Heat exchanger theory

Definition

A two-stream heat exchanger is modelled as follows. A hot stream and a cold stream flow steadily on the two sides of a wall of area $A$. Heat passes through the wall from the hot to the cold stream. Their mass flow rates are $\dot m_h$ and $\dot m_c$, and their specific heat capacities $c_{p,h}$ and $c_{p,c}$ are constant. The heat capacity rates are $C_h = \dot m_h c_{p,h}$ and $C_c = \dot m_c c_{p,c}$. The inlet and outlet temperatures are $T_{h,i}, T_{h,o}$ and $T_{c,i}, T_{c,o}$. The model consists of three assumptions.

1. No heat is lost to the surroundings, and no phase change occurs.
2. The total heat rate $q$ satisfies $q = C_h (T_{h,i} - T_{h,o}) = C_c (T_{c,o} - T_{c,i})$.
3. Through each element $dA$ of the wall, the heat rate is $dq = U \, (T_h - T_c) \, dA$. Here $T_h$ and $T_c$ are the local stream temperatures and $U$ is the overall heat transfer coefficient.

Heat exchanger theory is the study of this model and of its solutions for given flow arrangements.