Open Physics 2020; 18: 74–88 Review Article Tanveer Sajid*, Muhammad Sagheer, Shafqat Hussain, and Faisal Shahzad Impact of double-diffusive convection and motile gyrotactic microorganisms on magnetohydrodynamics bioconvection tangent hyperbolic nanofluid https://doi.org/10.1515/phys-2020-0009 to be explored widely because of its enormous applications in received July 07, 2019; accepted February 10, 2020 the field of pharmaceutical industry, purification of cultures, fl Abstract: The double-diffusive tangent hyperbolic nanofluid micro uidic devices, mass transport enhancement and containing motile gyrotactic microorganisms and magneto- mixing, microbial enhanced oil recovery and enzyme hydrodynamics past a stretching sheet is examined. By biosensors. Bioconvection systems could be categorized ff adopting the scaling group of transformation, the governing based on the directional motion of di erent species of equations of motion are transformed into a system of microorganisms. In particular, gyrotactic microorganisms are nonlinear ordinary differential equations. The Keller box the ones whose swimming direction is dependent on a [ ] scheme, a finite difference method, has been employed for the balance between gravitational and viscous torques 4,5 . [ ] solution of the nonlinear ordinary differential equations. The Oyelakin et al. 6 pondered the impact of bioconvection and fl behaviour of the working fluid against various parameters of motile gyrotactic microorganisms on the Casson nano uid physical nature has been analyzed through graphs and tables. past a stretching sheet and observed that the microorganism fi The behaviour of different physical quantities of interest pro le decreases as a result of an increment in the Peclet [ ] ff such as heat transfer rate, density of the motile gyrotactic number. Saini and Sharma 7 explored the e ects of - microorganisms and mass transfer rate is also discussed in the bioconvection and gyrotactic microorganisms on the nano fl fl form of tables and graphs. It is found that the modified Dufour uid ow over a porous stretching sheet. It is noted that parameter has an increasing effect on the temperature profile. the Lewis number escalates the bioconvection process. [ ] Thesoluteprofile is observed to decay as a result of an Dhanai et al. 8 explored the impact of bioconvection on fl fl augmentation in the nanofluid Lewis number. the uid ow over an inclined stretching sheet and assessed that the microorganism density profile is enhanced with Keywords: magnetohydrodynamics, bioconvection, an improvement in the bioconvection Schmidt number. gyrotactic microorganisms, nanofluid, magnetic field, Mahdy [9] pondered the effects of motile microorganisms Keller box method, stretching sheet, double diffusion on the fluid past a stretching wedge and noted that a positive variation in the Peclet number leads to an augmentation in 1 Introduction the microorganism profile. Avinash et al. [10] pondered the impact of bioconvection and aligned magnetic field on the nanofluid flow over a vertical plate and concluded that In fluid dynamics, bioconvection [1–3] occurs when the heat transfer rate increases with an improvement in the microorganisms, which are denser than water, swim Lewis number. Makinde and Animasaun [11] studied the upwards. The upper surface of the fluid becomes thicker effects of magnetohydrodynamics (MHD),bioconvection, due to the assemblage of microorganisms. As a result, the nonlinear thermal radiation and nanoparticles on fluid past upper surface becomes unstable and microorganisms fall an upper horizontal surface of a paraboloid of revolution and down, which creates bioconvection. Bioconvection continues found that the Brownian motion boosts the concentration profile. Khan et al. [12] studied the impact of MHD, gyrotactic fl * Corresponding author: Tanveer Sajid, Capital University of Science microorganisms, slip condition and nanoparticles on the uid and Technology (CUST), Islamabad, Pakistan, e-mail: tanveer.sajid15@ flow over a vertical stretching plate; it was observed that the yahoo.com magnetic field suppresses the dimensionless velocity inside Muhammad Sagheer: Capital University of Science and Technology the boundary layer. Later, the effects of different features of ( ) - CUST , Islamabad, Pakistan, e mail: [email protected] the gyrotactic microorganisms on the fluid flow are analyzed Shafqat Hussain: Capital University of Science and Technology [ – ] (CUST), Islamabad, Pakistan, e-mail: [email protected] in various investigations 13 15 . Faisal Shahzad: Capital University of Science and Technology (CUST), Nanotechnology has been considered the most sub- Islamabad, Pakistan, e-mail: [email protected] stantial and fascinating forefront area in physics, Open Access. © 2020 Tanveer Sajid et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 Public License. Impact of double-diffusive convection and motile gyrotactic microorganisms 75 engineering, chemistry and biology. The thermal conduc- distinct rate of diffusion. Double-diffusive convection occurs tivity of a nanofluid is greater than that of the base fluid. in a variety of scientific disciplines such as oceanography, The thermal conductivity of the fluid is considered to be biology, astrophysics, geology, crystal growth and chemical enhanced by the nanoparticles present in the fluid. reactions [28]. Nield and Kuznetsov [29] scrutinized the Buongiorno [16] established a model to examine the thermal nanofluid past a porous medium along with the double- conductivity of nanofluids. Baby and Ramaprabhu [17] diffusive convection effect. The impact of double-diffusive analyzed the heat transport of fluids using graphene convection on the fluid flow over a square cavity is analyzed nanoparticles. They reported that the thermal conductivity byMahapatraetal.[30]. Gireesha et al. [31] discussed the of hydrogen-exfoliated graphene is enhanced with an Casson nanofluid past a stretching sheet along with the increment in the volume fraction of the nanoparticles. MHD and double-diffusive convection. Rana and Chand [32] Khan and Gorla [18] pondered the mass transfer of the explored the effect of double-diffusive convection on nanofluid flow over a convective sheet using the Keller box viscoelastic fluid and deduced that a Rayleigh number scheme and noted that the heat transfer rate is high in the increases with an improvement in the Soret parameter. dilatant fluids compared with that in the pseudoplastic Gaikwad et al. [33] have monitored the fluid flow above a fluids. Das [19] discussed the rotating flow of a nanofluid stretching sheet together with double-diffusive convection with respect to the constant heat source. A boost in the and found that an augmentation in the Nusselt number volume fraction of nanoparticles was observed to cause an takes place with an improvement in the Dufour parameter. increment in the thermal boundary layer thickness. Gireesha Kumar et al. [34] inspected the influence of nanoparticles et al. [20] considered the Hall impact on a dusty nanofluid and double diffusion on viscoelastic fluid and monitored and concluded that the skin friction coefficient decreases that an increase in the velocity field occurs with an due to an improvement in the Hall current. increment in the Dufour Lewis number. The experimental and the theoretical scientificstudies Convection is a process common to particles, gases and of the non-Newtonian liquids together with MHD have vapours. Convection occurs when a fluid is in motion and achieved a considerable attention of researchers because of that motion carries with it a material of interest such as the their adequate applications in the field of aeronautics, particles or the droplets of an aerosol. There are two types of chemical, mechanical, civil and bio-engineering. The fluid convection: free convection and forced convection. In free becomes electrically conducting under the effect of MHD convection or natural convection, the fluid motion cannot led like ionized gases, plasmas and liquid metals such as by external sources such as fans, pumps, and suction devices mercury. The impact of MHD and nonlinear thermal etc. Gravity is the main driving force in the case of free radiationontheSiskonanofluid flow over a nonlinear convection. Free convection has various environmental and stretching surface is premeditated by Prasannakumara industrial applications such as plate tectonics, oceanic et al. [21].Rashidietal.[22] pondered the MHD viscoelastic currents, formation of microstructures during the cooling of fluid together with the Soret and Dufour effects and molten metals, fluid flows around shrouded heat dissipation observed that the velocity profile decreases with an fins, solar ponds and free air cooling without the aid of fans. improvement in the magnetic parameter. Kothandapani In forced convection, the fluid motion is generated externally and Prakash [23] studied the effect of magnetic field on with the help of pumps, fans, suction devices, etc. This peristaltic tangent hyperbolic nanofluid past a asymmetric mechanism has enormous applications in our daily life such channel. Gaffar et al. [24] showed the tangent hyperbolic as heat exchangers, central heating system, steam turbines fluid flow over a cylinder together with the MHD and partial and air conditioning. Mixed convection is the situation in slip effects. Nagendramma et al. [25] analyzed the tangent whichbothfreeconvectionandforcedconvectionareof hyperbolic fluid flow over a stretching sheet together with comparable order. Mixed convection is of great interest to the