| The big problems facing world-wide energy utilization are the low efficiency and bulky heat exchangers, which worsen its systematic economic feasibility. In an attempt to develop heat transfer technologies with high energy efficiency, a mathematical study is established, and optimization analysis using FSP (field synergy principle) is proposed to support meaning of heat transfer enhancement in such a plate finned tube heat exchanger.The parabolic energy equation is solved by utilizing the combined methodology of Green’s function solution integrated with the extended weighted residuals method to first obtain the temperature profile. The synergy field is then established by analyzing convective heat transfer coefficient subjected to the geometrical parameter and iso-thermal boundary condition of tube surface. For convenience solution and to customize ability of FLUENT, a separated general transport equation for synergy based on turbulent convective heat transfer is used. Numerical simulations are considered that have finite pressure gradient across translational periodic boundaries in circular and elliptical tube bundle. The indicated Nusselt number found that convective heat transfer depends not only on the temperature difference, flow velocity and fluid properties, but also depend on the synergy angle and synergy number for the flow and temperature fields. Heat transfer in elliptical tube bundle is enhanced significantly with increasing inlet velocity, field synergy number and decreasing of synergy angle. Under the same operating conditions of the two designs, the total average synergy angle is 78.97°and 66.31° in circular and elliptical tube bundle, respectively. Optimization of the plate finned tube heat exchanger by FSP shows that in case of elliptical tube bundle design, the average synergy number and heat transfer rate are increased by 22.68% and 35.98% respectively.Since there is no experimental demonstration to validate the first deduction of FSP, an experimental analysis is carried on a simple heated plate surface. Experiments are conducted using infrared thermal-vision system and professional high-speed camera. The field study concerns the hydrodynamic and water jet velocity ratio based on four different configurations under relatively low jet Reynolds number ranging from 2,602 to 6,505 and to be optimized by FSP. New analytical equations are developed to investigate experimentally the synergy between velocities streamline and temperatures field as well as synergy number especially in the mid integrals areas where the images of flow field have clear appearance along the lateral direction of the heated plate.The irreversibility of heat transfer process can be expressed with extremum entransy dissipation EED, minimum entropy generation MEG, external pump work consumption EPWC and exergy destruction minimization EDM. Convective laminar and turbulent heat transfer field synergy equations for the plate finned tube heat exchanger are developed based on the EED principle, while other heat transfer processes elaborated only for laminar convective heat transfer field synergy equations in order to reduce computational effort and time cost. The new proposed laminar heat synergy optimization equations are deduced by setting irreversibility of heat transfer process considering viscous dissipation and its mechanism of generating thermal energy as a single optimization objective constraint condition, with a momentum added with additional volume force which is constructed through functional variation of Lagrange multipliers to numerically simulate convective heat transfer in coupling with energy equation. Solution of the field synergy equations gives the optimal flow field of swirls flow near the surface tubes and lessens in the cavity area, which are followed by a gradual increase of Nusselt number up to following tube, having the best field synergy for a different viscous dissipation. The new method of optimization will derive optimum velocity field equations for steady laminar convective heat transfer.In addition, several explicit analytical solutions for full and non-synergy field in 2D incompressible flow are investigated numerically. These solutions are boundary field synergy which synergy occurs only along the boundary between fluid and tube surfaces. Besides their theoretical meaning for possibility existence of full and non-synergy field, they are meaningful to further check the accuracy and effectiveness of synergy field, which will offer guidance for selecting and designing an appropriate enhancement unit.Finally, using optimal velocity patterns as a guide, the design of solid inclined vortex generators VGs can be introduced in actual applications, so as to generate the desired swirls flow and enhance the overall coverage of laminar and turbulent heat exchange. As illustrative examples, the local field synergy angle analyses of plate finned tube heat exchanger with vortex generators are presented. Results show that the solid VGs mounted near downward and upper tube surfaces has a best average synergy angle 86.53° and PEC= 2.33. |
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