The present contribution focuses on heat transmission in the conjugate mixed bioconvection flow of Carreau nanofluid with swimming gyrotactic microorganisms through an inclined stretchable cylinder with variable magnetic field impact and binary chemical reaction. Additionally, the investigation involves the aspects of variable decrease or increase in heat source and non-uniform thermal conductivity. A passively controlled nanofluid pattern is used to estimate this nano-bioconvection flow case, which is believed to be more physically accurate than the earlier actively controlled nanofluid typically employed. One of essential features of this investigation is the imposition of a zero-mass flux condition at the surface of the cylinder. Through the implementation of an appropriate transformation, the nonlinear PDE system is mutated into similar equations. The flow equations thus obtained are solved numerically to explore the influence of the physical constraints involved through implementation with the aid of the MATLAB bvp4c code. The solutions were captured for both zero and non-zero bioconvection Rayleigh number, i.e., for flow with and without microorganisms. The present numerical results are compared with the available data and are determined to be in excellent agreement. The significant result of the present article is that the degree of nanoparticle concentration in the nanofluid exhibits an increasing trend with higher values of activation energy constraint.

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Numerical investigation of a chemically reactive second grade fluid flow towards an exponentially stretching sheet into a porous medium induced by thermal and concentration slips boundary conditions is carried out. Further, nonlinear thermal radiations, Joule heating, MHD and thermophoretic impacts are also taken into account. The modified Fourier and Fick’s law is used to analyse the thermal and solutal energy features. The nonlinear systems of partial differential equations, as well as boundary conditions, are transformed into systems of nonlinear ordinary differential equations by imposing appropriate similarity variables. Then these transformed equations are solved using the BVP4C Matlab approach numerically. The graphs and tables of a number of emerging parameters are plotted and discussed. It is noticed that by the improvement of the second grade fluid parameter, the velocity profile is reduced. Moreover, the upsurge of Eckert numbers Ec1 and Ec2 and thermal slip parameter S1 enhance the temperature of the fluid in the flow domain.

Nanofluids receive recognition from researchers and scientists because of their high thermal transfer rates. They have impactful industrial and technological modules in daily activities. In recent times, the heat transfer rate has been strengthened even more by a certain type of nanofluid known as “carbon nanotubes”. The water-based magnetohydrodynamic flow with the nanoparticles MWCNT and SWCNT over an axially rotating stretching disk is highlighted in this article. In addition, the perspectives of viscous dissipation and MHD were taken into consideration. In order to formulate the physical problem, Xue’s model is considered with the thermophysical properties and characteristics of carbon nanofluid. The current modeled system of partial differential equations is transformed into an ordinary differential equation system by the suggesting of the best similarity technique. Later, the transformed system of ordinary differential equations is solved numerically by using the Keller box method and the shooting method. Figures and charts are used to study and elaborate the physical behavior of the key subjective flow field parameters. The saturation in the base fluid is considered in both kinds of carbon nanotubes, the single-wall (SWCNTs) and the multiwall (MWCNTs). It is noted that the heat transfer mechanism shows some delaying behavior due to the increase in the Eckert number and the volume fraction elevation values. For the larger volume fraction values and the magnetic parameter, the skin friction increases. In addition, while the temperature profile increases with the Biot numbers, it falls for the increasing values of the Prandtl number. Furthermore, it is noted that the irreversibility of the thermal energy is influenced by the Biot number, temperature difference, Brinkmann number, and magnetic field, which all have dynamic effects on the entropy and the Bejan number.

The current work aims to investigate how to utilize rough set theory for generating a set of rules to investigate the combined effects of heat and mass transfer on entropy generation due to MHD nanofluid flow over a vertical rotating frame. The mathematical model describing the problem consists of nonlinear partial differential equations. By applying suitable transformations these equations are converted to non-dimensional form which are solved using a finite difference method known as “Runge-Kutta Fehlberg (RKF-45) method”. The obtained numerical results are depicted in tabular form and the basics of rough sets theory are applied to acquire all reductions. Finally; a set of generalized classification rules is extracted to predict the values of the local Nusselt number and the local Sherwood number. The resultant set of generalized classification rules demonstrate the novelty of the current work in using rough sets theory in the field of fluid dynamics effectively and can be considered as knowledge base with high accuracy and may be valuable in numerous engineering applications such as power production, thermal extrusion systems and microelectronics.