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Thermal analysis of radiative bioconvection magnetohydrodynamic flow comprising gyrotactic microorganism with activation energy

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Abstract

Bioconvection flows are very much related to engineering and real-life phenomena, for example, in the design of bio-cells, bio-conjugates and bio-microsystems, and become a hot topic in the current research. Therefore, the purpose of the present investigation is to explore theoretically the time-dependent electrically conducting flow with heat and mass transfer containing gyrotactic microorganism with activation energy toward an elongated surface with the effect of thermal radiation. Impact of velocity, thermal and concentration slips are also taken into account. The classical problem of Navier Stokes equations in the present model is reduced into ODEs by employing similarity approach. Numerical simulations are performed via boundary value problem solver based on finite difference numerical scheme using MATLAB. Impact of convergence parameters like motile microorganisms, concentration, temperature and velocity fields is elaborated through graphically and in the form of tables. The significant outcomes display that the density of motile microorganisms decreases with Peclet number and bioconvection Lewis number, while opposite behavior is noted for thermal buoyancy and buoyancy force ratio parameter on velocity profile.

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Abbreviations

A :

Unsteadiness parameter

B :

Uniform magnetic field

\(B_{0}\) :

Magnetic induction

C :

Species concentration (mol m−3)

\(C_{\text{w}}\) :

Species concentration at the wall (mol m−3)

\(C_{\infty }\) :

Species concentration far from the surface (mol m−3)

\(C_{\text{f}}\) :

Local skin friction coefficient

\(c_{\text{p}}\) :

Specific heat capacity (\({\text{J}}\;{\text{kg}}^{ - 1} \;{\text{K}}^{ - 1}\))

\(D_{\text{B}}\) :

Mass diffusivity (\({\text{m}}^{2} \;{\text{s}}^{ - 1}\))

\({\text{Gr}}\) :

Grashof number due to temperature

\({\text{Gr}}^{*}\) :

Grashof number due to concentration

\(J\) :

Slip factor of concentration

\(k^{*}\) :

Mean absorption coefficient

\(K\) :

Thermal slip factor

\(N_{0}\) :

Velocity slip factor

\(M\) :

Magnetic parameter

\(N\) :

Buoyancy force ratio parameter

\({\text{Nu}}_{\text{x}}\) :

Local Nusselt number

\(R_{\text{d}}\) :

Radiation parameter

\({ \Pr }\) :

Prandtl number

\(Q\) :

Local heat source/sink parameter

\(q_{\text{r}}\) :

Radiative heat flux (\({\text{W}}\;{\text{m}}^{ - 2}\))

\(J_{\text{w}}\) :

Surface mass flux (kg s−1 m−2)

\(q_{\text{w}}\) :

Surface heat flux (W m−2)

\({\text{Re}}_{\text{x}}\) :

Local Reynolds number

S :

Suction/injection parameter

\({\text{Sc}}\) :

Schmidt number

\(S_{\text{f}}\) :

Velocity slip parameter

\({\text{St}}\) :

Thermal slip parameter

\(S_{{{\text{c}}1}}\) :

Species concentration slip parameter

\({\text{Sh}}_{\text{x}}\) :

Local Shorewood number

\(n_{\infty }\) :

Microorganism far from the wall

\({\text{Lb}}\) :

Bioconvection Lewis number

σ1:

Bioconvection constant term

\(q_{\text{n}}\) :

Motile microorganism flux

T :

Temperature of the fluid

\(T_{\text{w}}\) :

Temperature at the wall

\(T_{\infty }\) :

Temperature of the fluid far away from the wall

\(u\) :

Velocity component along x-direction

\(v\) :

Velocity component along y-direction

\(U_{\text{w}}\) :

Stretching sheet wall velocity

\(U_{\infty }\) :

Free stream velocity

\(\lambda\) :

Buoyancy parameter due to temperature

\(\lambda_{1}\) :

Buoyancy parameter due to concentration

Ω:

Porosity parameter

\(\sigma\) :

Reaction rate parameter

\(\delta\) :

Temperature difference parameter

\(E\) :

Activation energy

\(\sigma^{*}\) :

Stefan Boltzmann constant

\(\tau_{\text{w}}\) :

Wall shear stress

\(\psi\) :

Stream function

\(\eta\) :

Transformed variable

\(\rho\) :

Density of the fluid

\(\mu\) :

Dynamic viscosity

\(\upsilon\) :

Kinematic viscosity

\(B_{\text{C}}\) :

Volumetric coefficient of the concentration expansion

\(B_{\text{T}}\) :

Volumetric coefficient of the thermal expansion

K :

Thermal diffusivity

a, b, c, d, m :

Constants

\(f^{\prime}\left( \eta \right)\) :

Velocity profile

\(\theta \left( \eta \right)\) :

Temperature profile

\(\phi \left( \eta \right)\) :

Concentration profile

\(\chi \left( \eta \right)\) :

Microorganism profile

\(W_{\text{c}}\) :

Maximum cell swimming speed

\(D_{\text{m}}\) :

Microorganism diffusivity

\(n_{\text{w}}\) :

Microorganism at the wall

\(n\) :

Motile microorganism

\({\text{Pe}}\) :

Bioconvection Peclet number

\({\text{Nn}}_{\text{x}}\) :

Density of motile microorganism

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Bacha Khan University, Charsadda, 24420, KPK, Pakistan

    Aaqib Majeed & Noorul Amin

  2. Department of Mathematics and Statistics, FBAS, International Islamic University Islamabad, H-10, Islamabad, 44000, Pakistan

    Ahmad Zeeshan

  3. Department of Mathematics and Statistics, University of Lahore, Sargodha Campus, Sargodha, 40100, Pakistan

    Nouman Ijaz

  4. Nonlinear Analysis and Applied Mathematics Research Group, Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Tareq Saeed

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  1. Aaqib Majeed
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Majeed, A., Zeeshan, A., Amin, N. et al. Thermal analysis of radiative bioconvection magnetohydrodynamic flow comprising gyrotactic microorganism with activation energy. J Therm Anal Calorim 143, 2545–2556 (2021). https://doi.org/10.1007/s10973-020-10207-x

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