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Bioconvective treatment for the reactive Casson hybrid nanofluid flow past an exponentially stretching sheet with Ohmic heating and mixed convection

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Abstract

Maintaining continuous thermal propagation is essential in many industrial and thermal systems because it helps improve the efficiency of thermal engineering engines and machines. Thus, the hybridization of magnetized nanoparticles in a heat-supporting non-Newtonian fluid is a good platform to enhance thermal power energy. As such, this study focuses on the bioconvective treatment for the reactive Casson hybrid nanofluid flow past an exponentially stretching sheet with Ohmic heating and mixed convection. The hybridization process considers Au (Gold) and Ag (Silver) nanoparticles in water base liquid. A partial derivative model is developed for the hybrid volume fraction, which is simplified to a dimensionless ordinary derivative model. A semi-analytical Chebyshev collocation scheme (CCS) is used to provide solutions to the transformed model. The physical impacts of the fluid parameters on the momentum, heat distribution, reacting species field and microbial species are illustrated in graphs for both Ag and Au nanoparticles. A limited case of the present work is compared with the earlier studies to validate our results. The results show that the velocity of mono/hybrid nanofluids upsurges with rising values of the mixed convection term. The bioconvective Schmidt number declines the motile microorganism profiles. The higher velocities, temperatures and concentrations are recorded for hybrid (Ag-Au/water) nanofluid, followed by unitary Au-water and Ag-water nanofluids separately.

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Abbreviations

\(B(x)\) :

Variable magnetic field

\({B}_{0}\) :

Applied magnetic field (Tesla i.e. Webers/m2)

\(Cr\) :

Chemical reaction

\({Cf}_{x}\) :

Local skin friction

\({C}_{\mathrm{w}}\) :

Wall concentration (Moles)

\({C}_{\infty }\) :

Ambient (freestream) concentration (Moles)

\({D}_{\mathrm{B}}\) :

Molecular diffusivity of the reactive species (m2 s-1)

\({D}_{\mathrm{n}}\) :

Microorganism diffusion coefficient

\(Ec\) :

Eckert number

g :

Gravitational acceleration (9.81 m s-2)

\(k:\) :

Thermal conductivity

\({k}^{*}\) :

Mean absorption coefficient

\(Kr\) :

Dimensional chemical reaction

\({K}_{\mathrm{p}}\) :

Porosity term

\(M\) :

Magnetic interaction parameter

\(N\) :

Microbial concentration

\({N}_{\mathrm{w}}\) :

Surface concentration of microorganism

\({N}_{\infty }\) :

Ambient concentration of microorganism

\({N}^{*}\) :

Buoyancy ratio

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

Local Nusselt number

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

Local density number

\(Pe\) :

Peclet bioconvection number

\(Pr\) :

Prandtl number

\({q}_{\mathrm{r}}\) :

Radiative flux

\(Q\) :

Heat source/sink parameter

\({Q}_{0}\) :

Heat generation/absorption coefficient (W m2•K-1).

\(R\) :

Radiation parameter

\({Sc}_{1}\) :

Schmidt number

\({Sc}_{2}\) :

Bio convection Schmidt number

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

Local Sherwood number

\({T}_{\text{w}}\) :

Wall temperature (K)

\({T}_{\infty }\) :

Ambient (free stream) temperature (K)

\(u,v\) :

Velocity along x and y directions (m s-1)

\({u}_{\text{w}},{v}_{\text{w}}\) :

Exponential velocities (m s-1)

\({W}_{c}\) :

Maximum cell swimming speed

\(x,y\) :

Coordinates along and transverse to sheet

\(\beta\) :

Casson parameter

\(\mu\) :

Dynamic viscosity (kg m-1s-1)

\(\rho\) :

Density (kg m-3)

\(\sigma\) :

Electrical conductivity (Siemens/m)

\(\upsilon\) :

Kinematic viscosity (m2/s-1)

\({\beta }^{*}\) :

Volumetric thermal expansion coefficient (K–1)

\({\left(\rho {c}_{\mathrm{p}}\right)}_{\mathrm{nf}}\) :

Specific heat capacity (J kg-1 K-1)

\(\varphi\) :

Nanoparticle volume fraction

\({\varphi }_{1},{\varphi }_{2}\) :

Nanoparticle property functions

σ * :

Stefan–Boltzmann radiative constant (5.6704 × 10−8 W m-2 K-1)

\(\theta\) :

Dimensionless temperature

\(\phi\) :

Dimensionless concentration

\(\chi\) :

Dimensionless concentration of microorganism

\(f\) :

Base fluid

\(nf\) :

Nanofluid

\(hnf\) :

Hybrid nanofluid

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Authors and Affiliations

  1. Department of Computer Science and Artificial Intelligence (Mathematics), SR University, Warangal, Telangana, 506371, India

    MD. Shamshuddin

  2. Department of Mathematics, Bowen University, Iwo, Nigeria

    S. O. Salawu

  3. Department of Pure and Applied Mathematics, School of Mathematical Sciences, Sunway University, 47500, Petaling Jaya, Selangor Darul Ehsan, Malaysia

    K. Ramesh

  4. Symbiosis Institute of Technology, Symbiosis International (Deemed University), Pune, 412115, India

    K. Ramesh

  5. Department of Mathematics, Government College of Engineering, Karad, 415124, India

    Vishwambhar S. Patil

  6. Department of Mathematics, Shivaji University, Kolhapur, 416004, India

    Pooja Humane

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Contributions

Dr. MDS involved in conceptualization, supervision, formal analysis, writing original draft and writing—review editing. Dr. SOS involved in methodology, software, visualization, validation and writing—review editing. Dr. KR involved in investigation, writing original draft and writing—review editing. Dr. VSP involved in resources and formal analysis. Dr. PPH involved in investigation and formal analysis.

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Correspondence to MD. Shamshuddin.

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Shamshuddin, M., Salawu, S.O., Ramesh, K. et al. Bioconvective treatment for the reactive Casson hybrid nanofluid flow past an exponentially stretching sheet with Ohmic heating and mixed convection. J Therm Anal Calorim 148, 12083–12095 (2023). https://doi.org/10.1007/s10973-023-12465-x

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