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Study of Arrhenius activation energy on the thermo-bioconvection nanofluid flow over a Riga plate

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Abstract

This article deals with a study of Arrhenius activation energy on thermo-bioconvection nanofluid propagates through a Riga plate. The Riga plate is filled with nanofluid and microorganisms suspended in the base fluid. The fluid is electrically conducting with a varying, parallel Lorentz force, which changes exponentially along the vertical direction, due to the lower electrical conductivity of the base fluid and the arrangements of the electric and magnetic fields at the lower plate. We consider only the electromagnetic body force over a Riga plate. The governing equations are formulated including the activation energy and viscous dissipation effects. Numerical results are obtained through the use of shooting method and are depicted graphically. It is noticed from the results that the magnetic field and the bioconvection Rayleigh number weaken the velocity profile. The bioconvection Schmidt and the Peclet number decrease the microorganism profile. The concentration profile is enhanced due to the increment in activation energy and the Brownian motion tends to increase the temperature profile. The latter is suppressed by an increment of the Prandtl number.

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Abbreviations

\({\mathbf{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{V} }}\) :

Velocity vector (m s−1)

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{p}\) :

Pressure (pa)

\(N_{\text{t}}\) :

Thermophoresis parameter

\(L_{\text{b}}\) :

Traditional Lewis number

\(\tilde{T}\) :

Temperature of the fluid (K)

\(T_{1}\) :

Reference temperature (K)

\(\Theta\) :

Average volume of a microorganism

\(\tilde{t}\) :

Time (T)

\(\tilde{C}_{0}\) :

Nanoparticle concentration

\({\mathbf{g}}\) :

Gravity vector (m s−2)

\(\mu\) :

Viscosity (Pa s)

\(\beta\) :

Volumetric coefficient of thermal expansion

\(\tilde{n}\) :

Concentration of microorganisms

\(M_{0}\) :

Magnetization of the permanent magnets

\(a\) :

Width of electrodes and magnets

\(E_{\text{k}}\) :

Eckert number

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

Prandtl number

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

Bioconvection Rayleigh number

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

Basic-density Rayleigh number

\(P_{\text{e}}\) :

Peclet number

\(\omega\) :

Chemical reaction parameter

\(A\) :

Activation energy

\(\overline{H} \left( {\tilde{C}} \right)\) :

Heaviside step function

\(\bar{b},W_{\text{mo}}\) :

Chemotaxis constant

F :

Lorentz force

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

Diffusivity of microorganisms

\(k\) :

Boltzmann constant (eV K−1)

\(E_{\text{a}}\) :

Activation energy

\(K_{\text{r}}^{2}\) :

Chemical reaction rate constant

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

Bioconvection Schmidt number

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

Radiation parameter

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

Thermal conductivity (W m−1 K−1)

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

Thermophoretic diffusion

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

Brownian motion parameter

\(J_{0}\) :

Current density (A m−2)

R a :

Thermal Rayleigh number

S c :

Schmidt number

R n :

Nanoparticle concentration number

N b :

Brownian motion parameter

\({\varvec{\upchi}}\) :

Flux of microorganisms

\(\Gamma\) :

Temperature difference

\(\rho\) :

Density (kg m3)

\(\mu\) :

Viscosity (N s m−1)

f, p:

Base fluid and nanoparticles

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Authors and Affiliations

  1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, Shandong, China

    M. M. Bhatti

  2. Department of Engineering, TCU, Fort Worth, TX, 76132, USA

    Efstathios E. Michaelides

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Bhatti, M.M., Michaelides, E.E. Study of Arrhenius activation energy on the thermo-bioconvection nanofluid flow over a Riga plate. J Therm Anal Calorim 143, 2029–2038 (2021). https://doi.org/10.1007/s10973-020-09492-3

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