A heat exchanger transfers thermal energy between fluid streams while ideally keeping the streams physically separate.

If the entire exchanger is chosen as one steady control volume, external heat loss and shaft work are often negligible. Then, for two streams,

$$\dot m_h(h_{h,in}-h_{h,out})=\dot m_c(h_{c,out}-h_{c,in}).$$

Energy lost by the hot stream is gained by the cold stream.

For example, suppose a hot stream flows at $2\ \mathrm{kg/s}$ and loses $100\ \mathrm{kJ/kg}$ of enthalpy. A cold stream flowing at $5\ \mathrm{kg/s}$ must gain

$$\Delta h_c=\frac{2(100)}{5}=40\ \mathrm{kJ/kg}.$$

This control-volume model determines energy transfer independently of the detailed heat-transfer mechanism. Conduction and convection determine the exchanger area, temperature profiles and rate coefficients; thermodynamics determines the compatible inlet and outlet energy states.