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Slip flow of Maxwell viscoelasticity-based micropolar nanoparticles with porous medium: a numerical study

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Abstract

This article presents the mass and heat transport aspects in viscoelastic nanofluid flows under the presence of velocity slip conditions. To explore the non-Newtonian behavior, a Maxwell viscoelasticity-based micropolar is considered. Moreover, a porous medium saturates the stretching sheet. A set of similarity variables is introduced to derive the dimensionless ordinary differential equations of velocity, concentration, and temperature profiles. The numerical solution is computed by using the MATLAB bvp4c package. The salient flow features of velocity, concentration, and temperature profiles are described and discussed through various graphs. It is observed that with an increase in the slip parameter, the micro-rotation velocity also increases. The temperature of nanoparticles gets maximum values by varying the viscoelastic parameter and the porosity parameter while an opposite trend is noted for the micro-rotation parameter. The local Nusselt number and the local Sherwood number increase by increasing the viscoelastic parameter, the porosity parameter, and the slip velocity parameter. The graphical computation is performed for a specified range of parameters, such as 0 ⩽ M ⩽ 2.5, 0 ⩽ σm ⩽ 2.5, 0 ⩽ K1 ⩽ 1.5, 0.5 ⩽ Pr ⩽ 3.0, 0 ⩽ σ ⩽ 1.5, 0.5 ⩽ Sc ⩽ 2.0,0.2 ⩽ Nb ⩽ 0.8, and 0.2 ⩽ Nt ⩽ 0.8.

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Abbreviations

u, v :

velocity components

β :

relaxation parameter

μ :

dynamic viscosity

ρ :

density of fluid

ν :

viscosity

σ*:

Stefan-Boltzmann constant

φ :

permeability of porous medium

k*:

absorption/generation constant

j :

micro-inertia per unit mass

N :

micro-angular velocity

l :

positive constant

γ :

spin-gradient viscosity

α :

thermal diffusivity

(ρc)f :

heat capacitance of liquid

(ρc)p :

effective heat capacitance of nanoparticles

Q :

volume fraction

D T :

thermophoretic coefficient

D B :

Brownian diffusivity

k c :

chemical reaction parameter

M :

Hartmann number

ψ :

stream function

η :

dimensionless coordinate

σ m :

viscoelastic parameter

K 1 :

porosity parameter

Pr :

Prandtl number

θ :

dimensionless temperature profile

ϕ :

concentration profile

σ :

slip velocity parameter

R :

local micro-angular velocity

Sc :

Schmidt number

N b :

Brownian movement parameter

N t :

thermophoresis parameter

Nu x :

local Nusselt number

Re :

local Reynolds number

Sh x :

local Sherwood number.

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Authors and Affiliations

  1. Department of Mathematics, Government College University Faisalabad, Faisalabad, 38000, Pakistan

    H. Waqas & M. Imran

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

    S. U. Khan, S. A. Shehzad & M. A. Meraj

Authors
  1. H. Waqas
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  2. M. Imran
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  3. S. U. Khan
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  4. S. A. Shehzad
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Corresponding author

Correspondence to S. A. Shehzad.

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Citation: WAQAS, H., IMRAN, M., KHAN, S. U., SHEHZAD, S. A., and MERAJ, M. A. Slip flow of Maxwell viscoelasticity-based micropolar nanoparticles with porous medium: a numerical study. Applied Mathematics and Mechanics (English Edition), 40(9), 1255–1268 (2019) https://doi.org/10.1007/s10483-019-2518-9

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Waqas, H., Imran, M., Khan, S.U. et al. Slip flow of Maxwell viscoelasticity-based micropolar nanoparticles with porous medium: a numerical study. Appl. Math. Mech.-Engl. Ed. 40, 1255–1268 (2019). https://doi.org/10.1007/s10483-019-2518-9

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