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The third-grade fluid model is one of the unique models in all the non-Newtonian fluids, which is evolved for its particular implementation in petrochemical engineering, confectionaries, earth science and lubricating systems. Hence, the current work scrutinises the entropy generation and thermal analysis of non-Newtonian fluid in a permeable oblique microchannel. The effects of heat generation, thermal radiation and Hall effects on fluids in a microchannel have been explored. The rheological expressions of third-grade fluid are considered. By considering the desirable similarity variables the equation of motion was reduced to nonlinear ordinary differential equations. The Runge–Kutta-Fehlberg’s fourth-fifth-order technique along with the shooting method was adopted to solve these dimensionless expressions. The repercussion of this investigation upholds that the enhancement of distance parameters augments the thermal field. The amplification of the porosity parameter occurs with a decrement in the thermal profile. The secondary velocity profile declines with an enhanced value of the Hall parameter and seen improvement in the primary velocity profile.

Natural convection flow of third-grade fluid along an oblique permeable micro-channel with Hall effects: an irreversibility analysis