Analytical study of micropolar fluid flow and heat transfer in a channel with permeable walls M. Fakour a, ⁎, A. Vahabzadeh a , D.D. Ganji b , M. Hatami c a Young Researchers Club, Sari Branch, Islamic Azad University, Sari, Iran b Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran c Department of Mechanical Engineering, Esfarayen University of Technology, Esfarayen, North Khorasan, Iran abstract article info Article history: Received 11 December 2014 Received in revised form 27 December 2014 Accepted 20 January 2015 Available online 21 January 2015 Keywords: Permeable channel Micropolar fluid Peclet number Heat transfer Least square method (LSM) In this study, micropolar fluid flow in a channel subject to a chemical reaction is investigated analytically using least square method (LSM) and numerically. Some efforts are done to show reliability and performance of the present method compared with the numerical method (Runge–Kutta fourth-order) to solve this problem. The re- sults reveal that the LSM can achieve suitable results in predicting the solution of these problems. Also, the effect of consequential parameters such as Reynolds number (Re), micro rotation and Peclet number on the stream function, velocity and temperature distribution is discussed. The results show that the stream function decreases with increase of Reynolds number and velocity boundary layer thickness decreases as Re increases. With increase of Peclet number (Pe) the oscillation of temperature fluid and concentration profile increases. Furthermore, the effect of the Reynolds and Peclet numbers on Nusselt and Sherwood numbers is completely investigated from the physical view point in the present study. © 2015 Published by Elsevier B.V. 1. Introduction The theory of a micropolar fluid derives from the need to model the flow of fluids that contain rotating micro-constituents. A micropolar fluid is the fluid with internal structures which coupling between the spin of each particle and the macroscopic velocity field is taken into ac- count. It is a hydro dynamical framework suitable for granular systems which consist of particles with macroscopic size. Eringen [1] was the first pioneer of formulating the theory of micropolar fluids. His theory introduced new material parameters, an additional independent vector field – the microrotation – and new constitutive equations which must be solved simultaneously with the usual equations for Newtonian fluid flow. Although the field of micropolar fluids is rich in literature, some gaps can be observed and needs more study in this field. For instance, Gorla [2], Rees and Bassom [3] investigated the flow of a micropolar fluid over a flat plate. Also, Kelson and Desseaux [4] studied the flow of micropolar fluids on stretching surfaces. Heat and mass transfer have important role in many industrial and technological processes such as manufacturing and metallurgical processes which heat and mass transfer occur simultaneously. The influence of a chemical reaction and thermal radiation on the heat and mass transfer in MHD micropolar flow over a vertical moving plate in a porous medium with heat generation was studied by Mohamed and Abo-Dahab [5]. Recently effect of using micropolar fluid, nanofluid, etc. on flow and heat transfer has been studied by several authors [6–15]. There are some simple and accurate approximation techniques for solving nonlinear differential equations called the Weighted Residuals Methods (WRMs). Collocation, Galerkin and Least Square Method (LSM) are examples of the WRMs which are introduced by Ozisik [16] for using in heat transfer problem. Stern and Rasmussen [17] used collo- cation method for solving a third order linear differential equation. Vaferi et al. [18] have studied the feasibility of applying the Orthogonal Collocation method to solve diffusivity equation in the radial transient flow system. Recently Hatami et al. [19] used LSM for heat transfer study through porous fins, also the problem of laminar nanofluid flow in a semi-porous channel in the presence of transverse magnetic field is investigated. Hatami and Ganji [20] found that LSM is more appropri- ate than other analytical methods for solving the nonlinear heat transfer equations. This method has been successfully applied to solve many types of nonlinear problems [21–24]. In this study LSM is applied to find the approximate solutions of non- linear differential equations governing the micropolar fluid flow in a channel. A comparison between the LSM results and the numerical solu- tion has been provided. The velocity, temperature and concentration profiles are shown and the influence of Reynolds numbers, micro Journal of Molecular Liquids 204 (2015) 198–204 ⁎ Corresponding author. E-mail addresses: mehdi_fakour@yahoo.com, mehdi_fakoor8@yahoo.com (M. Fakour), vahabzadeh_a@yahoo.com (A. Vahabzadeh), ddg_davood@yahoo.com (D.D. Ganji), m.hatami2010@gmail.com (M. Hatami). http://dx.doi.org/10.1016/j.molliq.2015.01.040 0167-7322/© 2015 Published by Elsevier B.V. Contents lists available at ScienceDirect Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq