Numerical simulations for swimming of gyrotactic microorganisms with Williamson nanofluid featuring Wu’s slip, activation energy and variable thermal conductivity
“…22 . Here, density number of motile microorganisms increases for growing values of and declines for rise in values of Figures 23 and 24 are sketched for stream functions subject to various flow parameters 28 . Figure 23 Streamlines for flow parameters when and Figure 24 Contour plots of isotherms for when ( a ) and ( b ) …”
In this study, a mathematical model is developed to scrutinize the transient magnetic flow of Cross nanoliquid past a stretching sheet with thermal radiation effects. Binary chemical reactions and heat source/sink effects along with convective boundary condition are also taken into the consideration. Appropriate similarity transformations are utilized to transform partial differential equations (PDE’s) into ordinary ones and then numerically tackled by shooting method. The impacts of different emerging parameters on the thermal, concentration, velocity, and micro-rotation profiles are incorporated and discussed in detail by means of graphs. Results reveal that, the escalation in magnetic parameter and Rayleigh number slowdowns the velocity and momentum of the fluid. The increase in Biot number, radiation and heat sink/source parameters upsurges the thermal boundary but, converse trend is seen for escalating Prandtl number. The density number of motile microorganisms acts as a growing function of bioconvection Lewis number and declining function of bioconvection Peclet number.
“…22 . Here, density number of motile microorganisms increases for growing values of and declines for rise in values of Figures 23 and 24 are sketched for stream functions subject to various flow parameters 28 . Figure 23 Streamlines for flow parameters when and Figure 24 Contour plots of isotherms for when ( a ) and ( b ) …”
In this study, a mathematical model is developed to scrutinize the transient magnetic flow of Cross nanoliquid past a stretching sheet with thermal radiation effects. Binary chemical reactions and heat source/sink effects along with convective boundary condition are also taken into the consideration. Appropriate similarity transformations are utilized to transform partial differential equations (PDE’s) into ordinary ones and then numerically tackled by shooting method. The impacts of different emerging parameters on the thermal, concentration, velocity, and micro-rotation profiles are incorporated and discussed in detail by means of graphs. Results reveal that, the escalation in magnetic parameter and Rayleigh number slowdowns the velocity and momentum of the fluid. The increase in Biot number, radiation and heat sink/source parameters upsurges the thermal boundary but, converse trend is seen for escalating Prandtl number. The density number of motile microorganisms acts as a growing function of bioconvection Lewis number and declining function of bioconvection Peclet number.
“…where K n is Knudsen number, ι � min(1/K n , 1), ε is the momentum accommodation coefcient with 0 ≤ ε ≤ 1, and ς is the molecular mean free path. Such higher-order slip efects were initially suggested by Wu [48], and later on, such facts were used by several authors in their fow analyses [49][50][51]. Such slip features interact with one another to produce slip factors, which make it possible to efectively control the boundary layer's development.…”
Section: And V Slip Represents the Kinematic Viscosity Density Of Flu...mentioning
The overall goal of this paper is to look at how non-Fick’s and non-Fourier’s concepts affect the quadratic convection flow of a couple stress nanofluid across an extending surface under Wu’s slip, convective heating, and convective mass transfer conditions. The governing equations in the investigation are also initially stated as higher-order partial differential equations and thereafter rehabilitated into ordinary differential equations via similarity conversions. Finally, the numerical approach of the bvp5c solver in MATLAB R2019a is engaged to solve the resultant equations. It has been researched and shown using graphs and tables how physical characteristics affect the velocity, temperature, and concentration fields. The results show that the velocity profile along the x-direction grows with intensifying values of the couple stress, quadratic convection, buoyancy, and third-order slip constraints, whereas it declines with intensifying values of the fourth-order slip and magnetic field constraints. Also, the results show that as the velocity ratio constraint is increased, the velocity field along the y-axis increases. Furthermore, an augment in the values of the quadratic convection constraint and Schmidt number, respectively, causes a diminution in temperature and concentration distributions. The results of the current study can be used to increase lubricant production and reduce machinery deterioration. Furthermore, this theoretical and numerical deliberation has the potential to be beneficial in the field of bio-fluid dynamics and biomedicine.
“…The Carreau nanofluid for radiative nanofluid flow via numerical treatment was conducted by Imran et al 5 . Mabood et al 6 enrolled the additional slip features to observe the thermal treatment of nanofluid. Xu et al 7 prepared the thermal nanofluid model with third grade base fluid to boost the heat transfer pattern.…”
Owing to advanced thermal features and stable properties, scientists have presented many novel applications of nanomaterials in the energy sectors, heat control devices, cooling phenomenon and many biomedical applications. The suspension between nanomaterials with microorganisms is important in biotechnology and food sciences. With such motivations, the aim of current research is to examine the bioconvective thermal phenomenon due to Reiner–Philippoff nanofluid under the consideration of multiple slip effects. The assessment of heat transfer is further predicted with temperature dependent thermal conductivity. The radiative phenomenon and chemical reaction is also incorporated. The stretched surface with permeability of porous space is assumed to be source of flow. With defined flow constraints, the mathematical model is developed. For solution methodology, the numerical simulations are worked out via shooting technique. The physical aspects of parameters are discussed. It is claimed that suggested results claim applications in the petroleum sciences, thermal systems, heat transfer devices etc. It has been claimed that the velocity profile increases due to Bingham parameter and Philippoff constant. Lower heat and mass transfer impact is observed due to Philippoff parameter.
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