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MHD flow of radiative micropolar nanofluid in a porous channel: optimal and numerical solutions

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Abstract

The flow of a radiative and electrically conducting micropolar nanofluid inside a porous channel is investigated. After implementing the similarity transformations, the partial differential equations representing the radiative flow are reduced to a system of ordinary differential equations. The subsequent equations are solved by making use of a well-known analytical method called homotopy analysis method (HAM). The expressions concerning the velocity, microrotation, temperature, and nanoparticle concentration profiles are obtained. The radiation tends to drop the temperature profile for the fluid. The formulation for local Nusselt and Sherwood numbers is also presented. Tabular and graphical results highlighting the effects of different physical parameters are presented. Rate of heat transfer at the lower wall is seen to be increasing with higher values of the radiation parameter while a drop in heat transfer rate at the upper wall is observed. Same problem has been solved by implementing the numerical procedure called the Runge–Kutta method. A comparison between the HAM, numerical and already existing results has also been made.

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Abbreviations

u :

Component of velocity in x-direction

v :

Component of velocity in y-direction

ρ :

Density of nanofluid

T :

Temperature of the fluid

C :

Concentration of the fluid

C 1 :

Concentration at the lower plate of the channel

T 1 :

Temperature at the lower plate of the channel

C 2 :

Concentration at the upper plate of the channel

T 2 :

Temperature at the upper plate of the channel

f :

Dimensionless stream function

g :

Dimensionless form of the microrotation profile

B 0 :

Strength of the applied magnetic field

θ :

Dimensionless temperature profile

ϕ :

Dimensionless concentration profile

D T :

Thermophoresis coefficient

D B :

Brownian motion coefficient

Pr :

Prandtl number

N b :

Brownian motion parameter

N t :

Thermophoresis parameter

Sc :

Schmidt number

M :

Magnetic parameter

R d :

Radiation parameter

C f :

Skin friction coefficient

Nu x :

Local Nusselt number

η :

Dimsensionless similarity variable

μ :

Dynamic viscosity of the fluid

k :

The material parameter

(ρ)f :

Density of the base fluid

(ρc)f :

Heat capacity of the base fluid

(ρc)p :

Effective heat capacity of the nanoparticle

σ :

Electric conductivity

τ :

Parameter defined by \(\frac{{(\rho c)_{\text{p}} }}{{(\rho c)_{\text{f}} }}\)

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, HITEC University, Taxila Cantt, Pakistan

    Syed Tauseef Mohyud-Din, Saeed Ullah Jan, Umar Khan & Naveed Ahmed

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  1. Syed Tauseef Mohyud-Din
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  2. Saeed Ullah Jan
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Correspondence to Syed Tauseef Mohyud-Din.

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Mohyud-Din, S.T., Jan, S.U., Khan, U. et al. MHD flow of radiative micropolar nanofluid in a porous channel: optimal and numerical solutions. Neural Comput & Applic 29, 793–801 (2018). https://doi.org/10.1007/s00521-016-2493-3

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  • DOI: https://doi.org/10.1007/s00521-016-2493-3

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