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Why is the logarithmic mean temperature difference (LMTD) so critical? The mathematical principle of heat exchangers you have never heard of is revealed!
In the field of thermal engineering, logarithmic mean temperature difference (LMTD) is a key indicator to determine the driving force of heat transfer in flow systems, especially in the design and analysis of heat exchangers. LMTD is the logarithmic average of the temperature difference between the hot flow and the cold flow inlet and outlet at both ends of the heat exchanger. This value has a direct impact on the heat transfer efficiency.
In a given heat exchanger, if its shape and heat transfer coefficient remain unchanged, the larger the LMTD, the more heat is transferred. This is clear from the design principles of the heat exchanger. Because of this, LMTD has become an indispensable tool in heat exchanger analysis.
"Understanding the basic definition of LMTD is the first step to mastering heat exchanger analysis."
The definition and application of LMTD
When analyzing a general heat exchanger, we can label its two ends as "A" and "B", and the hot and cold flows enter or exit from different locations at both ends. In this case, LMTD can be defined as the logarithmic average of the temperature difference between the two ends.
The calculation of LMTD is based on the comparison of heat flow at different points, which also explains how LMTD is used to calculate the heat exchanged in a heat exchanger. The formula is as follows:
Q = U × A × LMTD
In this formula, Q is the heat transferred in the Japanese system, U is the heat transfer coefficient, and A is the heat exchange area. The use of LMTD is particularly important if the estimation of U is very complex, such as when co-current or counter-current is used.
The derivation process of LMTD
In the operation of a heat exchanger, heat transfer occurs along specific axes. Since different temperature differences will occur when fluids undergo heat exchange, we can use the relationship between local heat flow and temperature difference to derive the expression of LMTD.
In other words, the amount of heat transferred per unit space is proportional to the temperature difference between the fluids. This relationship will make the calculation of LMTD simpler when the fluid temperature does not change much.
"Every heat exchange process is a game between heat and temperature."
Assumptions and limitations of LMTD
When performing LMTD calculations, we usually assume that the specific heat capacity of the fluid is constant, which is very important for applicability in actual situations. When the specific heat capacity of the fluid changes, the accuracy of this method will decrease and may even become unavailable in some cases.
During the heat exchange process, certain specific situations such as condensers and reboilers also require special attention, because the phase changes in these situations will affect the efficiency of heat transfer.
"Any slight change in the heat exchange process may affect the final result."
Conclusion
The logarithmic mean temperature difference (LMTD) is not only a mathematical formula, but also a key to helping us understand and analyze how the heat exchanger affects heat transfer in actual operation. In the face of constantly advancing technology, the application of LMTD has become more and more important. So, how will we better use this principle to solve more complex heat exchange problems in the future?
