Abstract
The three-dimensional (3D) nanofluid flow among the rotating circular plates filled with nanoparticles and gyrotactic microorganisms is studied. A generalized form of the magnetic Reynolds number is used for the mathematical modeling of the ferro-nanofluid flow. The torque effects on the lower and upper plates are calculated. A differential transform scheme with the Padé approximation is used to solve the coupled highly nonlinear ordinary differential equations. The results show that the squeeze Reynolds number significantly suppresses the temperature, microorganism, and nanoparticle concentration distribution, and agree well with those obtained by the numerical method.
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Abbreviations
- H θ :
-
axial components
- H z :
-
azimuthal components
- μ 1 :
-
magnetic permeability inside the plate
- μ 2 :
-
magnetic permeability outside the plate
- μ f :
-
free space permeability (N·A−2)
- B(r, θ, z):
-
induced magnetic field
- T 1 :
-
constant temperature of the lower plate (K)
- T u :
-
constant temperature of the upper plate (K)
- C 1 :
-
concentration at the lower plate
- C u :
-
concentration at the upper plate
- p :
-
pressure (Pa)
- ρ :
-
fluid density (kg·m−3)
- μ :
-
fluid viscosity (N·s·m−2)
- δ :
-
electrical conductivity (S·m−1)
- T :
-
temperature (K)
- C :
-
concentration
- T m :
-
mean fluid temperature (K)
- c p :
-
specific heat (J·kg−1·K−1)
- D B :
-
Brownian diffusivity
- D T :
-
thermophoretic diffusion coefficient
- j :
-
microorganism flux
- R M :
-
magnetic force strength in the axial direction
- M T :
-
magnetic force in the tangential direction
- M R :
-
magnetic Reynolds number
- T b :
-
Brownian motion parameter
- T t :
-
thermophoresis parameter
- Pr :
-
Prandtl number
- Sc :
-
Schmidt number
- B n :
-
bioconvection number
- f :
-
axial velocity
- g :
-
tangential velocity
- ξ :
-
angular velocity
- b :
-
radius of the disk
- T up :
-
dimensionless torque applied on the upper plate
- T low :
-
dimensionless torque applied on the lower plate
- b̄ :
-
chemotaxis constant
- W max :
-
maximal speed
- D mo :
-
diffusivity of microorganisms
- R Q :
-
squeeze Reynolds number
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Zhang, L., Arain, M.B., Bhatti, M.M. et al. Effects of magnetic Reynolds number on swimming of gyrotactic microorganisms between rotating circular plates filled with nanofluids. Appl. Math. Mech.-Engl. Ed. 41, 637–654 (2020). https://doi.org/10.1007/s10483-020-2599-7
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DOI: https://doi.org/10.1007/s10483-020-2599-7
Key words
- swimming of microorganism
- generalized magnetic Reynolds number
- nanofluid
- differential transform solution
- circular rotating plate