<small>In natural convection, the fluid motion occurs by natural means
such as buoyancy. Heat transfer by natural convection happens in many
physical problems and engineering applications such as geothermal
systems, heat exchangers, petroleum reservoirs and nuclear waste
repositories. These problems and phenomena are modeled by ordinary or
partial differential equations. In most cases, experimental solutions
cannot be applied to these problems, so these equations should be solved
using special techniques. In this paper, natural convection of a
non-Newtonian fluid flow between two vertical flat plates is
investigated analytically and numerically. Collocation Method (CM) and
fourth-order Runge -Kutta numerical method (NUM) are used to solve the
present problem. These methods are powerful and convenient algorithms in
finding the solutions for the equations. While these are capable of
reducing the size of calculations. In order to compare with exact
solution, velocity and temperature profiles are shown graphically. The
obtained results are valid with significant accuracy.</small
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