The motive of the current analysis is to examine the role of gyro-tactic microorganisms to reveal their behaviour in heat and mass transfer in time-dependent MHD flow of Cross fluid accounted through nanoparticles. Non-linear thermal radiative, viscous dissipation, Soret and Dufour effect are also scrutinized with constraining conditions. By applying the suitable alteration the system of PDE’s is transmuted into ODE’s. The transmuted ODE’s are utilized through RK-4 along with shooting technique. Moreover, the impact of various emerging variables on the velocity, temperature, concentration and density of motile microorganisms are deliberated numerical and graphical. The outcomes are presented through plots. The outcomes illustrated those enhancements in the value of Weissenberg number We result in a reduction in motile density microorganism while the opposite effect is examined in the velocity slip effect. In addition, an intensifying microorganism profile is observed with velocity slip effect, Peclet number. Comparisons have been prepared with previously published literature and found an outstanding agreement.

The present article studies the facet of MHD cross nanofluid over vertical stretching sheet and Cattaneo-Chirstov flow model has established to investigate the feature of thermal relation time. The heat and mass transport phenomena is accomplished through activation energy, viscous dissipation. The two pragmatic boundary constraints introduce for convective and zero nanoparticles mass flux condition. By applying suitable similarity transformations, the constitutive equation of Cattaneo-Christov fluid with energy and concentration equations transformed to highly ordinary differential equations. Further, the highly ordinary differential equations have been utilized numerically via bvpc4 method. The obtained results are then portray for numerous estimations of the physical parameter and elaborated. Moreover, the temperature distribution is clearly less for augment thermal relaxation time β₁ within the range 0<ɳ≤5 and activation energy Ae result in the increment of nanoparticles concentration field in the range 0<ɳ≤6. To validate our obtained outcomes, a comparison in a limiting case is also given.

The current approach considered the unsteady 2D laminar second law analysis on Williamson hybrid nanoliquid in a porous medium under the effect of the thermal radiative flow towards a convectively heated stretching sheet. Propylene glycol P G ( C 3 H 8 O 2 ) is employed as the base liquid in this study, and the nanoparticles are Molybdenum disulfide M O S 2 and Zinc Oxide Z n O . The purpose of the current study is to maximize the energy and mass transfer rate for industrial and engineering applications. The primary contribution of this study is to discuss heat transmission via thermal radiation, suction, and the porous parameter on the flow of a William hybrid nanoliquid. The constitutive Maxwell flow model, heat transport, and entropy generation can be reduced to ordinary differential equations by similarity transformations. The Bvp4c technique is used on these generating ODEs for the numerical technique in the methodology section. Fluid friction, heat transmission, and Joule heating are used to calculate the entropy generation number. Graphs and tables are used to investigate the effects of dimensionless parameters on flow variables and entropy generation. The primary results suggest that hybrid Maxwell nanofluid is a more efficient heat conductor than regular nanofluid. A significant drop in the velocity field is supported by the Williamson W e , Unsteady β , and porosity γ factors γ . The temperature profile is significantly raised by the Biot number B i , thermal radiation R d , and suction factor S . Moreover, it has been found that entropy increases with radiation R d but reduces in Brinkman number B r against the Bejan number profile. Our results for a few specific situations were compared with previously published data to establish the validity of the current study, and it was discovered that they were in strong agreement.