Next step, do a detailing.

To Calculate LMTD, we need to understand the flow and type of process (Isothermal or not)

Generally we have complication, when either of fluid is showing isothermal characteristics. see the following variation.

Two ﬂuids are separated by a heat transfer surface (wall), these ﬂuids ideally do not mix, and there are no moving parts.In this blog the thermal design theory of recuperates is presented. In a heat exchanger, when hot and cold ﬂuids are maintained at constant temperatures of Th and Tc as shown in above Fig(a)..The driving force for overall heat transfer in the exchanger, referred to as mean temperature diﬀerence (MTD), is simply Th-Tc.

Such idealized constant temperatures on both sides may occur in idealized single-component condensation on one ﬂuid side and idealized single-component evaporation on the other ﬂuid side of the exchanger. However, a number of heat transfer applications have condensation or evaporation of
single-component ﬂuid on one side and single-phase ﬂuid on the other side. In such cases, the idealized temperature distribution is shown in Fig(b) and (c)

The First major step in Thermal design, is to understand the assumptions that are considered while we disign the heat exchanger, but we forgot to understand them, they are:-

1. The heat exchanger operates under steady-state conditions [i.e., constant ﬂowrates and ﬂuid temperatures (at the inlet and within the exchanger) independent of time].

2. Heat losses to or from the surroundings are negligible (i.e. the heat exchanger outside walls are adiabatic).

3. There are no thermal energy sources or sinks in the exchanger walls or ﬂuids, suchas electric heating, chemical reaction, or nuclear processes.

4. The temperature of each ﬂuid is uniform over every cross section in counter flow and parallel flow exchangers (i.e., perfect transverse mixing and no temperature gradient normal to the ﬂow direction). Each ﬂuid is considered mixed or unmixed from the temperature distribution viewpoint at every cross section in single-pass cross flow exchangers, depending on the specifications. For a multi pass exchanger, the foregoing statements apply to each pass depending on the basic ﬂow arrangement of the passes; the ﬂuid is considered mixed or unmixed between passes as speciﬁed.

5. Wall thermal resistance is distributed uniformly in the entire exchanger.

6. Either there are no phase changes (condensation or vaporization) in the ﬂuidstreams ﬂowing through the exchanger or the phase change occurs under thefollowing condition. The phase change occurs at a constant temperature as for a single-component ﬂuid at constant pressure.

7. Longitudinal heat conduction in the ﬂuids and in the wall is negligible.

8. The individual and overall heat transfer coefficients are constant (independent of temperature, time, and position) throughout the exchanger, including the case of phase-changing ﬂuids in assumption 6.

9. The speciﬁc heat of each ﬂuid is constant throughout the exchanger, so that the heat capacity rate on each side is treated as constant. Note that the other ﬂuid properties are not involved directly in the energy balance and rate equations, but are involved implicitly in NTU and are treated as constant.

10. For an extended surface exchanger, the overall extended surface efﬁciency is considered uniform and constant.

11. The heat transfer surface area A is distributed uniformly on each ﬂuid side in a single-pass or multi pass exchanger. In a multi pass unit, the heat transfer surface area is distributed uniformly in each pass, although different passes can have different surface areas.

12. For a plate-bafﬂed (1–n) shell-and-tube exchanger, the temperature rise (or drop) per bafﬂe pass (or compartment) is small compared to the total temperature rise (or drop) of the shell ﬂuid in the exchanger, so that the shell ﬂuid can be treated as mixed at any cross section. This implies that the number of bafﬂes is large in the exchanger.

13. The velocity and temperature at the entrance of the heat exchanger on each ﬂuidside are uniform over the ﬂow cross section. There is no gross ﬂow maldistribution at the inlet.

14. The ﬂuid ﬂow rate is uniformly distributed through the exchanger on each ﬂuid side in each pass i.e., no passage-to-passage or viscosity-induced maldistribution occurs in the exchanger core. Also, no ﬂow stratiﬁcation, ﬂow bypassing, or ﬂow leakages occur in any stream. The ﬂow condition is characterized by the bulk (or mean) velocity at any cross section.

Question??? So many assumption… still we are ‘designing’ a heat exchanger with Guarantee on performance!! sure we are Engineers 😉

Following Table will show the impact of various parameters on design of heat exchanger.
(NTU stands for number of transfer unit, and alternate to LMTD method)

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