Nanofluids substantially enhance the physical and thermal characteristics of the base or conducting fluids specifically when interacting with the magnetic field. Several engineering processes like geothermal energy extraction, metal casting, nuclear reactor coolers, nuclear fusion, magnetohydrodynamics flow meters, petrochemicals, and pumps incorporate magnetic field interaction with the nanofluids. On the other hand, an enhancement in heat transfer due to nanofluids is essentially required in various thermal systems. The goal of this study is to figure out that how much a magnetic field affects nanofluid flow in an enclosure because of a dipole. The nanofluid is characterized using a single-phase model, and the governing partial differential equations are computed numerically. A Pseudo time based numerical algorithm is developed to numerically solve the problem. It can be deduced that the Reynolds number and the magnetic parameter have a low effect on the Nusselt number and skin friction. The Nusselt number rises near the dipole location because of an increase in the magnetic parameter Mn and the Reynolds number Re. The imposed magnetic field alters the region of high temperature nearby the dipole, while newly generated vortices rotate in alternate directions. Furthermore, nanoparticle volume fraction causes a slight change in the skin friction while it marginally reduces the Nusselt number.

In this article, an unsteady free convection flow of MHD viscous fluid over a vertical rotating plate with Newtonian heating and heat generation is analyzed. The dimensionless governing equations for temperature and velocity fields are solved using the Laplace transform technique. Analytical solutions are obtained for the temperature and components of velocity fields. The obtained solutions satisfy the initial and boundary conditions. Some physical aspects of flow parameters on the fluid motion are presented graphically.

Nanofluids have many applications in industries as well as engineering such as biomedicine, manufacturing, and electronics. Nanofluid is used for improvement of thermal and mass transmission. Based on the aforementioned applications, in the present study, a two-dimensional Maxwell nanofluid with thermal radiation effect on the existence of motile microorganisms over a vertically stretchable surface is explored. The consequence of heat absorption, the efficiency of heat flux in a porous medium, viscous dissipations, and Joule heating impacts are considered. The Brownian and thermophoretic diffusion effects have been evaluated. In addition, the binary chemical reaction is taken into account to evaluate the magnetohydrodynamics (MHD) mixed convection flow. Graphene nanoparticles are suspended in so-called engine oil (base fluid). The proposed liquid model depends on the governing nonlinear equations of velocity, temperature, the concentration of nanoparticles, and motile gyrotactic microorganisms. In order to transform highly nonlinear partial differential equations into nonlinear ordinary differential equations, an appropriate similarity transformation is exploited. For the solution of the present study, the homotopy analysis method-technique in Mathematica-12 is used. The fluctuation of velocity, temperature, concentration, and gyrotactic microorganisms’ characteristics for numerous flow parameters is discussed in detail. Some important fallouts of the existing study are that the Maxwell liquid parameter, Eckert number, and magnetic parameter lessen the nanoliquid velocity. But the fluid temperature becomes higher for growing estimates of the Brownian motion and thermophoretic factors. The radiation and chemical reaction parameters have declining impacts on the solutal profile. The motile microorganism profile shows a decrement in bioconvection Lewis and Rayleigh numbers. The nanofluid thermal profile is improved but the nanofluid velocity declined through the augmentation of volume fraction. Also, the coefficient of skin friction and Nusselt number are obtained versus various flow parameters.

As the slip at the solid boundary is an essential attribute for fluid flow in different mechanical situations. Therefore this article aims to explain the slip effect over the free convection and rotating flow of viscous fluid over an extended plate with heat and mass transfer in the presence of magnetic field of the constant magnitude through a porous medium. The respective fluid is chemically reacting fluid hence the effect of chemical reaction with the effect of heat absorption is considered in the development of governing equations. To get the better physical understanding of flow model the governing equations are reduced to dimensionless form. The dimensionless governing equations are solved with aid of Laplace transform and closed form solutions are developed for the thermal, concentration and velocity fields. The real and imaginary components of velocity field are also plotted for the variation of different physical parameters and parametric discussion is posted with assistance of these plotted graphs. In the light of parametric discussion it is concluded that with heat and mass transfer there is more bouncy effect in flow domain. Further in the presence of hall effect fluid speeds up while it is slow down with increasing value of magnetic and slip parameters