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Mathematical Modeling and Theoretical Analysis of Bioconvective Magnetized Sutterby Nanofluid Flow Over Rotating Disk with Activation Energy

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Abstract

In this article, flow behavior of magnetized Sutterby nanoliquid due to rotating permeable disk is investigated. Suspended solid nanoparticles are stabilized with the help of bioconvection and buoyancy forces. Energy and concentration relations are respectively modeled taking thermal radiation and Arrhenius energy. Additionally, binary chemical reaction in nanomaterial flow is accounted. Flow governing radiated Sutterby nanomaterial is expressed by dimensional equations using boundary layer suppositions. Using appropriate transformations, the dimensional system is altered to a nondimensional one. The nondimensional governing equations are solved via Runge–Kutta-Fehlberg method (RKF-45). The effective consequences of diverse flow regulating variables on fluid velocity, thermal field, mass concentration, and motile microorganisms density are studied via various curves. Surface drag force, heat transfer, density number, and Sherwood number are computed numerically and analyzed. It is observed that velocity components diminished versus rising Hartman number, Reynolds number, fluid material variable, and porosity parameter. Further, it is observed that chemical reaction and activation energy have opposite impacts on mass concentration. Major observations of current exploration are itemized at the end.

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Abbreviations

μ :

Dynamic viscosity (kgm−1s−1)

T :

Nanofluid temperature (K)

C p :

Specific heat (Jkg−1K−1)

(u, w):

Velocity components (ms−1)

σ ∗ :

Electrical conductivity (kg−1m−3s3A2)

τ :

Heat capacity ratio (−)

α :

Thermal diffusivity (Wm−1K−1)

l :

Characteristic cylinder length (m)

b :

Chemotaxis constant (m)

C ∞ :

Concentration at infinity (−)

C :

Nanofluid concentration (−)

D B :

Brownian motion coefficient (m2s−1)

C w :

Wall concentration (−)

T ∞ :

Temperature at infinity (K)

B 0 :

Magnitude of magnetic field (kg s−2A−1)

n :

Variable (−)

φ(η):

Concentration of nanoparticles (−)

θ(η):

Temperature of fluid (−)

λ :

Fluid material variable (−)

Lb :

Bioconvection Lewis number (−)

n :

Dimensionless quantity (−)

Re:

Reynolds number (−)

J w :

Local mass flux (kgm−2s−1)

Rd :

Radiation variable (−)

Sc :

Schmidt number (−)

Ec :

Eckert number (−)

q w :

Surface heat flux (Wm−2)

A :

Ratio variable (−)

Pr:

Prandtl number (−)

(τ w, r, τ w, θ):

Shear stresses (Nm−2)

(r, z):

Coordinates of cylinder (m)

ρ :

Fluid density (kgm−3)

n 1 :

Fitted rate constant (−)

k ∗ :

Mean absorption coefficient (m−1)

K p :

Surface permeability (m2)

E a :

Activation energy (kg m2 s−2)

Kr 2 :

Reaction rate parameter (s−1)

N ∞ :

Microorganisms density at ambient (−)

v :

Kinematic viscosity (m2s−1)

N :

Concentration of microorganisms (−)

T w :

Wall temperature (K)

D m :

Diffusivity of microorganisms (m2s−1)

W c :

Maximum speed of swimming cells (ms−1)

N w :

Wall concentration of microorganisms (−)

D T :

Thermophoretic diffusion (m2s−1)

g :

Gravitational acceleration (ms−2)

χ(η):

Volume fraction of microorganisms (−)

f '(η):

Fluid velocity (−)

N ∞ :

Ambient concentration of microorganisms (−)

Ha :

Hartmann number (−)

Nt :

Thermophoresis variable (−)

K 1 :

Porosity parameter (−)

K ∗ :

Curvature parameter (−)

Nb :

Brownian dispersion parameter (−)

δ :

Ratio of temperature difference (−)

Ω:

Microorganisms difference ratio parameter (−)

Pe :

Bioconvection Peclet number (−)

E 1 :

Activation energy parameter (−)

γ :

Chemical reaction parameter (−)

⥄q n :

Wall motile microorganisms flux (Wm−2K−1)

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Funding

Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2023R399), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Karakoram International University, Gilgit, 15100, Pakistan

    Fazal Haq & Mujeeb Ur Rahman

  2. Department of Mathematics and Statistics, Riphah International University I-14, Islamabad, 44000, Pakistan

    M. Ijaz Khan

  3. Department of Mechanical Engineering, Lebanese American University, Kraytem, Beirut, 1102-2801, Lebanon

    M. Ijaz Khan

  4. Doctor of Pedagogical Sciences, Vice-Rector for Scientific Affairs, Tashkent State Pedagogical University, Tashkent, Uzbekistan

    Barno Sayfutdinovna Abdullaeva

  5. Department of Physics, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia

    Reem Altuijri

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  1. Fazal Haq
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Contributions

Fazal Haq and Barno Sayfutdinovna Abdullaeva conceived and designed the analysis and wrote the paper text. Mujeeb ur Rahman and Reem Altuijri contributed the analysis tools. M. Ijaz Khan supervised overall activities.

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Correspondence to Fazal Haq.

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Haq, F., Rahman, M.U., Khan, M.I. et al. Mathematical Modeling and Theoretical Analysis of Bioconvective Magnetized Sutterby Nanofluid Flow Over Rotating Disk with Activation Energy. BioNanoSci. 13, 1849–1862 (2023). https://doi.org/10.1007/s12668-023-01166-2

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