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Reiner-Rivlin nanomaterial heat transfer over a rotating disk with distinct heat source and multiple slip effects

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Abstract

The thermodynamic features of the Reiner-Rivlin nanoliquid flow induced by a spinning disk are analyzed numerically. The non-homogeneous two-phase nanofluid model is considered to analyze the effect of nanoparticles on the thermodynamics of the Reiner-Rivlin nanomaterial, which also includes a temperature-dependent heat source (THS) and an exponential space-dependent heat source (ESHS). Further, the transfer of heat and mass is analyzed with velocity slip, volume fraction jump, and temperature jump boundary conditions. The finite difference method-based routine is used to solve the complicated differential equations formed after using the von-Karman similarity technique. Limiting cases of the present problem are found to be in good agreement with benchmarking studies. The relationship of the pertinent parameters with the heat and mass transport is scrutinized using correlation, which is further evaluated based on the probable error estimates. Multivariable models are fitted for the friction factor at the disk and heat transport, which accurately predict the dependent variables. The Reiner-Rivlin nanoliquid temperature is influenced comparatively more by the ESHS than by the THS. The Nusselt number is decreased by the ESHS and THS, whereas the friction factor at the disk is predominantly decremented by the wall roughness aspect. The increment in the non-Newtonian characteristic of the liquid leads more fluid to drain away in the radial direction far from the disk compared with the fluid nearby the disk in the presence of the centrifugal force during rotation. The increased thermal and volume fraction slip lowers the nanoliquid temperature and nanoparticle volume fraction profiles.

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Abbreviations

u, v, w :

velocity components (m·s−1)

T :

fluid temperature (K)

c :

nanoparticle volume fraction

q T :

linear heat source factor (J·m−3·K−1·s−1)

q E :

exponential space-dependent heat source (ESHS) factor (J · m−3 · K−1 · s−1)

r, ϕ, z :

cylindrical coordinates

T w :

temperature of the fluid near the disk (K)

T ∞ :

temperature of the ambient fluid (K)

c w :

nanoparticle volume fraction near the disk

c ∞ :

ambient nanoparticle volume fraction

D T :

thermophoretic diffusion coefficient (m2 · s−1)

D B :

Brownian diffusion coefficient (m2 · s−1)

Pr :

Prandtl number

(ρc p)f :

heat capacity of the fluid (J · m−3 · K−1)

(ρc p)p :

heat capacity of nanoparticles (J·m−3 · K−1)

P :

pressure (N · m−2)

q w :

heat flux near the disk (W · m−2)

N t :

thermophoresis parameter

N B :

Brownian motion parameter

Q T :

linear heat source parameter

Q E :

exponential heat source parameter

Re :

Reynolds number

C f :

skin friction coefficient

C (ζ):

dimensionless nanoparticle volume fraction

k :

thermal conductivity (W · m−1 · K−1)

Nu :

Nusselt number

K :

material parameter of the Reiner-Rivlin fluid

Sc :

Schmidt number

F (ζ):

dimensionless axial velocity component

F′(ζ):

dimensionless radial velocity component

G(ζ):

dimensionless azimuthal velocity component

n :

dimensionless exponential index

Le :

Lewis number

ν f :

kinematic viscosity (m2 · s−1)

α m :

thermal diffusivity (m2 · s−1)

θ(ζ):

dimensionless temperature

μ f :

dynamic viscosity (kg · m−1 · s−1)

ρ f :

density(kg · m−3)

β 1, β 2, ν 3, ν 4 :

coefficients of radial, azimuthal, thermal, and nanoparticle volume fraction slip

ω :

angular velocity (m · s−1)

μ c :

cross-viscosity coefficient

γ :

thermal slip parameter

δ :

nanoparticle volume fraction slip parameter

λ 1, λ 2 :

wall slip parameters

τ ij :

stress tensors

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Acknowledgement

The authors thank the anonymous reviewers and the editors for their constructive comments that improved the quality of the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, St. Thomas College (Autonomous), Thrissur, 680001, Kerala, India

    A. S. Sabu & A. Mathew

  2. Center for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, 560029, Karnataka, India

    J. Mackolil & B. Mahanthesh

Authors
  1. A. S. Sabu
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  2. J. Mackolil
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  3. B. Mahanthesh
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  4. A. Mathew
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Correspondence to B. Mahanthesh.

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Sabu, A.S., Mackolil, J., Mahanthesh, B. et al. Reiner-Rivlin nanomaterial heat transfer over a rotating disk with distinct heat source and multiple slip effects. Appl. Math. Mech.-Engl. Ed. 42, 1495–1510 (2021). https://doi.org/10.1007/s10483-021-2772-7

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  • DOI: https://doi.org/10.1007/s10483-021-2772-7

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