙ c p ( T 2 − T 1 ) (III) Here, the work input to the heater is the electric power

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ISBN: 8220106796979

Author: CENGEL

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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 145RP

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The current supplied to the heater.

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Chapter 5.5, Problem 144RP

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The current supplied to the heater.

Solution Summary: The author calculates the energy rate balance equation for one inlet and one outlet system.

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