**Nomenclature**

case of Ag-water nanofluid, the velocity is slightly less as compared with Cu-water nanofluid. **Figure 6** illustrates the impact of the porosity parameter k on the temperature profile and it is noted that with the increasing values of the porosity parameter, the temperature of the fluid increases. The temperature of Ag-water nanofluid is more as compared with Cu-water nanofluid. **Figure 7** shows the effect of nanoparticle volume fraction *ϕ* on the temperature of the nanofluids. From the figure, it is clear that the fluid temperature increases as the nanoparticle's volume fraction *ϕ* increases. The temperature distribution in Ag-water nanofluid is higher than that of Cu-water nanofluid. It is also observed that as the nanoparticle volume fraction increases, the thermal boundary layer thickness increases because as volume fraction increases, the thermal conductivity of the fluid increases. **Figure 8** shows the effect of the porosity parameter k and the nanoparticle volume fraction *ϕ* on the wall skin friction. It is observed that the skin friction increases with the increase in the porosity parameter k and the nanoparticle volume fraction *ϕ* for both the Cu-water and Ag-water nanofluids. The wall skin friction is higher in the case of Ag-water nanofluid than in Cu-water. Hence, the Ag-water nanofluid gives a higher drag in opposition to the flow than the Cu-water nanofluid. **Figure 9** shows the effect of the magnetic parameter M and porosity parameter k on the wall heat

ð Þ 0 *for various values of Pr.*

**Cu-Water Ag-Water**

0.1 1.17475 1.1747 1.22507 1.2251 0.15 1.20886 1.2089 1.27215 1.2722 0.2 1.21804 1.2180 1.28979 1.2898

0.1 1.32825 1.3282 1.37296 1.3730 0.15 1.33955 1.3396 1.39694 1.3969 0.2 1.33036 1.3304 1.39634 1.3963

0.1 1.46576 1.4658 1.50640 1.5064 0.15 1.45858 1.4586 1.51145 1.5115 0.2 1.43390 1.4339 1.49532 1.4953

0.1 1.70789 1.7079 1.74289 1.7429 0.15 1.67140 1.6714 1.71773 1.7177 0.2 1.62126 1.6213 1.67583 1.6758

ð Þ 0 *for various values of M and ϕ.*

*M* Φ **Hamad [53] Present Hamad [53] Present** 0 0.05 1.10892 1.1089 1.13966 1.1397

0*:*5 0.05 1.29210 1.2921 1.31858 1.3186

1 0.05 1.45236 1.4524 1.47597 1.4760

2 0.05 1.72887 1.7289 1.74875 1.7487

″

Pr **Vajravelu [54] Present** 0*:*72 0.4590 0.4596 7 1.8953 1.8954

**Table 1.**

**Table 2.**

**134**

*Comparison of results of the skin friction coefficient* �*f*

*Nanofluid Flow in Porous Media*

*Comparison of values of local Nusselt number* �*θ*<sup>0</sup>



**References**

2006;**357**:298-305

Analytic solution for

2013;**22**

**15**:83-95

2011;**40**:391-395

1663-1668

**137**

Chinese Physics B. 2013;**22**

[1] Crane LJ. Flow past a stretching plate. Journal of Applied Mathematics

*DOI: http://dx.doi.org/10.5772/intechopen.83732*

caused by the deformation of a plane surface. Magneto Hydrodynamics. 1974;

[10] Andersson HI. MHD flow of a viscoelastic fluid past a stretching surface. Acta Mechanica. 1992;**95**:

[11] Bhatti MM, Abbas MA, Rashidi MM. A robust numerical method for solving stagnation point flow over a permeable shrinking sheet under the influence of MHD. Applied Mathematics and Computation. 2018;**316**:381-389

[12] Sheikholeslami M, Shehzad SA. CVFEM for influence of external magnetic source on *Fe*3*O*<sup>4</sup> *H*2*O* nanofluid behavior in a permeable cavity considering shape effect. International Journal of Heat and Mass

Transfer. 2017;**115**:180-191

[13] Sheikholeslami M, Barzegar Gerdroodbary M, Moradi R, Shafee A, Li Z. Application of neural network for estimation of heat transfer treatment of *Al*2*O*<sup>3</sup> *H*2*O* nanofluid through a channel. Computer Methods in Applied Mechanics and Engineering. 2019;**344**:

[14] Sheikholeslami M, Sadoughi MK. Simulation of CuO-water nanofluid heat transfer enhancement in presence of melting surface. International Journal of Heat and Mass Transfer. 2018;**116**:1-12

[15] Sheikholeslami M, Jafaryar M, Saleem S, Li Z, Shafee A, Jiang Y. Nanofluid heat transfer augmentation and exergy loss inside a pipe equipped

International Journal of Heat and Mass

[16] Sheikholeslami M, Shehzad SA. Thermal radiation of ferrofluid in existence of Lorentz forces considering

with innovative turbulators.

Transfer. 2018;**126**:156-163

**10**:146-148

*MHD Flow and Heat Transfer of Casson Nanofluid through a Porous Media over a Stretching…*

227-230

1-12

and Physics. 1970;**21**:645-647

[2] Cortell R. Effects of viscous dissipation and work done by

deformation on the MHD flow and heat transfer of a viscoelastic fluid over a stretching sheet. Physics Letters A.

[3] Bhattacharyya K, Hayat T, Alsaedi A.

magnetohydrodynamic boundary layer flow of Casson fluid over a stretching/ shrinking sheet with wall mass transfer.

[4] Mukhopadhyay S. Casson fluid flow and heat transfer over a nonlinearly stretching surface. Chinese Physics B.

[5] Rashidi MM, Mohimanian Pour SA. Analytic approximate solutions for unsteady boundary-layer flow and heat transfer due to a stretching sheet by homotopy analysis method. Nonlinear Analysis: Modelling and Control. 2010;

[6] Ishak A. MHD boundary layer flow due to an exponentially stretching sheet with radiation effect. Sains Malaysiana.

[7] Bachok N, Ishak A, Pop I. Boundarylayer flow of nanofluids over a moving surface in a flowing fluid. International Journal of Thermal Sciences. 2010;**49**:

[8] Mandal IC, Mukhopadhyay S. Heat transfer analysis for fluid flow over an exponentially stretching porous sheet with surface heat flux in porous medium. Ain Shams Engineering

[9] Pavlov KB. Magneto hydrodynamic flow of an incompressible viscous fluid

Journal. 2013;**4**:103-110
