Recent studies have attempted to find methods and techniques that enable the development of heat transfer within thermal transformers. For this purpose, this paper includes a numerical simulation of a non-Newtonian fluid inside a chamber with four hot bodies. The chamber is exposed to a magnetic field of constant and uniform intensity. Also, the upper wall of the chamber has a horizontal movement. The study is based on the quality of heat transfer between the heated parts of the chamber and the complex fluid under the influence of a set of criteria, namely Reynolds number (= 1 to 40); Hartmann number (= 0 to 100); power-law index (= 0.6 to 1.4) and Richardson number (0 to 100). The interpretation of the results is done by displaying the path-lines and isotherms distribution. Also, the amount of thermal transfer of the hot bodies is given in terms of the Nusselt number. The results showed that the positioning of the hot bodies plays an important role in heat transfer. Moreover, increasing the value of the power-law index makes the fluid stickier, which reflects its negative effect on heat transfer.
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