Thermal management is a crucial task in the present era of miniatures and other gadgets of compact heat density. This communication presents the momentum and thermal transportation of nanofluid flow over a sheet that stretches exponentially. The fluid moves through a porous matrix in the presence of a magnetic field that is perpendicular to the flow direction. To achieve the main objective of efficient thermal transportation with increased thermal conductivity, the possible settling of nano entities is avoided with the bioconvection of microorganisms. Furthermore, thermal radiation, heat source dissipation, and activation energy are also considered. The formulation in the form of a partial differential equation is transmuted into an ordinary differential form with the implementation of appropriate similarity variables. Numerical treatment involving Runge–Kutta along with the shooting technique method was chosen to resolve the boundary values problem. To elucidate the physical insights of the problem, computational code was run for suitable ranges of the involved parameters. The fluid temperature directly rose with the buoyancy ratio parameter, Rayleigh number, Brownian motion parameter, and thermophoresis parameter. Thus, thermal transportation enhances with the inclusion of nano entities and the bioconvection of microorganisms. The findings are useful for heat exchangers working in various technological processors. The validation of the obtained results is also assured through comparison with the existing result. The satisfactory concurrence was also observed while comparing the present symmetrical results with the existing literature.

In this paper, MHD Brinkman-type fluid flow containing titanium dioxide and silver nanoparticle hybrid nanoparticles with generalized Mittag–Leffler kernel-based fractional derivative is investigated in the presence of bioconvection. The governing equations with dimensional analysis and fractional approach are obtained by using the fractional Fourier’s law for heat flux and Fick’s law for diffusion. As a result, the bioconvection Rayleigh number, which is responsible for the declining in the fluid velocity and fractional parameters used to control the thermal and momentum boundary layers thickness of fluid properties. The obtained solutions can be beneficial for proper analysis of real data and provide a tool for testing possible approximate solutions where needed.

The present paper deals with the advancement of non-Newtonian fluid containing some nanoparticles between two parallel plates. A novel fractional operator is used to model memory effects, and analytical solutions are obtained for temperature and velocity fields by the method of Laplace transform. Moreover, a parametric study is elaborated to show the impact of flow parameters and presented in graphical form. As a result, dual solutions are predicted for increasing values of fractional parameters for short and long times. Furthermore, by increasing nanoparticle concentration, the temperature can be raised along with decreasing velocity. A fractional approach can provide new insight for the analytical solutions which makes the interpretation of the results easier and enable the way of testing possible approximate solutions.

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In the present work, an unsteady convection flow of Casson fluid, together with an oscillating vertical plate, is examined. The governing PDEs corresponding to velocity and temperature profile are transformed into linear ODEs with the help of the Laplace transform method. The ordinary derivative model generalized to fractional model is based on a generalized Fourier law. The solutions for energy and velocity equations are obtained after making the equations dimensionless. To check the insight of the physical parameters, especially the symmetric behavior of fractional parameters, it is found that for small and large values of time, fluid properties show dual behavior. Since the fractional derivative exhibits the memory of the function at the chosen value of time, therefore the present fractional model is more suitable in exhibiting memory than the classical model. Such results can be useful in the fitting of real data where needed. In the limiting case when fractional parameters are taken β=γ = 0 and α = 1 for both velocity and temperature, we get the solutions obtained with ordinary derivatives from the existing literature.