Heat exchanger

A heat exchanger is used to exchange heat between two flows. It therefore has two inlets and two outlets. Inlet 1 corresponds to outlet 1, and inlet 2 corresponds to outlet 2.

The heat exchanger is assumed to operate adiabatically. The temperatures in the outlet streams are calculated from the total energy balance and an additional constraint. Currently four options are implemented.

In all cases inconsistency are reported by means of adequate warnings. Calculations can be continued with maximum heat transfer, or aborted, depending on the selected option.

A pressure drop can be specified for each stream.

The two streams between which heat is exchanged can be of different type, but the compound list that applies to the inlet and outlet of corresponding streams should match.

Direct specifications

No iteration is required for direct specifications, but the specifications may not be feasible in the sense that the resulting temperatures are outside of the range of the cold and hot inlet temperature. In this case the heat exchanger may result an error, or may continue with the temperature limits reset, depending on the chosen option for error handling.

• The outlet temperature of stream 1 is specified: The outlet temperatures are constrained. For counter-current operation, the cold stream cannot be heated above the inlet temperature of the hot stream and an analogous constraint holds for the hot stream. Therefore, the specified temperature must range between the inlet temperatures:

In case this equation is violated, the temperature is restricted to the corresponding limit.

Similarly, for co-current operation, the limiting case is given by equal outlet temperatures.

• The heat flux from the hot to the cold stream is fixed: For the counter-current case, the maximum heat transferred from the hot to the cold stream is given by:

If the specified heat transferred exceeds the maximum, temperatures are calculated from the maximum heat flow.

Similarly, for co-current operation, the limiting case is given by equal outlet temperatures.

LMTD based calculations

The overall heat transfer coefficient and area are supplied: Operation in co- or countercurrent flow has to be specified. The model assumes that the heat transfer coefficient and heat capacities are constant along the heat exchanger and there is no longitudinal heat transfer. The LMTD for a co-current heat exchanger is given by:

and for a counter-current heat exchanger by:

In this operation mode, the heat exchanger is solved iteratively. Convergence tolerance and maximum iterations can be specified.

The equations are solved iteratively.

The LMTD method is an analytical solution of the case in which the heat capacity of each stream is constant between in the entry and exit temperature of the stream.

Note that for very high or very low UA, small temperature differences cause this approach to be numerically instable.

Maximum heat transfer

In co-current operation mode, this implies that the outlet streams have the same temperatures. In counter-current operation mode, either the hot outlet has the temperature of the cold inlet, or the cold outlet has the temperature of the hot inlet (depending on which of these two is the limiting case). The overall heat transfer coefficient for this mode is always infinitely large, and will be reported as zero.

The co-current case is solved iteratively.

NTU based specifications

NTU based calculations are based on the maximum possible heat transfer in counter-current operation (see above). The actual amount of heat transferred is reduced from the maximum amount of heat transferred by the effectivity E:

The heat capacity of each stream i (where i = cold or i = hot) is approximated from:

and assumed constant over the entire range Tc,i to Th,i (as opposed to the LMTD method, where the heat capacity is assumed constant between entry and exit temperature for each stream).

The heat capacity ratio Cp,rel follows from:

The number of transfer units relates to the overall heat transfer coefficient and area as:

The effectiveness can be calculated for a counter current heat exchanger from:

or for the co-current case:

The following specifications are supported:

• the effectiveness (in this case co- or counter current flow does not play a role)
• the number of transfer units (NTU)
• the overall heat transfer coefficient and area (UA)