The differential equations governing streams
DOI 10.1615/hedhme.a.000098
1.2 DEFINITIONS AND RELATIONSHIPS
1.2.5 Differential Equations Governing Streams
D. Brian Spalding
A. DIFFERENTIAL EQUATIONS FOR ENTHALPY
Figure 1 represents an elementary portion of stream 1 in a heat exchanger. The length of the path in the flow direction is dz1 and the associated interface area is dA. If the flow is steady, and effects of kinetic heating, external work, and gravitational potential energy are negligible, the application of the steady-flow energy equation, 1.2.1(3), yields
\[\label{eq125_1} \frac{\dot {M}_1 dh_1 }{dz_1 } = - \dot {q}_{1 \to 2} \frac{dA}{dz_1 } \tag{1}\]
where q̇1→2 is the heat flux per unit area from stream 1 to stream 2. This heat flux can of course be calculated from
\[\label{eq125_2} \dot {q}_{1 \to 2} = U\left( {T_1 - T_2 } \right) \tag{2}\]
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