**5. Conclusions**

In this work, thermal radiation and thermal diffusion effects over an electrically conducting, Newtonian fluid in a steady laminar magnetohydrodynamic convective flow over a porous rotating infinite disk with the consideration of heat and mass transfer in the presence of Soret and Dufour's diffusion effects have been obtained and studied numerically. Magnetic field parameter, porosity parameter, temperature buoyancy parameter, concentration buoyancy parameter, Prandtl number, radiation parameter, Soret and Dufour's number, Joule heating parameter, heat source parameter, Schmidt number, chemical reaction parameter, suction parameter, slip parameter effects were considered in the separate cases. The subsequent outcome may be drawn as:

1. The components (radial, axial and tangential) of the velocity, temperature, concentration and pressure profiles under the porosity parameter. The (radial, axial and tangential) components of the velocity and pressure profile decrease with increasing porosity parameter, while the temperature and the concentration profiles increase with increasing porosity parameter. And also, that increase porosity parameter *S* leads to a decrease in the all tangential skin

*Thermal Radiation and Thermal Diffusion for Soret and Dufour's Effects on MHD Flow over… DOI: http://dx.doi.org/10.5772/intechopen.82186*

friction �*G<sup>=</sup>* ð Þ 0 , heat transfer rate �*θ<sup>=</sup>* ð Þ <sup>0</sup> and mass transfer rate �*φ=*ð Þ <sup>0</sup> , while an increase in the radial skin friction *<sup>F</sup>=*ð Þ <sup>0</sup> .


## **Nomenclature**

parameter. The (radial, axial and tangential) components of the velocity, temperature, concentration and pressure profiles decrease with increase of suction parameter. The effects of *γ* on the velocity (radial, axial and tangential) and pressure profiles are shown in **Figure 14a** and **b**, respectively. It is observed that the (radial and axial) components of the velocity, and pressure profiles increase with the increasing slip parameter. While the tangential component of the velocity profile

The radial and tangential skin frictions and the heat and mass transfer coefficients are tabulated in **Table 2** for various values of *M*, *S*, *α*, *N*, *Pr*, *Rd*, *Du*&*S*0, *J*, *δ*, *Sc*, *β*, *Ws* and *γ*. We observed that increase for all magnetic field parameter *M* and

increase in the radial skin friction *<sup>F</sup>=*ð Þ <sup>0</sup> , the increase for all radial skin friction, tangential skin friction, heat transfer rate and mass transfer rate, with increasing of the temperature buoyancy parameter *α* and the concentration buoyancy parameter *N*. We found that the radial skin friction, tangential skin friction, mass transfer rate decreases while heat transfer rate increase with increasing of Prandtl number, Dufour number decreases and Soret number increases. It can that be seen that the radial skin friction, tangential skin friction and mass transfer rate increase while heat transfer rate decrease with increasing values of *Rd* and *δ*. It is observed that an increase in the Joule heating parameter, results in a decrease in the tangential Skinfriction coefficient, Nusselt number and Sherwood number. The tangential skin friction and heat transfer rate decrease but the radial skin friction and mass transfer rate increase with increasing the Schmidt number. It also can be seen from this table that increasing the chemical reaction parameter to decrease in the radial skin friction, tangential skin friction and heat transfer rate while increase the mass transfer rate. We found also the tangential skin friction increase but the radial skin friction, Nusselt number and Sherwood number decrease with increasing the suction parameter. Finally, the radial skin friction and the tangential skin friction

decrease but Nusselt number and Sherwood number increase with increasing slip

In this work, thermal radiation and thermal diffusion effects over an electrically conducting, Newtonian fluid in a steady laminar magnetohydrodynamic convective flow over a porous rotating infinite disk with the consideration of heat and mass transfer in the presence of Soret and Dufour's diffusion effects have been obtained and studied numerically. Magnetic field parameter, porosity parameter, temperature buoyancy parameter, concentration buoyancy parameter, Prandtl number, radiation parameter, Soret and Dufour's number, Joule heating parameter, heat source parameter, Schmidt number, chemical reaction parameter, suction parameter, slip parameter effects were considered in the separate cases. The subsequent

1. The components (radial, axial and tangential) of the velocity, temperature, concentration and pressure profiles under the porosity parameter. The (radial, axial and tangential) components of the velocity and pressure profile decrease

concentration profiles increase with increasing porosity parameter. And also, that increase porosity parameter *S* leads to a decrease in the all tangential skin

with increasing porosity parameter, while the temperature and the

ð Þ <sup>0</sup> and mass transfer rate �*φ=*ð Þ <sup>0</sup> , while an

porosity parameter *S* leads to an decrease in the all tangential skin friction

, heat transfer rate �*θ<sup>=</sup>*

decrease.

*Nanofluid Flow in Porous Media*

�*G<sup>=</sup>* ð Þ 0 

parameter.

**118**

**5. Conclusions**

outcome may be drawn as:



**Author details**

**121**

Gamal M. Abdel-Rahman<sup>1</sup>

Abdulrahman University, Riyadh, KSA

provided the original work is properly cited.

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

\* and Faiza M.N. El-fayez<sup>2</sup>

*Thermal Radiation and Thermal Diffusion for Soret and Dufour's Effects on MHD Flow over…*

*DOI: http://dx.doi.org/10.5772/intechopen.82186*

2 Mathematical Science Department, College of Sciences, Princess Nourah Bint

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

© 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,

*Thermal Radiation and Thermal Diffusion for Soret and Dufour's Effects on MHD Flow over… DOI: http://dx.doi.org/10.5772/intechopen.82186*
