**Author details**

*J*

! electric current density

*p*<sup>∞</sup> constant pressure

*Nanofluid Flow in Porous Media*

*<sup>J</sup>* Joule heating parameter <sup>¼</sup> *<sup>σ</sup> <sup>B</sup>*<sup>2</sup>

*<sup>Q</sup>* volumetric heat generation/absorption rate, W m�<sup>3</sup> ½ �

*S*<sup>0</sup> Soret number ½ � ¼ *DkT*ð Þ *Tw* � *T*<sup>∞</sup> *=νTm*ð Þ *Cw* � *C*<sup>∞</sup>

ing ð Þ *<sup>r</sup>; <sup>φ</sup>; <sup>z</sup>* , respectively, m s�<sup>1</sup> ½ �

*ξ* tangent momentum accommodation coefficient

*<sup>ν</sup>* kinematic viscosity of the ambient fluid, m<sup>2</sup> <sup>s</sup>�<sup>1</sup> ½ �

*<sup>α</sup>* temperature buoyancy parameter <sup>¼</sup> *<sup>g</sup>βT*ð Þ *Tw* � *<sup>T</sup>*<sup>∞</sup> *<sup>=</sup>LR*Ω<sup>2</sup>

*Pr* Prandtl number <sup>¼</sup> *νρcp=<sup>k</sup> <sup>p</sup>* pressure distribution, N m�<sup>2</sup> ½ �

*qr* radiative heat flux, W m�<sup>2</sup> ½ � *Rd* radiation parameter <sup>¼</sup> *<sup>k</sup>*<sup>∗</sup>

*<sup>S</sup>* porosity parameter <sup>¼</sup> *<sup>ν</sup>=k*<sup>1</sup>

*Sc* Schmidt number ½ � ¼ *ν=D Sh* Sherwood number

*T* temperature distribution K½ � *Tm* mean fluid temperature K½ � *Tw* uniform temperature K½ � *T*<sup>∞</sup> constant temperature K½ �

*Ut* tangential velocity, m s�<sup>1</sup> ½ �

*<sup>μ</sup><sup>m</sup>* magnetic permeability, kg m�<sup>1</sup> <sup>s</sup>�<sup>1</sup> ½ �

*<sup>μ</sup>* dynamic viscosity, kg m�<sup>1</sup> <sup>s</sup>�<sup>1</sup> ½ �

*<sup>δ</sup>* heat source parameter <sup>¼</sup> *<sup>Q</sup>=*Ω*ρcp*

*θ* dimensionless temperature distribution *φ* dimensionless concentration distribution

*<sup>β</sup>* chemical reaction parameter <sup>¼</sup> *<sup>k</sup>=*Ω*L*<sup>2</sup>

*w,* ∞ conditions at the surface and in the free stream

*w*<sup>0</sup> uniform suction

*λ* mean free path

*γ* slip factor

*η* similarity variable

*σ* electrical conductivity *σ* Stephan-Boltzmann constant Ω constant angular velocity

*β<sup>T</sup>* coefficient of temperature *β<sup>C</sup>* coefficient of concentration

*<sup>ρ</sup>* fluid density, kg m�<sup>3</sup> ½ �

Greek symbols

Subscripts

**120**

<sup>0</sup>Ω*L=ρcp*ð Þ *Tw* � *T*<sup>∞</sup> 

*k=*4*σ*<sup>∗</sup>*T*<sup>3</sup> ∞

ð Þ *u; v; w* components of the flow velocity are in the directions of increas-

Gamal M. Abdel-Rahman<sup>1</sup> \* and Faiza M.N. El-fayez<sup>2</sup>

1 Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt

2 Mathematical Science Department, College of Sciences, Princess Nourah Bint Abdulrahman University, Riyadh, KSA

\*Address all correspondence to: gamalm60@yahoo.com

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
