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Darcy-Forchheimer flow by rotating disk with partial slip

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Abstract

The viscous dissipation and heat transfer in the Darcy-Forchheimer flow by a rotating disk are examined. The partial slip conditions are invoked. The optimal series solutions are computed via the optimal homotopic analysis method (OHAM). The thermophoresis and Brownian motions are studied. The Darcy-Forchheimer relation characterizes the porous space. The roles of influential variables on the physical quantities are graphically examined. A reduction in the local Nusselt number is observed through thermophoresis and thermal slip parameters. The local Sherwood number depicts an increasing trend for the higher Brownian motion and concentration slip parameters.

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Abbreviations

u, v, w :

velocity components

υ nf :

kinematic nanofluid viscosity

r, ϕ, z :

polar coordinates

K*:

permeability of porous space

μ f :

dynamic viscosity of fluid

υ f :

kinematic viscosity of fluid

ρ f :

density of base fluid

α m :

thermal diffusivity

Cb*:

drag coefficient

F :

non-uniform inertia coefficient

ρ nf :

nanofluid density

D B :

Brownian diffusion

(ρcp)f :

specific heat capacity of base fluid

D T :

thermophoresis diffusion

Ω :

angular frequency

L 1 :

velocity slip parameter

L 2 :

thermal slip parameter

L 3 :

concentration slip parameter

T w :

surface temperature

C w :

surface concentration

T ∞ :

ambient temperature

C ∞ :

ambient concentration

λ :

local porosity parameter

F r :

Forchheimer number

N t :

thermophoresis parameter

Sc :

Schmidt number

γ 1 :

dimensionless velocity slip parameter

Pr :

Prandtl number

N b :

Brownian motion parameter

Ec :

Eckert number

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Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam University, Islamabad, 44000, Pakistan

    T. Hayat, F. Haider & T. Muhammad

  2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    T. Hayat & A. Alsaedi

Authors
  1. T. Hayat
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  2. F. Haider
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  3. T. Muhammad
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  4. A. Alsaedi
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Correspondence to F. Haider.

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Hayat, T., Haider, F., Muhammad, T. et al. Darcy-Forchheimer flow by rotating disk with partial slip. Appl. Math. Mech.-Engl. Ed. 41, 741–752 (2020). https://doi.org/10.1007/s10483-020-2608-9

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  • DOI: https://doi.org/10.1007/s10483-020-2608-9

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