In this study, we propose a reliable algorithm to develop an analytical solution for the problem of laminar steady magnetohydrodymanics (MHD) nanofluid flow in a semi-permeable channel using the differential transformation method (DTM). The working fluid is water with copper nanoparticles. The effects of Hartmann number and Reynolds number on velocity profiles have been also considered for various numerical cases. The effective thermal conductivity and viscosity of nanofluid are calculated by the Maxwell and Brinkman models, respectively. A close agreement between the obtained solution and some well-known results has been established.

In this paper, the unsteady magnetohydrodynamic (MHD) squeezing flow between two parallel disks (which is filled with nanofluid) is considered. The Galerkin optimal homotopy asymptotic method (GOHAM) is used to obtain the solution of the governing equations. The effects of Hartman number, nanoparticle volume fraction, Brownian motion parameter and suction/blowing parameter on nanofluid concentration, temperature and velocity profiles have been discussed. Furthermore, a comparison between obtained solutions and numerical ones have been provided

In the current research, the unsteady two dimensional Graphene Oxide water based nanofluid heat transfer between two moving parallel plates is analyzed using an intelligent black-box identifier. The developed intelligent tool is known as evolvable evolutionary fuzzy inference system (EE-FIS) which is based on the integration of low-level fuzzy programming and hyper-level evolutionary computing concepts. Here, the authors propose the use of a modified evolutionary algorithm (EA) which is called hybrid genetic mutable smart bee algorithm (HGMSBA). The proposed HGMSBA is used to evolve both antecedent and consequent parts of fuzzy rule base. Besides, it tries to prune the rule base of fuzzy inference system (FIS) to decrease its computational complexity and increase its interpretability. By considering the prediction error of the fuzzy identifier as the objective function of HGMSBA, an automatic soft interpolation machine is developed which can intuitively increase the robustness and accuracy of the final model. Here, HGMSBA-FIS is used to provide a nonlinear map between inputs, i.e. nanoparticles solid volume fraction (ϕ), Eckert number (Ec) and a moving parameter which describes the movements of plates (S), and output, i.e. Nusselt number (Nu). Prior to proceeding with the modeling process, a comprehensive numerical comparative study is performed to investigate the potentials of the proposed model for nonlinear system identification. After demonstrating the efficacy of HGMSBA for training the FIS, the system is applied to the considered problem. Based on the obtained results, it can be inferred that the developed HGMSBA-FIS black-box identifier can be used as a very authentic tool with respect to accuracy and robustness. Besides, as the proposed black-box is not a physics-based identifier, it frees experts from the cumbersome mathematical formulations, and can be used for advanced real-time applications such as model-based control. The simulations indicate that the gradient of Nu has a direct nonlinear relation with the values of ϕ and Ec. It is also observed that an increase in the value of S decreases the value of Nu