Another the flat tubes have higher surface area

Another technique, which is utilized2 for heat transfer increment, is using flattened tubes instead of circular tubes. Compared to the circular tubes, the flat tubes have higher surface area to cross sectional area ratio, which can be used to increase the compactness and enhance the heat transfer. Razi et al. 7 experimentally considered heat transfer and pressure drop of CuO–oil nanofluid in various flat tubes and finally presented relations for Nusselt number and pressure drop of nanofluid flow in horizontal flat tubes. Vajjha et al. 8 numerically investigated nanofluid flow in a single flat tube of an automobile radiator. They used convection heat transfer coefficient for the wall boundary condition and finally presented the correlation for local Nusselt number and friction factor of the automobile flat tube. Safikhani, and Abbassi 9 numerically simulated a nanofluid flow in different flat tubes with constant heat flux and investigated the effects of tube flattening on the fluid dynamic and heat transfer. In another research, Safikhani et al. 10 presented an optimization of nanofluid flow in flat tubes using CFD, ANN and Genetic algorithm. The design variables were flat tube, internal height, volumetric flow rate, heat flux, nanoparticles volume fraction and diameter of nanoparticles and the ultimate goal was to simultaneously increase the heat transfer coefficient and reduce the pressure drop in flat tubes.

Recently research also has been focused on practical tube applications based on emerging both soft computing fields like Computational fluid dynamic (CFD), and computational intelligence. Adaptive-Network-Based Fuzzy Inference System (ANFIS) 11 is one of the leading artificial neural networks that used to predict results in some engineering problems. For instance, the ANFIS method was used to predict the performance of energy systems such as ground-coupled heat pump systems 12-14, solar systems 15, thermal energy storage 16, refrigeration systems 17-20, modeling the performance in heat exchangers 21-26 (HVAC) systems. 27. Artificial Neural Network (ANN) and ANFIS were used to predict the natural convection in a triangular enclosure by Varol et al. 38. It was observed that the ANFIS method gives more significant value to actual one than the ANN. Rezaei et al. utilized ANFIS to predict the free convection in a partitioned cavity consisting of an adiabatic partition. The training data for optimizing the ANFIS structure was obtained experimentally and for the best ANFIS structure, the mean relative errors of the train and test data were found to be 0.05% and 1.73% respectively. In case of heat transfer in tubes Swain and Kumar Das 29 researched the applicability of ANFIS to model the flow boiling heat transfer over a tube bundle. The heat flux, mass flux, and row height are investigated as input and the heat transfer coefficient as output. The model predict experimental heat transfer coefficient within an error of ±5%. Tahseen et al. 30 used the ANFIS predict the heat transfer and pressure drop for in-line flat tube configuration in a cross flow. The mean relative error for average Nusselt number and pressure drop were obtained less than 1.9% and 2.97% respectively. Hasiloglu et al. 31 studied is the usefulness of ANFIS to predict transient heat transfer of circular duct flow with varying inlet temperature. The results show that the ANFIS can be used to model the transient heat transfer in ducts. Mehrabi et al. 32 investigated the ANFIS for modeling the heat transfer and fluid flow characteristics of helicoidally double-pipe heat exchangers using some experimental results for training and test data. The results showed that proposed modeling by ANFIS was effective and reliable.

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Increasing the amount of heat transfer usually leads to an increase in pressure drop. Therefore, an arbitrary configuration with maximum heat transfer and a minimum pressure loss achieved by a multi-objective optimization. A significant share of the research has been devoted to heat exchangers. The ultimate goal in optimizing each heat exchanger is to maximize heat exchange while minimizing the pressure drop of fluids. By doing so, the initial and operational costs of these exchangers can be reduced and small size of heat exchangers could be used. Wang et al 33 proposed a kind of shell-and-tube heat exchangers with fold baffles. Second-order polynomial response surface method and multi-objective genetic algorithm was adopted. A set of Pareto-optimal points were obtained, and the optimization results showed a good agreement with CFD simulation data with the relative deviation less than ±3%. The empirical correlations of the Nusselt number and friction coefficient were obtained with the adjusted coefficient of 0.943 and 0.999, respectively. Liu et al 34 developed a CFD simulation and multi-objective optimization of a plate-fin heat exchanger for the hydraulic retarder. The NSGA-II Algorithm was employed. This research only focused on the improvement of heat transfer performance and the other parameter such as cost, maintenance, etc. was not considered. In a numerical simulation, Zheng et al 36 examined the thermal-hydraulic performance of a heat exchanger tube with vortex rod inserts. To achieve the best configuration for the maximum heat transfer enhancement with the minimum pressure drop Multi-objective optimization has been implemented and the optimal Pareto front obtained. By combining   Genetic   Aggregation   response   surface   and Multi-Objective Genetic Algorithm, Wang et al. 37 studied the effects of configuration parameters of shell-and-tube heat exchanger. The average heat transfer coefficient of improved configuration is enhanced by 2.93%, while the average pressure drop is reduced by 40.27%.

In this research, by considering geometrical parameters such as the tube flattening, porous layer thickness ratio, porosity of porous layer, wall heat and entrance flow rate a multi-objective optimization has been carried out in order to maximize the heat transfer and minimize the pressure drop in a flat tube. To this purpose, a number of flat tube geometries have been numerically solved by the use of CFD approach. Results have been used to acquire the polynomials of the GMDH type neural network. The GMDH neural network is the heuristic self-organization method to model the complex systems and mostly used for converting discrete data to continuous functions 37.