Abstract
A non-linear three-dimensional inverse shape design problem was investigated for a pipe type heat exchanger to estimate the design variables of continuous lateral ribs on internal Z-shape lateral fins for maximum thermal performance factor η. The design variables were considered as the positions, heights, and number of ribs while the physical properties of air were considered as a polynomial function of temperature; this makes the problem non-linear. The direct problem was solved using software package CFD-ACE+, and the Levenberg–Marquardt method (LMM) was utilized as the optimization tool because it has been proven to be a powerful algorithm for solving inverse problems. Z-shape lateral fins were found to be the best thermal performance among Z-shape, S-shape, and V-shape lateral fins. The objective of this study was to include continuous lateral ribs to Z-shape lateral fins to further improve η. Firstly, the numerical solutions of direct problem were solved using both polynomial and constant air properties and then compared with the corrected solutions to verify the necessity for using polynomial air properties. Then, four design cases, A, B, C and D, based on various design variables were conducted numerically, and the resultant η values were computed and compared. The results revealed that considering continuous lateral ribs on the surface of Z-shape lateral fins can indeed improve η value at the design working condition Re = 5000. η values of designs A, B and C were approximately 13% higher than that for Z-shape lateral fins, however, when the rib numbers were increased, i.e., design D, the value of η became only 11.5 % higher. This implies that more ribs will not guarantee higher η value.
Highlights
It is well known that if a furnace produced industrial waste heat that can be recycled by utilizing economizers or regenerators before it is discharged into the environment, the thermal efficiency of the system can be improved significantly
Letting the desired η(Θ) of PTHE-ZR be denoted as φ, the fin shape design problem can be stated as follows: utilize φ to design PTHE-ZR for yielding optimal thermal performance factor η(Θ)
The optimal design algorithm with Levenberg–Marquardt method (LMM) was considered in the present study to estimate the design variables of the ribs for the internal Z-shape lateral fins in PTHE-ZR
Summary
It is well known that if a furnace produced industrial waste heat that can be recycled by utilizing economizers or regenerators before it is discharged into the environment, the thermal efficiency of the system can be improved significantly. If the exhaust gas can be cooled down to a reasonably low temperature before its discharge this will be environmentally friendly. Economizers and regenerators are basically the so-called pipe type heat exchangers, and internally longitudinal finned tubes are usually utilized to effectively enhance heat transfer for the tube side. They can be used in many practical industrial applications such as petroleum industries, boiler systems, power plants and chemical engineering industries. Webb [1] has discussed internally finned tubes in detail, and Fabbri [2,3]
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