The suspension of nanoparticles in the base fluid has been tested to improve the heat transfer properties of the fluid since solid metals are characterized with higher thermal conductivity than the convectional working fluid. This present work focuses on the suspension of nanoparticles into the upper convected Maxwell fluid model (UCM) so as to improve the heat transfer efficacy of the fluid. The governing partial differential equations and their related boundary conditions are transformed and parameterized by applying appropriate transformations into a system of non-linear ordinary differential equations and the series solutions are obtained through homotopy analysis method. The impact of various parameters on velocity, temperature and nanoparticles concentration profiles are reviewed and discussed. It is discovered that increasing the Brownian motion increases the thermal conductivity of fluid and hence promotes the effective movement of the nanoparticles.

Stratification is characterized as having applications in a variety of energy storage disciplines, including solar thermal energy usage systems. The effect of heat production, magnetic field, and varied fluid characteristics on the flow of Casson fluid across unstratified and stably stratified paraboloid of revolution is investigated in this work. The velocity index $m<1$ is suitable to describe the fluid flow on an upper horizontal surface of a paraboloid of revolution. It is imperative to mention that the upper horizontal surface of a paraboloid of revolution is likened to the pointed surface of an aircraft which is also described as a surface with variable thickness. The governing partial differential equations are transformed into the nonlinear ordinary differential equations using the similarity transformation. The dimensionless nonlinear ordinary differential equations are solved with the help of the Bvp4c numerical algorithm. The effects of relevant parameters are revealed on various profiles and discussed. It is observed that both the temperature and concentration distributions decrease with increase in thermal stratification $S_t$ and solutal stratification $S_o$ parameters when the velocity index parameter $m<1.$

We develop a non-local mathematical model in the current study that uses the time-fractional Fourier’s law to describe the thermal phenomena. The time-fractional generalized Atangana–Baleanu fractional derivative is used to define the new time-fractional constitutive equations. We establish analytical solutions for generalized convection flows of viscous fluid between two parallel plates with general boundary conditions by combining the Laplace transform with the finite sine-Fourier transform. The impacts of fractional and physical factors on the thermal and velocity fields were examined using numerical calculations and graphical representations prepared with the Mathcad program. From the generalized Atangana–Baleanu fractional derivative, we can recover the Atangana–Baleanu fractional derivative, Caputo–Fabrizio fractional derivative, and Caputo fractional derivative as a special case.

The present work aims to analyze the effects of magnetohydrodynamics, heat and mass transfer, and gyrotactic microorganism behavior on the bioconvective micropolar nanofluid flow subject to triple stratifications and Cattaneo–Christov double diffusion over a stretched surface. The dimensional system of differential equations has been simplified to dimensionless with suitable non-dimensional quantities and suitable similarity transformations. An efficient numerical technique bvp4c through MATLAB has been implemented to devise the solution of the non-dimensionalized system of governing equations. The significant outcomes of the current analysis are that the amplification of magnetic parameter intensifies the flow velocity and shows the reverse effect for the fluid temperature. The enhancement of micropolar parameter upgrades microrotation, while it exhibits opposite effect for the fluid temperature and nanoparticle concentration. Microorganism concentration peters out with a rise in Peclet number. Gyrotactic microorganism thermal stratification augmentation leads to the diminution of velocity and thermal boundary layer thickness. When gyrotactic microorganism concentration difference parameter rises from 0.1 to 0.8, skin friction whittles down by 12.5%, and wall motile microorganism number ameliorates by 50%.