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Viscous dissipation impact on electrical resistance heating distributed Carreau nanoliquid along stretching sheet with zero mass flux

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Abstract

The present paper envisages on the electric resistance heating distribution on three-dimensional Carreau dissipated NF along a nonlinear stretching sheet. The characteristics of heat and mass transfer are conferred by utilizing nonlinear radiation and zero mass flux. The passive control on NPhas its own application in drug targeting therapy. Convectively hot fluid is placed near the stretching sheet. The governing Prandtl boundary layer equations are modeled using relative laws and transformed to highly nonlinear ordinary differential equations with similarity conversion variables. The dependent variables in governing equation are solved by shooting method with R-K scheme. A comparative study of Pseudoplastic and Dilatant fluids is deliberated in this study. Varied physical parameters, whose behaviors on the velocity, energy and species concentration are analyzed. Shear thickening fluid nature superiors the shear thinning fluid nature when the fluid flow swifts, whereas energy exchange from the system is more in Dilatant fluid. Heat transfer rate is higher when the fluid flow swifts. Heat transfer from the fluid to the surface is slow as the Eckert number along both x–y directions. The examination of present outcomes with the existing work has been made, which is good agreed. The present study reveals that the liquid stream velocity declines for the larger values of ratio of stretching rates parameter c and conflicting behavior is detected in tangential velocity.

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Abbreviations

B :

Magnetic induction strength (T)

\( B_{0} \) :

Uniform magnetic field strength (T)

C:

Concentration (kg/m3)

h f :

Coefficient of heat transfer

\( k \) :

Thermal conductivity (W/(m K))

k f :

Thermal conductivity (W/(m K))

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

Mean absorption coefficient

n:

Index of flow behavior

p f :

Pressure (Pa)

T :

Temperature (K)

T f :

Hot fluid temperature

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

Radiative heat flux (W/m2)

u,v,w :

Velocity components (m/s)

u w,v w :

Stretching velocities (m/s)

We:

Weissenberg number

x,y,z :

Cartesian co-ordinates

η :

Independent variable

f :

Axial velocity

g :

Tangential velocity

θ :

Temperature

θ w :

Nonlinear radiation parameter

ϕ :

Species concentration

c :

Stretching ratio parameter

Cfx :

LocalSkin friction along x-axis

Cfy :

LocalSkin friction along y-axis

C f :

Solutal wall concentration

C ∞ :

Solutal concentration away from fluid

Cpf :

Specific heat at constant pressure

D B :

Coefficient of mass diffusivity

D T :

Thermophoresis parameter

Ecx :

Eckert number along x-direction

Ecy :

Eckert number along y-direction

Le:

Lewis number

\( R \) :

Radiation parameter

m :

Nonlinear stretching parameter

Nb:

Brownian motion parameter

Nt:

Thermophoresis parameter

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

Local Nusselt number

Pr:

Prandtl number

Rex :

Local Reynolds number along x-axis

Rey :

Local Reynolds number along y-axis

T ∞ :

Temperature far away fluid

α f :

Thermal diffusivity (m2/s)

γ :

Thermal Biot number

Γ:

Fluid parameter

μ f :

Dynamic viscosity (Pa s or kg/ms)

\( \nu \) :

Kinematic viscosity of basefluid (m2/s)

\( \rho C_{\text{p}} \) :

Heat capacitance (J/(kg K))

\( \sigma \) :

Electric conductivity (S/m)

σs :

Stefan–Boltzmann constant (W/m2K4)

ν f :

Kinematic viscosity (m2/s)

ρ f :

Density (kg/m3)

NF:

Nanofluid/NF

NP:

Nanoparticle

RK:

Runge–Kutta

CF:

Carreau fluid

PF:

Pseudoplastic fluid/pseudoplastic flow

DF:

Dilatant flow/dilatant fluid

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Authors and Affiliations

  1. Department of Humanities and Sciences, Sri Venkateswara Engineering College, Tirupati, A.P., 517 502, India

    P. Sreenivasulu

  2. Fluid Dynamics Division, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamilnadu, 632014, India

    T. Poornima

  3. Department of Mathematics, S.V. University, Tirupati, A.P., 517 502, India

    B. Malleswari & N. Bhaskar Reddy

  4. Department of Physics, College of Science, King Faisal University, PO Box 380, Al-Ahsa, 31982, Saudi Arabia

    Basma Souayeh

  5. Laboratory of Fluid Mechanics, Physics Department, Faculty of Sciences of Tunis, University of Tunis El Manar, 2092, Tunis, Tunisia

    Basma Souayeh

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  1. P. Sreenivasulu
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  2. T. Poornima
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  3. B. Malleswari
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  4. N. Bhaskar Reddy
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  5. Basma Souayeh
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Correspondence to T. Poornima or Basma Souayeh.

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Sreenivasulu, P., Poornima, T., Malleswari, B. et al. Viscous dissipation impact on electrical resistance heating distributed Carreau nanoliquid along stretching sheet with zero mass flux. Eur. Phys. J. Plus 135, 705 (2020). https://doi.org/10.1140/epjp/s13360-020-00680-6

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