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Magnetized flow of sutterby nanofluid through cattaneo-christov theory of heat diffusion and stefan blowing condition

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Abstract

Stefan blowing phenomenon in electrically conducting Sutterby material flow over stretchable rotating disk is demonstrated in this research. Cattaneo-Christov (CC) model of energy diffusion is adopted to analyze the heat transmission. Buongiorno model is carried out to evaluate the involvement of nanoparticles. The formulated system of partial differential expressions is re-structured by the enactment of similarity functions. Runge–Kutta-Fehlberg (RKF) fourth-fifth order process has been executed to communicate the solution of velocity, thermal and solutal fields. The velocity, concentration, thermal fields, skin friction, rate of mass and heat transportations are explored for the embedded non-dimensional parameters graphically. Result reveals that the rise in Stefan blowing factor leads to an enhancement in radial and tangential velocities gradients. The velocity of nanomaterial is reduced by the incrementing material parameter values. The augmenting magnetic parameter values reduced the liquid velocity but improves the temperature. The thermophoretic force and Brownian motion involvement resulted the higher thermal field.

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Abbreviations

\((u,w)\) :

Velocity components \(\left( {ms^{ - 1} } \right)\)

\(C_{w}\) :

Surface concentration

\((x,r)\) :

Directions \(\left( m \right)\)

\(T_{w}\) :

Surface temperature \(\left( K \right)\)

\(C_{\infty }\) :

Ambient concentration

\(\Lambda\) :

Shear rate

\(\beta_{0}\) :

Magnetic field \((m^{(1/2)} kg^{(1/2)} s^{( - 2)} )\)

\(\sigma_{e}\) :

Electrical conductivity \(\left( {kg^{ - 1} m^{ - 3} c^{2} s} \right)\)

\(\mu\) :

Dynamic viscosity \((kg\;s^{ - 1} m^{ - 1} )\)

\(\rho\) :

Density of liquid \((kgm^{ - 3} )\)

\(C_{p}\) :

Specific heat \((K^{ - 1} s^{ - 2} m^{2} )\)

\(k_{o}\) :

Thermal conductivity \((W/mK)\)

\(p\) :

Pressure

\(Sh_{r}\) :

Local Sherwood number

\(C\) :

Concentration

\(T\) :

Temperature \(\left( K \right)\)

\(D_{T}\) :

Thermophoretic diffusion co-efficient \((m^{2} s^{ - 1} )\)

\(\tau_{1}\) :

Ratio of nanoparticles heat capacity and the base fluid

\(T_{\infty }\) :

Ambient temperature \(\left( K \right)\)

\(\mu_{0}\) :

Viscosity at low shear rate

\(M\) :

Magnetic parameter

\(\,C_{f\,\theta }\) :

Skin friction in tangential direction

\(N\) :

Dimensionless parameter

\(D_{B}\) :

Brownian diffusion \((m^{2} s^{ - 1} )\)

\(A_{1}\) :

Rilvin Erickson tensor

\(\varepsilon\) :

Material parameter

\(\Omega\) :

Angular velocity \((s^{ - 1} )\)

\(\tau_{0}\) :

Heat flux relaxation time \((s)\)

\(b\) :

Characteristic time \((s)\)

\(\lambda\) :

Thermal relaxation time parameter

\(Nt\) :

Thermophoresis parameter

\(Nb\) :

Parameter of Brownian movement

\(Sc\) :

Schmidt number

\(A\) :

Stretching constraint

\(f_{w}\) :

Stefan blowing factor

\(C_{f\,r}\) :

Skin friction in radial direction

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

Local Reynolds number

\(\Pr\) :

Prandtl number

\(Nu_{r}\) :

Local Nusselt number

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Authors and Affiliations

  1. Department of Studies and Research in Mathematics, Davangere University, Davangere, Karnataka, India

    R. J. Punith Gowda, R. Naveen Kumar & B. C. Prasannakumara

  2. Department of Mathematics, COMSATS University Islamabad, Sahiwal, 57000, Pakistan

    A. Rauf & S. A. Shehzad

Authors
  1. R. J. Punith Gowda
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  2. R. Naveen Kumar
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  3. A. Rauf
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  4. B. C. Prasannakumara
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  5. S. A. Shehzad
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Correspondence to S. A. Shehzad.

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Gowda, R.J.P., Kumar, R.N., Rauf, A. et al. Magnetized flow of sutterby nanofluid through cattaneo-christov theory of heat diffusion and stefan blowing condition. Appl Nanosci 13, 585–594 (2023). https://doi.org/10.1007/s13204-021-01863-y

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