Bioconvection assessment in Maxwell nanofluid configured by a Riga surface with nonlinear thermal radiation and activation energy
Introduction
Nowadays the study of nanofluids has gained considerable attention to the current investigators. This is due to the many applications in various industries/processes such as cooling of engine, heat exchanger devices, machining and electronics, improving the efficiency in diesel generator and heat transfer of chillers, solar water heating, air-conditioners/refrigerators, fuel cells, hybrid-powered and other higher energy equipment. In general, the nanofluids possess higher thermal properties than conventional fluids, for this reason they also called as advanced/next generation heat transfer fluids. The thermal engineers have focused on the nanofluids because they have interested and useful properties such as higher conductivities and nanoparticles larger relative surface area. The suspended nanoparticles in nanofluid remarkably ameliorate the stability of the suspension and capabilities of heat transfer. Nanofluids possess extensive possibilities as it can augment the performance of heat transfer in comparison to that of pure liquids. In view of the aforesaid theory and applications in mind the current researches have started their work in nanofluid flows in diverse geometries. Lodhi et al. [1] have provided the experimental investigation on the heat transfer effects of nanofluid flow in the circular microchannel. Rauf and Mahsud [2] have presented the analytical solutions for the effect of time exponential temperature on the natural convective nanofluid flow over a vertical plates. Sasmito et al. [3] have considered the flow of nanofluids through coiled square tubes using CFD approach. Guan et al. [4] have employed the Buongiorno model to describe the two-phase (immiscible) nanofluid flow using the level-set method. Uddin et al. [5] have used implicit finite-difference numerical method to study the two-dimensional Sakiadis and Blasius flows of nanofluid past a moving plate. Mahdavi et al. [6] have discussed the cooling effects of nanoliquid on the hot surface and validated with experimental results. He et al. [7] have investigated the flow of hybrid nanofluid in the sinusoidal wavy walls of the micro-channel.
The non-Newtonian Maxwell nanofluids are one of the complex models in the non-Newtonian nanofluids. The examples of these nanofluids can be considered as clay, honey, colloids, gels and ketchup. The study of these nanofluids has received great interest among the researchers due to the applications in engineering and industry such as microelectronics cooling, printing, plastic fracturing , crystal growth, fiber technology wire coating and ceramic materials. A well signified valuable contribution of magnetohydrodynamic phenomenon is examined in era of engineering, medical and industry such as thinning of copper wires, magnetic resonance imaging, optical modulators, magnetic cell separation, gastric medications, removal of cancer wounds, asthma treatment and optical switches. Very few authors have studied the combined effects of bioconvection and magnetohydrodynamics [8], [9], [10], [11].
The development of patterns in the suspensions of microorganisms causes bioconvection for example algae and bacteria. The movement is resources for the joint swimming of microorganisms. The properties of the fluids can be affected due to the self-oriented microorganisms in provided geometry. Due to the numerous applications of gyrotactic microorganisms in various fields such as ethanol, bio-microsystems, fertilizers and bio-fuel, the researchers have started their research in the field of gyrotactic microorganisms in various fluid flow situations. Tlili et al. [12] have discussed the bioconvective flow of micropolar nanofluid with the solutal and thermal stratifications at the surface via Homotopy Analysis Method (HAM). The numerical flow model performed by Waqas et al. [13] explored the unsteady MHD flow of Falkner-Skan bioconvective Williamson nanofluid under the motile gyrotactic microorganisms. Acharya et al. [14] have considered the nanofluid through the permeable surface under additional impact of MHD and gyrotactic microorganisms via Runge-Kutta method together with shooting technique. Zaman and Gul [15] have used bvp4c technique to solve the fluid flow problem of Williamson nanomaterial flow under the effects of MHD and bioconvection. Khan et al. [16] have studied the effects of gyrotactic microorganisms on the MHD motion of thixotropic nano-liquids using homotopic analysis technique. Alsaedi et al. [17] have addressed the motile microorganisms transfer rate, gyrotactic microorganisms and MHD on the stretched flow of nanofluid via convergent solutions. Khan and co-researchers [18] utilized the surface slip mechanisms in nanofluid flow with gyrotactic microorganisms through the channel via numerical results.
Riga plate is an electromagnetic actuator (which is the combination of permanent magnets and electrodes on the plane surface). Riga plates create the magnetic and electric fields which can produce Lorentz force (controlling force) parallel to the fluid flow [19]. It is clear that the fluids that having precipitous electrical conductivity with imposing the magnetic field greatly affected. This scenario influenced by many researchers to investigate the fluid flows over the Riga plate. Ahmad et al. [20] have employed the reliability of the asymptotic method to discuss the effect of strong suction and mixed convection on the boundary layer flow of nanoliquid past a Riga plate. Hayat et al. [21] have formulated and discussed the flow of nanofluid by heated Riga plate with the help of analytical solutions. Abbas et al. [22] have presented the shooting method solutions for the influence of EMHD and bioconvection on the motion of nanoliquid past a porous Riga plate with gyrotactic microorganisms. Nadeem et al. [23] have discussed the nanofluid stagnation point flow by Riga surface with induced magnetic effects with the help of MATLAB bvp4c technique. Ganesh et al. [24] have modelled the two-dimensional nanofluid flow over a stretchable Riga plate under the EMHD effects with appliances of shooting numerical procedure. Zhang et al. [25] intended the bioconvective flow of nanofluid by a Riga plate under the Darcy-Brinkman-Forchheimer porous medium. Bhatti and Michaelides [26] have considered the influence of Arrhenius activation energy on the flow of bioconvective nanofluid through a Riga plate via shooting method.
To the best of the investigators knowledge, no study has been made on the bioconvective Maxwell nanofluid with the effect of MHD, nonlinear thermal radiation and gyrotactic microorganisms through a Riga plate. With the aforementioned studies, applications and to fill the gap in the said direction, in the current article we have presented, thermal consequences of Maxwell nanofluid containing gyrotactic microorganism over a Riga surface. The constituted flow problem is numerically treated with applications of shooting algorithm. A comprehensive physical importance of flow parameters are studied with help of different graphs. Some recent developments and improvements [27], [28], [29], [30], [31], [32], [33], [34], [35] in fluid flow subject to various geometries and results are calculated with different methods and techniques.
Section snippets
Flow model
A laminar and two-dimensional flow pattern of non-Newtonian liquid has been observed over a Riga surface. The Maxwell nanofluid along with gyrotactic microorganisms is assumed to predict the rheological characteristics and bioconvection aspects. For incompressible fluid flow, the cartesian system is incorporated to model the flow pattern. The x-direction velocity component (u) and y-direction component of velocity (v) are assumed to report the velocity profile. The electro magnetohydrodynamic
Numerical scheme
The se of derived Eqs. (9)–(12) along with boundary conditions (13) are numerically treated with shooting algorithm. For this purpose, the boundary value approximations of higher order are reduced to first order equations. Following steps are carried out to complete this task:
Discussion
This section describes the numerical simulations for the various fluid flow parameters (with the considered range of parameters) such as Deborah number (β = 0 to 2) mixed convection parameter (λ = 0 to 2) modified Hartmann number (Q = 0 to 2), bioconvection Rayleigh constant (Rb = 0 to 1.2) nanoparticles concentration number (Nr = 0 to 2), Brownian motion parameter (Nb = 0.5 to 2.5), thermophoresis parameter (Nt = 0.5 to 2.5), radiation parameter (Rd = 0.5 to 2), surface heating parameter (θw
Conclusions
The mixed convection and activation energy consequences in thermally developed flow of Maxwell fluid which contain gyrotactic microorganisms has been examined in this investigation. The flow is induced by a Riga surface and flow assessment are performed by using convective-Nield's boundary conditions. The numerical scheme namely shooting technique is employed to compute the solution. The most important observations are expressed in following points:
- Ø
The velocity of fluid is controlled with
Author statement
All the authors of the research articles are agreed to publish in the International Communications in Heat and Mass Transfer.
Declaration of Competing Interest
The authors declared that they have no conflict of interest and the paper presents their own work which does not been infringe any third-party rights, especially authorship of any part of the article is an original contribution, not published before and not being under consideration for publication elsewhere.
Acknowledgment
The authors extend their appreciation to the deanship of scientific research at King Khalid University for funding this work through research groups program under grant number (R. G. P.2/77/41).
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