# Heat Exchanger Design and Performance

UPDATED: 03/29/2022

The usual treatment of heat exchanger thermal design and analysis is based on two analysis-based solution methods applied to the governing, coupled heat balance equations for the two fluids. Because the solution of these differential equations by analytical means is challenging for all but the simplest configurations, the numerical results have been graphed in non-dimensional form and the resulting charts have been used routinely for the past three quarters of a century. The LMTD method is commonly used for heat exchanger design, that is, determining the required thermal size, while the Effectiveness – NTU method is used for performance calculations. Unfortunately, the charts and equations associated with these two methods do not give a complete picture of what is happening inside the exchanger, only a single overall measure. In this two-part module, the same governing heat balance equations are solved in real time in discretized form using modern numerical techniques, yielding not only the same “bottom line” results as the traditional methods, but giving a complete picture of what is happening within the device.  In addition, not having to look up a “correction factor” manually means the user can test parameters at will until an improved design is had.

Module Description

Our software for heat-exchanger education consists of a single module that covers both “1-D” and “2-D” exchangers:

• The first tab (algorithm) is used for double-pipe, shell-and-tube (with multiple shell passes) and 2-pass, 2-pass plate heat exchangers (i.e., configurations which may be approximated as “one-dimensional”),
• The second tab (algorithm) is designed for single-pass, crossflow heat-exchangers with the two fluids mixed or unmixed.

Both algorithms solve discretized, coupled heat-balance equations along the paths of the two fluids as they each traverse the heat exchanger. Separate algorithms (on the two tabs) have been developed because in one case, a coupled set of ordinary differential equations apply, while in the other a coupled set of partial differential equations govern. The detailed temperature distribution is presented to the user in both tabs, and the performance and design numbers associated with the conventional (LMTD and effectiveness-NTU) methods are reported in both cases for comparison. Samples of the main user-interface for both algorithms are shown below.

Both algorithms allow for several geometric options. The single pass, crossflow heat exchanger module allows the four generic textbook options: neither fluid mixed, both fluids mixed and either one or the other, but not both mixed. A fifth selection, a two-pass geometry related to an experiment we have done in our undergraduate lab, is also included. The user selects this option in the top left corner and a small schematic of the selected geometry appears.

The 1-D option (tab seen below) allows for several generic geometries, including double pipe designs (parallel and counterflow), shell-and-tube designs and 2-pass, 2-pass plate configurations. After selection of the “Configuration” option, the user specifies a few other inputs relevant to that particular case. In the case of a shell-and-tube configuration, the baffle arrangement is used as a convenient means of discretizing the shell for the numerical solution.

In both modules after the geometry has been selected, the user specifies the heat-capacity rates for both fluids and indicates which of the two calculation methods to use. For the “Design” option, the user then specifies the desired outlet temperature of the hot fluid. For the Performance option the user inputs the product of the overall heat transfer coefficient and area (UA product). (Input boxes are shown in white on all user interfaces while numbers appearing on the gray background are program outputs.)

Based on this user input, the temperature distributions in both fluids are computed and displayed in a fraction of a second. For the crossflow module the temperature distribution in both fluids is depicted in the form of color contour plots as seen above. The hot fluid is shown flowing vertically in the leftmost plot. The cold fluid flows from left to right and is shown in the center. The local mean temperature of the two fluids, which can be helpful in assessing the quality of a design, is shown in the right-hand plot.

For one-dimensional geometries HTT_HX returns a plot of the temperatures of both fluids as a function of position. In fact, three curves are plotted. In the interface seen above, the temperature of the shell fluid is shown in light blue. That of the tube fluid is plotted twice; the yellow line shows the tube fluid temperature plotted in the conventional way, i.e., as counterflow. The third (green line) shows the tube temperature as “seen” by the shell fluid as it passes through the exchanger. So, for instance, shell fluid entering the top of the three shells used in this example first encounters fluid that is exiting the shell, then fluid that has just entered that shell, then fluid that is nearly ready to exit, etc. This accounts for what appears to be a “ringing” behavior in the curves. (The analytical solutions are based on the exchange of heat between the shell fluid and the mean of the two local pipe fluid temperatures at that horizontal position.)

In addition to the detailed temperature distributions, both interfaces return all the design and performance measures used with the traditional methods so that all results may be verified by comparison with the conventional charts. While not currently configured, either module could be adapted to handle situations which inherently cannot be handled by the analysis-based methods, including non-uniform thermal properties, non-uniform overall heat transfer coefficient and condensation or evaporation of either fluid occurring in only a portion of the device. Such capability is available in commercial HX design software.

Video Introduction to the HTT_HX module (3:52).

Virtual Laboratory

A virtual laboratory assignment by Jorge Navalho based on the HTT_HX module can be downloaded here.

Reference

A complete description of the numerical algorithm used in these two modules may be found in: Ribando, R.J., O’Leary, G.W., and Carlson-Skalak, S.E., “A General, Numerical Scheme for Heat Exchanger Thermal Analysis and Design,” Computer Applications in Engineering Education, Vol. 5, No. 4, 1997, pp 231-242.