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On blood-based binary Casson nanofluid convection using viscosity and conductivity variations embedded with Darcy porous medium

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Abstract

The onset of double-diffusive convection with conductivity and viscosity variations has been investigated for blood-based Casson nanofluids and Darcy model is used to modify the momentum equation. The conductivity and viscosity of nanofluid are assumed to be linear functions of their volume fraction and the problem incorporates Brownian motion and thermophoresis. The resulting eigenvalue problem is solved using single term Galerkin method that gives the criterion for both stationary and oscillatory motions. It is observed that nanoparticle parameters and solute parameters except solute Rayleigh number destabilize the system while porosity parameter and solute Rayleigh number postpone the onset of convection. Darcy-Rayleigh number for glycol, honey and blood-based nanofluids is much higher than that of water-based nanofluids. Hence the system is more stable for non-Newtonian fluids. The goal and novelty of the present work lies in the fact that it examines, different base-fluids (water, blood, honey and glycol) with different porous phases (glass, limestone and sand) for their conductivity patterns to observe that conductivity variation pattern for different porous media is: glass < limestone < sand and for different base-fluids is: water < honey < blood < glycol. Further, important result is the fact that although non-Newtonian Casson parameter destabilizes the fluid layer system yet Casson nanofluids are more stable when compared to regular nanofluids. Reason behind is that the Casson parameter though with the positive sign, but lies in the denominator in the expression of Darcy-Rayleigh number.

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Abbreviations

\(a\) :

Wave number

\(c\) :

Nanofluid specific heat (J/kg K)

\(C\) :

Solute concentration (mol/kg)

\(C_{0}\) :

Solute concentration at lower layer (mol/kg)

\(C_{1}\) :

Solute concentration at upper layer (mol/kg)

\(d\) :

Depth of the layer (m)

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

Brownian diffusion coefficient (m2/s)

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

Diffusivity of Soret type (m2/s)

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

Solutal diffusivity (m2/s)

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

Thermophoresis diffusion coefficient (m2/s)

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

Diffusivity of Dufour type (m2/s)

\(e_{ij}\) :

Deformation rate (\({\text{Pas}}\))

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

Acceleration due to gravity (m/s2)

\(k\) :

Thermal conductivity of nanofluid (W/mK)

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

Effective conductivity of fluid (W/mK)

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

Conductivity of the fluid (W/mK)

\(k_{m}\) :

Overall thermal conductivity (W/mK)

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

Conductivity of the particles (W/mK)

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

Conductivity of solid material (W/mK)

\(K\) :

Permeability (\({\text{m}}^{2}\))

\(m_{x}\) :

Wave number in x-pivot

\(n_{y}\) :

Wave number in y-pivot

\(p\) :

Pressure (Pa)

\(s\) :

Growth rate (\({\text{m}}\))

\(t\) :

Time (\({\text{s}}\))

\(T\) :

Temperature (\({\text{K}}\))

\(T_{0}\) :

Temperature at lower layer (\({\text{K}}\))

\(T_{1}\) :

Temperature at upper layer (\({\text{K}}\))

\({\mathbf{V}}\) :

Velocity of the fluids (\({\text{m}}/{\text{s}}\))

\({\mathbf{V}}_{{\text{d}}}\) :

Darcian-velocity of fluid (\(= \varepsilon {\mathbf{V}}\)) (\({\text{m}}/{\text{s}}\))

\(Y_{y}\) :

Yield stress for Casson fluid (\({\text{N}}/{\text{m}}^{2}\))

\(\alpha_{m}\) :

Thermal diffusivity of fluid (\({\text{m}}^{2} /{\text{s}}\))

\(\beta\) :

Casson parameter

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

Thermal volumetric coefficient (\({\text{K}}^{ - 1}\))

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

Solute volumetric coefficient (\({\text{K}}^{ - 1}\))

\(\gamma\) :

Conductivity variation parameter

\(\varepsilon\) :

Porosity

\(\mu\) :

Viscosity of the nanofluid (\({\text{N}}\,{\text{s}}/{\text{m}}^{2}\))

\(\mu_{{{\text{eff}}}}\) :

Effective viscosity (\({\text{N}}\,{\text{s}}/{\text{m}}^{2}\))

\(\mu_{f}\) :

Dynamic viscosity (\({\text{Pa}}\;{\text{s}}\))

\(\phi\) :

Nanoparticle volume fraction

\(\tilde{\pi }\) :

Product of component of deformation rate (\({\text{Pa}}\;{\text{s}}\))

\(\tilde{\pi }_{{\text{c}}}\) :

Critical value of \(\tilde{\pi }\), defined by Eq. (1)

\(\nu\) :

Viscosity variation parameter

\(\tau\) :

Stress tensor (\({\text{N}}/{\text{m}}^{2}\))

\(\rho_{p}\) :

Nanoparticle density (\({\text{kg}}/{\text{m}}^{3}\))

\(\rho_{0}\) :

Fluid density at temperature \(T_{0}\)  (\({{\text{kg}}/{\text{m}}^{3} }\))

\(\rho c\) :

Heat capacity (\({\text{J}}/{\text{K}}\))

\(\sigma\) :

Thermal capacity ratio (\({\text{J}}/{\text{K}}\))

\(\phi\) :

Relative nanoparticle volume fraction \(\frac{{\phi - \phi_{0} }}{{\phi_{1} - \phi_{0} }}\)

\(L_{e}\) :

Solute Lewis number

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

Nanofluid Lewis number

\(N_{a}\) :

Diffusivity ratio

\(N_{b}\) :

Particle density increment

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

Soret parameter

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

Dufour parameter

\(R_{a}\) :

Thermal Rayleigh number

\(R_{m}\) :

Basic-density Rayleigh number

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

Nanoparticle Rayleigh number

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

Solute Rayleigh number

^:

Perturbed variable

\(*\) :

Non-dimensional variable

~ :

Basic solutions

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Acknowledgements

One of the authors, Mamta Devi is thankful to Council of Scientific and Industrial Research, New Delhi-110012, India, for the financial assistance in the form of SRF [Ref. No.: 09/135 (0895)/2019-EMR-I].

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Authors and Affiliations

  1. Energy Research Centre, Panjab University, Chandigarh, 160014, India

    Mamta Devi

  2. Dr. S.S. Bhatnagar University Institute of Chemical Engineering and Technology, Panjab University, Chandigarh, 160014, India

    Urvashi Gupta

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  1. Mamta Devi
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Correspondence to Urvashi Gupta.

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Devi, M., Gupta, U. On blood-based binary Casson nanofluid convection using viscosity and conductivity variations embedded with Darcy porous medium. Indian J Phys 97, 1833–1847 (2023). https://doi.org/10.1007/s12648-022-02584-w

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