**1. Introduction**

The boundary layer flows, heat and mass transfer in a quiescent Newtonian and non-Newto‐ nian fluid driven by a continuous stretching sheet are of significance in a number of industrial engineering processes such as the drawing of a polymer sheet or filaments extruded continu‐

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ously from a die, the cooling of a metallic plate in a bath, the aerodynamic extrusion of plastic sheets, the continuous casting, rolling, annealing and thinning of copper wires, the wires and fibre coating. During its manufacturing process, a stretched sheet interacts with ambient fluid thermally and mechanically. Both the kinematics of stretching and the simultaneous heating or cooling during such processes have a decisive influence on the quality of the final product. In [1],theeffectsofchemicalreactionandmagneticfieldonviscousflowoveranon-linearstretching sheet were reported. Mabood et al. [2] studied numerically MHD flow and heat transfer of nanofluid over a non-linear stretching sheet. Abel et al. [3] investigated the steady buoyancydriven dissipative magneto-convective flow from a vertical non-linear stretching sheet. In [4], an analysis of heat transfer over an unsteady stretching sheet with variable heat flux in the presence of heat source or sink was made. Several other studies have addressed various aspects of regular/nanofluids [5–10].

Micropolar fluids are fluids with microstructure and asymmetrical stress tensor. Physically, they represent fluids consisting of randomly oriented particles suspended in a viscous medium. These types of fluids are used in analysing liquid crystals, animal blood, fluid flowing in brain, exotic lubricants, the flow of colloidal suspensions, etc. The theory of micropolar fluids was first proposed by Eringen [11]. In this theory, the local effects arising from the micro‐ structure and the intrinsic motion of the fluid elements are taken into account. The compre‐ hensive literature on micropolar fluids, thermomicropolar fluids and their uses in engineering and technology was presented by Kelson and Desseaux [12]. Gorla and Nakamura [13] discussed the combined convection from a rotating cone to micropolar fluids with an arbitrary variation of surface temperature. Prathap Kumar et al. [14] studied the effect of surface conditions on the micropolar flow driven by a porous stretching sheet. In [15], the case of mixed convection flow of a micropolar fluid past a semi-infinite, steadily moving porous plate with varying suction velocity normal to the plate in the presence of thermal radiation and viscous dissipation was discussed. Mansour et al. [16] studied heat and mass transfer effects on the magnetohydrodynamic (MHD) flow of a micropolar fluid on a circular cylinder. El-Hakiem [17] proposed the dissipation effects on the MHD-free convective flow over a non-isothermal surface in a micropolar fluid. Joule heating and mass transfer effects on the MHD-free convective flow in micropolar fluid are investigated by El-Hakiem et al. [18] and El-Amin [19], respectively. In [20], the derivation of the unsteady MHD-free convection flow of micropolar fluid past a vertical moving porous plate in a porous medium was presented. Many researchers investigated different aspects of micropolar fluid [21–23].

The study of heat source/sink effects on heat transfer is another important issue in the study of several physical problems. The effect of non-uniform heat source, only confined to the case of viscous fluids, was also included in [24–27], while Mabood et al. [28] investigated nonuniform heat source/sink effects and Soret effects on MHD non-Darcian convective flow past a stretching sheet in a micropolar fluid with radiation.

Combined heat and mass transfer problems with chemical reactions are important in many processes of interest in engineering and have received significant attention in recent years. These processes include drying, evaporation at the surface of a water body, energy transfer in a wet cooling tower and the flow in a desert cooler [29]. Chemical reactions are classified as either homogeneous or heterogeneous. A homogeneous reaction is one which occurs uni‐ formly through a given phase, while a heterogeneous reaction takes place in a restricted region or within the boundary of a phase. A reaction is said to be a first-order reaction if the rate of reaction is directly proportional to the concentration [30, 31]. The effect of chemical reaction on thermal radiation for MHD micropolar flow and heat and mass transfer was investigated by Das [32]. Hayat et al. [33] considered MHD flow and mass transfer of an upper-convected Maxwell fluid past a porous shrinking sheet with chemical reaction. The behaviour of chemically reactive solute and distribution in MHD boundary layer flow over a permeable stretching sheet were investigated by Bhattacharyya and Layek [34]. Kandasamy et al. [35] studied the effect of transfer of chemically reactive species in MHD-mixed convective flow past over a porous wedge. The solution for diffusion of chemically reactive species in a flow of a non-Newtonian fluid over a stretching sheet immersed in a porous medium was reported by Afify [36], while Mabood et al. [37] reported the effects of chemical reaction and transpira‐ tion on MHD stagnation point flow and heat transfer over a stretching sheet.

The main objective of this chapter is to apply a recently developed numerical technique known as Spectral Quasi-Linearization Method (SQLM) in solving MHD micropolar fluid, heat and mass transfer over an unsteady stretching sheet through porous media in the presence of a heat source/sink and chemical reaction. The SQLM was first implemented by Motsa et al. [38].
