# American Institute of Mathematical Sciences

August  2018, 11(4): 583-594. doi: 10.3934/dcdss.2018033

## Numerical investigation of Cattanneo-Christov heat flux in CNT suspended nanofluid flow over a stretching porous surface with suction and injection

 a. DBS & H CEME, National University of Sciences and Technology, Islamabad, Pakistan b. Department of Mechanical Engineering, Manipal University Jaipur, Rajasthan-303007, India c. Department of Mathematics, University of Malakand, Dir (Lower), Khyber Pakhtunkhwa, Pakistan

* Corresponding author: Noreen Sher Akbar

Received  October 2016 Revised  May 2017 Published  November 2017

The present study analyzes the heat energy transfer in nano fluids flow through the porous stretching surface. Cattanneo-Christov heat flux model is employed to study the heat energy transfer. Darcy law is used to discuss the flow characteristics over the different types of permeable sheets with suction and injection. Nanofluids is considered as water based single-walled carbon nanotubes (SWNTs) and multi-walled carbon nanotubes (MWNTs) nanofluids. A comparative study for SWCNT and MWCNT is also made. Governing equations are transformed into set of ordinary differential equations using similarity transformations. The computational results are obtained by using Runge-Kutta fourth order method along with shooting technique. Numerical and graphical results are presented to discuss the effects of various physical parameters on velocity profile, temperature profile, Nusselt number, Sherwood number and skin friction coefficient for different type of nanoparticles for suction and injection cases. Stream lines and isotherms are also plotted for three different cases viz. permeable sheet with suction, impermeable sheet and permeable sheet with injection. A comparative analysis with existing results is tabulated which validate that the numerical results of present study have good correlation with existing results. The outcomes of the results show that skin friction coefficient is more for SWCNT in caparison of MWCNT and the boundary layer thickness is maximum for permeable stretching sheet with suction parameter.

Citation: Noreen Sher Akbar, Dharmendra Tripathi, Zafar Hayat Khan. Numerical investigation of Cattanneo-Christov heat flux in CNT suspended nanofluid flow over a stretching porous surface with suction and injection. Discrete and Continuous Dynamical Systems - S, 2018, 11 (4) : 583-594. doi: 10.3934/dcdss.2018033
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##### References:
Schematic representation of SWCNT and MWCNT nanofluids flow over porous stretching Surface
Velocity profile for different values of solid nanoparticles volume fraction with porosity parameter. (a) Suction parameter. (b) Impermeable sheet. (c) Injection parameter
Temperature profile for different values of solid nanoparticles volume fraction with porosity parameter. (a) Suction parameter. (b) Impermeable sheet. (c) Injection parameter
Temperature profile for different values of solid nanoparticles volume fraction with thermal relaxation time. (a) Suction parameter. (b) Impermeable sheet. (c) Injection parameter
Skin friction coefficient for SWCNT and MWCNT with porosity parameter. (a) Suction parameter (b) Impermeable sheet. (c) Injection parameter
Nusselt number for SWCNT and MWCNT with porosity parameter (a) Suction parameter. (b) Impermeable sheet. (c) Injection parameter
Nusselt number for SWCNT and MWCNT with thermal relaxation time (a) Suction parameter. (b) Impermeable sheet. (c) Injection parameter
Streamlines for (a) Suction parameter (b) Impermeable sheet (c) Injection parameter at $\phi =0.2, \gamma=1,N=0.5$
Isotherms for (a) Suction parameter (b) Impermeable sheet (c) Injection parameter at $\phi =0.2, \gamma=1,N=0.5$
Thermophysical properties of different base fluid and CNT's
 Physical properties Base fluid Nanoparticles Water SWCNT MWCNT $\rho$ (kg/m$^3$) 997 2,600 1,600 $c_p$(J/kg K) 4,179 425 796 $k$(W/m K) 0.613 6,600 3,000 r (nm) 0.1 10 10
 Physical properties Base fluid Nanoparticles Water SWCNT MWCNT $\rho$ (kg/m$^3$) 997 2,600 1,600 $c_p$(J/kg K) 4,179 425 796 $k$(W/m K) 0.613 6,600 3,000 r (nm) 0.1 10 10
Comparison of results for the skin friction for pure fluid $(\phi = 0)$
 N Present results Salahuddin et al. [32] Noreen et al. [5] 0.0 1 1 1 0.5 -1.11703 -1.11701 -1.11703 1 -1.41321 -1.41318 -1.41321 5 -2.44849 -2.44842 -2.44849 10 -3.31653 -3.31656 -3.31653 100 -10.04978 -10.04971 -10.04978 500 -22.38313 -22.38383 -22.38313 1000 -31.63849 -31.63856 -31.63869
 N Present results Salahuddin et al. [32] Noreen et al. [5] 0.0 1 1 1 0.5 -1.11703 -1.11701 -1.11703 1 -1.41321 -1.41318 -1.41321 5 -2.44849 -2.44842 -2.44849 10 -3.31653 -3.31656 -3.31653 100 -10.04978 -10.04971 -10.04978 500 -22.38313 -22.38383 -22.38313 1000 -31.63849 -31.63856 -31.63869
Comparison of results for the Nusselt number for pure fluid $(\phi = 0)$ with $N=0$ and $\gamma=0$
 Pr Present results Khan et al. [21] Khan Pop. [23] Wang [40] Kandasamy et al. [22] 0.07 0.0664 0.0664 0.0664 0.0655 0.0662 0.20 0.1692 0.1692 0.1692 0.1692 0.1692 0.70 0.4538 0.4538 0.4538 0.4538 0.4543 2 0.9113 0.9113 0.9114 0.9115 0.9115 7 1.8953 1.8953 1.8953 1.8953 1.8952 20 3.3538 3.3538 3.3538 3.3538 - 70 6.4621 6.4623 6.4622 6.4623 -
 Pr Present results Khan et al. [21] Khan Pop. [23] Wang [40] Kandasamy et al. [22] 0.07 0.0664 0.0664 0.0664 0.0655 0.0662 0.20 0.1692 0.1692 0.1692 0.1692 0.1692 0.70 0.4538 0.4538 0.4538 0.4538 0.4543 2 0.9113 0.9113 0.9114 0.9115 0.9115 7 1.8953 1.8953 1.8953 1.8953 1.8952 20 3.3538 3.3538 3.3538 3.3538 - 70 6.4621 6.4623 6.4622 6.4623 -
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