Temperature distributions of the heat exchangers in cocurrent and countercurrent mode are given. T_H and T_c represent the temperature of the hot fluid and the cold fluid, respectively.
∆T represents the temperature difference between hot and cold fluids along the heat exchangers. And, x is a point along the channels of the heat exchanger. In the countercurrent mode, ∆T does not vary along the channels as much as the ∆T in the cocurrent mode. Moreover, in cocurrent mode, ∆T is very large at the inlet of the channels and getting smaller progressively. Countercurrent heat exchanger can be evaluated as more efficient with respect to cocurrent heat exchanger since countercurrent mode requires smaller heat transfer area to provide the same heat transfer rate.
At the steady state, the total flow rates of Q_A and Q_B is equal to a steady state rate equation and it is used for the verification of the models. Steady state heat rate equation for a heat exchanger is written as follows:
Q=UA∆Teog
where U is the average overall heat transfer coefficient, A is the area of the heat transfer surface and ∆Teog is the average temperature driving force. UA is described as:UA=Lω(γ_A γ_B)/(γ_A+γ_B )
where L is the length, ω is the perimeter of the channels, γ_A and γ_B are the heat transfer coefficients of fluid A and B respectively.
∆Teog is written as:
| Parameters | Comment |
|---|---|
| L | length of the channels |
| N | number of nodes |
| wB | mass flow rate of fluid B |
| areaA | cross sectional area of channel A |
| areaB | cross sectional area of channel B |
| rhoA | density of fluid A |
| rhoB | density of fluid B |
| cpA | specific heat capacity of fluid A |
| cpB | specific heat capacity of fluid B |
| cpW | specific heat capacity of the wall |
| gammaA | heat transfer coefficient of fluid A |
| gammaB | heat transfer coefficient of fluid B |
| omega | perimeter |
| UA | average overall heat transfer coefficient * area of the heat transfer surface |