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Flow and heat transfer analysis of carbon nanotubes-based Maxwell nanofluid flow driven by rotating stretchable disks with thermal radiation

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Abstract

A mathematical model is constructed to examine the impact of magnetic field and thermal radiation on flow and heat transfer analysis of carbon nanotubes-based nanofluids by taking base fluid as the water between two revolving stretchable disks with convective boundary conditions in the present investigation. The most extensively validated finite element technique is employed to solve the reduced nonlinear ordinary differential equations together with boundary conditions. Velocity and temperature distributions are calculated and are displayed through graphs for various values of pertinent parameters entered into the problem. Furthermore, the values of rates of change of velocity and temperature are examined in detail and are portrayed in tabular form. The values of skin friction coefficient at both upper and lower disks elevates in the boundary layer regime with rising values of Deborah number in both nanofluids, and this augmentation is higher in MWCNTs–water- than SWCNTs–water-based Maxwell nanofluid. Temperature of the fluid in both nanofluids deteriorates as the values of nanoparticle volume fraction parameter upsurge, and this deterioration in temperature distributions is higher in SWCNTs–water- than the MWCNTs–water-based Maxwell nanofluid.

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Abbreviations

B 0 :

Magnetic field strength

B 5 :

Upper disk thermal Biot number

B 2 :

Stretching parameter at upper disk

T ∞ :

Ambient temperature attained

T :

Fluid temperature

C f :

Skin friction coefficient

ρ f :

Density of the base fluid

f(η):

Dimensionless stream function

g :

Gravitational acceleration

μ :

Fluid viscosity

\(K^{*}\) :

Mean absorption coefficient

σ :

Electrical conductivity

k s :

Thermal conductivity of nanoparticle

M :

Magnetic parameter

Nr :

Buoyancy ratio parameter

Nu x :

Nusselt number

P :

Pressure

Pr :

Prandtl number

q r :

Radiative heat flux

R :

Radiation parameter

Re :

Reynolds number

B 4 :

Lower disk thermal Biot number

B 3 :

Rotation parameter

B 1 :

Stretching parameter at lower disk

T w :

Temperature at the cone surface

ρ p :

Nanoparticle mass density

\(\left( {\rho c_{\text{p}} } \right)_{\text{nf}}\) :

Heat capacitance of the nanofluid

\(\left( {\rho c_{\text{p}} } \right)_{\text{p}}\) :

Heat capacitance of the nanofluid

ρ nf :

Density of the nanofluid

ψ :

Stream function

\((\rho c_{\text{p}} )_{\text{f}}\) :

Heat capacitance of the base fluid

a :

Constant

\(\sigma^{*}\) :

Stephan–Boltzmann constant

ε :

Pressure parameter

τ w :

Shear stress

θ(η):

Dimensionless temperature

(x, y):

Cartesian coordinates

(u, v):

Velocity components in x- and y-axis

q w :

Wall heat flux

α :

Thermal diffusivity of base fluid

η :

Similarity variable

(μ)nf :

Viscosity of the nanofluid

φ :

Volume fraction of nanoparticles

λ :

Maxwell parameter

β :

Thermal expansion coefficient

k nf :

Thermal conductivity of nanofluid

ν f :

Kinematic viscosity of the base fluid

β :

Deborah number

f:

Base fluid

w:

Condition at cone surface

nf:

Nanofluid

∞:

Condition far away from cone surface

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Authors and Affiliations

  1. Department of Mathematics, RGM College of Engineering and Technology, Nandyal, AP, India

    P. Sudarsana Reddy & K. Jyothi

  2. Research Scholar, JNTU Anantapuramu, Anantapur, AP, India

    K. Jyothi

  3. Department of Mathematics, JNTUACEP, Pulivendula, AP, India

    M. Suryanarayana Reddy

Authors
  1. P. Sudarsana Reddy
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  2. K. Jyothi
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  3. M. Suryanarayana Reddy
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Correspondence to P. Sudarsana Reddy.

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Technical Editor: Cezar Negrao, PhD.

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Sudarsana Reddy, P., Jyothi, K. & Suryanarayana Reddy, M. Flow and heat transfer analysis of carbon nanotubes-based Maxwell nanofluid flow driven by rotating stretchable disks with thermal radiation. J Braz. Soc. Mech. Sci. Eng. 40, 576 (2018). https://doi.org/10.1007/s40430-018-1494-9

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