In this chapter, we apply Adomian's Decomposition Method to find appropriate solutions of heat and mass transfer in the two-dimensional and axisymmetric unsteady flow between parallel plates and squeezing flow and heat transfer between two parallel disks with velocity slip, temperature jump which are of utmost importance in applied and engineering sciences.
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ADM abilities have attracted many authors to use this method for solving fluid dynamic problems. Sheikholeslami et al. (2012) studied the effects of magnetic field and nanoparticle on the Jeffery-Hamel flow using Adomian decomposition method. They show that increasing Hartmann number will lead to backflow reduction. In greater angles or Reynolds numbers, high Hartmann number is needed for reduction of backflow. Also the results show that momentum boundary layer thickness increases as nanoparticle volume fraction increases A. Sadighi and Ganji (2007) introduced ADM to obtain the exact solutions of Laplace equation with Dirichlet and Neumann boundary conditions. Ganji et al (2011) used the analytical tool of ADM to solve the nonlinear problem. They studied the velocity profile of the conductive fluid inside the divergent channel for various values of Hartmann number. Hashim (2006) presented the Adomian decomposition method for solving BVPs for fourth-order integro-differential equations and the Blasius equation (Hashim, 2005). Arslanturk (2005) inspected on the fins efficiency of convective straight fins with temperature-dependent thermal conductivity using the decomposition method. ADM also have been used by several researchers to solve a wide range of physical problems in various engineering fields to solve a real-life problem that exhibits coupling between the mechanical and thermal fields by Sadighi and Ganji (2005) and other nonlinear systems (Daftardar-Gejji & Jafari, 2006; Lesnic, 2005).
The study of unsteady squeezing of a viscous incompressible fluid between two parallel plates in motion normal to their own surfaces independent of each other and arbitrary with respect to time has been regarded as one of the most important research topics due to its wide spectrum of scientific and engineering applications such as hydrodynamical machines, polymer processing, compression, injection molding and lubrication system. in many branches of science and engineering, the interest in the study of heat and mass transfer has been increased. Coincident heat and mass transfer with chemical reaction effect plays a vital role in design of chemical processing equipment, formation and dispersion of fog, damage of crops due to freezing, food processing and cooling towers, distribution of temperature and moisture over grove fields, etc. Biazar and Amir taimoori (2005) solved the heat equation, which governs on numerous scientific and engineering experimentations. Abd-El Aziz (2010) considered the outcome of time-dependent chemical reaction on the flow of a viscous fluid passed an unsteady stretching sheet. Magneto hydrodynamic squeezing flow of a viscous fluid between parallel disks was analyzed by Domairry and Aziz (2009).