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Summary The optimization of the total annual cost in heat exchanger networks has been one of the overarching goals when synthesizing these networks. Several methodologies and techniques have been developed to achieve optimal costs in mixed material heat exchanger networks. This paper demonstrates the application of two decomposition methodologies (total decomposition and partial decomposition) for typical cost rules. The objective function was defined as the optimization and minimization of the total annual cost in mixed materials heat exchanger network. Three optimization algorithms, hybrid genetic‐particle swarm optimization (GA‐PSO), shuffled frog leaping algorithm (SFLA) techniques, and ant colony optimization (ACO), were used to further optimize the total cost in mixed materials heat exchanger network. The results indicate that the total annual cost in partial decomposition method was smaller than that in full integration method and total decomposition method. The reduction of the total annual cost was about 27% for GA‐PSO algorithm, 24% for SFLA and 10% for ACO relative to the results reported in this work. In partial decomposition method, at least one mixed material of heat exchanger was used to reduce the hot and cold utility for decreasing the total annual cost. Partial decomposition method resulted in the highest reduction of the total annual cost compared with other methods. Percentage of difference of the total annual cost were 0.36%, 1.92%, and 5.05% for full integration, total decomposition, and partial decomposition methods, respectively, in comparison with the previous studies. Results have been compared with the results of other studies to demonstrate the accuracy of the applied algorithms.

The effect of MHD on the total heat transfer from a porous fin attached to a vertical isothermal surface has been investigated. The Maxwell equations have been used, and also Rosseland approximation for radiation heat transfer and Darcy model for simulating the flow in porous medium have been adapted. The governing equations are reduced to a nonlinear ODE. The fin is supposed to be an infinite fin, which is exposed to a magnetic field. The dimensionless temperature profile, and the average Nusselt number profiles have been obtained for different Rayleigh numbers and porosities. Validation is carried out by comparing the results obtained in this study with those predicted by Darcy-Brinkman-Forchheimer model. KeywordsHeat transfer · Porous fin · Darcy model · Darcy-Brinkman-Forchheimer · MHD List of Symbols ACross sectional area (m 2 ) B 0 Magnetic field intensity (T)Thermal conductivity (W m −1 K −1 ) k r Thermal conductivity ratio, k eff /k f A. Taklifi (B) 123 216 A. Taklifi et al. KPermeability of the porous fin (m 2 ) mMass flow rate (kg s −1 ) P Fin perimeter (m) RdRadiation-conduction parameter,Temperature at the fin base (K) uAxial velocity (m s −1 ) v Normal velocity (m s −1 ) V Macroscopic velocity of electrons (m s −1 ) ϑ w Average velocity of the fluid passing through the fin at any point (m s −1 ) x Axial coordinate y Transverse coordinateGreek Symbols α Thermal diffusivity (m 2 s −1 )Kinematic viscosity (m 2 s −1 ) σ Electric conductivity ( −1 m −1 ) σ st Stefan-Boltzmann constant (W m 2 K 4 ) ρDensity of the fluid (kg m −3 ) ρ ε Electrical density (A m −3 )

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