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In the current investigation a mathematical model is simplified to explore the numerical treatment for the thermal and flow behavior in a magneto hydrodynamics Casson fluid through a micro channel by taking [Formula: see text] nanoparticles. The combined effects of temperature jump, porous medium and velocity slip are incorporated. Using the dimensionless variables one can obtain the governing differential equations thereafter resolved numerically using RKF45 method. The velocity, temperature, skin friction and Nusselt number coefficient are addressed for different pertaining parameter. The upshots of the current investigation are visualized through graphically elucidation. Out comes shows that larger values of solid volume fraction decreases both velocity and temperature field. Furthermore drag coefficient is increases for increase in magnetic parameter, also hybrid nanofluid gives more impact than nanofluid.

Two kinds of hybrid nanomaterial flow through cylindrical fin are examined under the presence of conduction, convection and radiation. Darcy law model is used to develop the heat equation. With the help of Maple, the non-dimensional thermal equation is numerically solved using the fourth and fifth order of Runge–Kutta Fehlberg. The impact of convection parameter, wet porous parameter, radiation parameter, power law index, ambient temperature and solid volume fraction are discussed through the graphs. It is found that higher values radiation parameter reduces the temperature whereas solid volume fraction enhances the temperature.

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Carbon nanotubes are used to achieve high heat transfer rates in a variety of engineering applications include thermal storage systems, electronic component cooling, high-performance building insulation, heat exchangers and drying technologies. Hence the aim of this article is to examine the addition of single walled carbon nanotubes (SWCNT) and multi-walled carbon nanotubes (MWCNT) to water in a vertical microchannel to improve heat transfer. The effects of MHD, slip, convective boundary condition and heat source/sink are incorporated. The Brinkman-Forchheimer flow model and type II hybrid nanofluid model is adopted. Converted dimensionless differential equations are solved numerically via Dsolve command with the aid of Maple. The simulation assessment is worked out by graphs. One of the main tasks of the analysis is to compare MWCNT/water and SWCNT-MWCNT/water. It is shown that the improvement of the heat source/sink parameter improves the temperature and the rate of heat transfer in MWCNT/water is higher than SWCNT-MWCNT/water. Also larger values of Lorentz force and buoyancy force decreases the drag coefficient.