# American Institute of Mathematical Sciences

August  2018, 11(4): 617-630. doi: 10.3934/dcdss.2018036

## Unsteady MHD slip flow of non Newtonian power-law nanofluid over a moving surface with temperature dependent thermal conductivity

 1 College of Electrical and Mechanical Engineering, National University of Sciences and Technology, Rawalpindi, 46070, Pakistan 2 Department of Mathematics, Capital University of Science and Technology, Islamabad 44000, Pakistan

* Corresponding author: Asim Aziz

Received  December 2016 Revised  April 2017 Published  November 2017

In this paper, unsteady magnetohydrodynamic (MHD) boundary layer slip flow and heat transfer of power-law nanofluid over a nonlinear porous stretching sheet is investigated numerically. The thermal conductivity of the nanofluid is assumed as a function of temperature and the partial slip conditions are employed at the boundary. The nonlinear coupled system of partial differential equations governing the flow and heat transfer of a power-law nanofluid is first transformed into a system of nonlinear coupled ordinary differential equations by applying a suitable similarity transformation. The resulting system is then solved numerically using shooting technique. Numerical results are presented in the form of graphs and tables and the effect of the power-law index, velocity and thermal slip parameters, nanofluid volume concentration parameter, applied magnetic field parameter, suction/injection parameter on the velocity and temperature profiles are examined from physical point of view. The boundary layer thickness decreases with increase in strength of applied magnetic field, nanoparticle volume concentration, velocity slip and the unsteadiness of the stretching surface. Whereas thermal boundary layer thickness increase with increasing values of magnetic parameter, nanoparticle volume concentration and velocity slip at the boundary.

Citation: Asim Aziz, Wasim Jamshed. Unsteady MHD slip flow of non Newtonian power-law nanofluid over a moving surface with temperature dependent thermal conductivity. Discrete and Continuous Dynamical Systems - S, 2018, 11 (4) : 617-630. doi: 10.3934/dcdss.2018036
##### References:

show all references

##### References:
Geometry of the problem
Velocity profiles for different values of parameter $A$
Temperature profiles for different values of parameter $A$
Velocity profiles for different values of parameter $M$
Temperature profiles for different values of parameter $M$
Velocity profiles for different values of parameter $\phi$
Temperature profiles for different values of parameter $\phi$
Velocity profiles for different values of parameter $\delta$
Temperature profiles for different values of parameter $\delta$
Velocity profiles for different values of parameter $S$
Temperature profiles for different values of parameter $S$
Velocity profiles for different values of parameter $S$
Temperature profiles for different values of parameter $S$
Values of $-f''(0)$ for the variation of parameters and fixed $Pr= 6.2$, $\Delta = 1.0$ and $\phi = 0.0$
 $M$ $S$ $\delta$ $A$ $-f''(0)$ $-f''(0)$ $-f''(0)$ T.Hayat Khadeejah Present 0.25 1.0 1.0 0.2 0.60157 0.60157 0.60160 1.0 0.2 1.0 0.2 0.57563 0.57563 0.57560 1.0 0.5 1.0 0.2 0.602285 0.602265 0.60228
 $M$ $S$ $\delta$ $A$ $-f''(0)$ $-f''(0)$ $-f''(0)$ T.Hayat Khadeejah Present 0.25 1.0 1.0 0.2 0.60157 0.60157 0.60160 1.0 0.2 1.0 0.2 0.57563 0.57563 0.57560 1.0 0.5 1.0 0.2 0.602285 0.602265 0.60228
Thermophysical properties of the base fluid and nanoparticles
 Physical properties Base fluid Nanoparticles Water Cu $C_{p}(J/kgK)$ 4179 385 $\rho(kg/m^{3})$ 997.1 8933 $k(W/mK)$ 0.613 400 $\sigma (\Omega.m)^{-1}$ 0.05 $5.96\times10^{7}$
 Physical properties Base fluid Nanoparticles Water Cu $C_{p}(J/kgK)$ 4179 385 $\rho(kg/m^{3})$ 997.1 8933 $k(W/mK)$ 0.613 400 $\sigma (\Omega.m)^{-1}$ 0.05 $5.96\times10^{7}$
 [1] Marilena Filippucci, Andrea Tallarico, Michele Dragoni. Simulation of lava flows with power-law rheology. Discrete and Continuous Dynamical Systems - S, 2013, 6 (3) : 677-685. doi: 10.3934/dcdss.2013.6.677 [2] Frank Jochmann. Power-law approximation of Bean's critical-state model with displacement current. Conference Publications, 2011, 2011 (Special) : 747-753. doi: 10.3934/proc.2011.2011.747 [3] José A. Carrillo, Yanghong Huang. Explicit equilibrium solutions for the aggregation equation with power-law potentials. Kinetic and Related Models, 2017, 10 (1) : 171-192. doi: 10.3934/krm.2017007 [4] Tao Wang. One dimensional $p$-th power Newtonian fluid with temperature-dependent thermal conductivity. Communications on Pure and Applied Analysis, 2016, 15 (2) : 477-494. doi: 10.3934/cpaa.2016.15.477 [5] Steinar Evje, Huanyao Wen. Weak solutions of a gas-liquid drift-flux model with general slip law for wellbore operations. Discrete and Continuous Dynamical Systems, 2013, 33 (10) : 4497-4530. doi: 10.3934/dcds.2013.33.4497 [6] María Teresa González Montesinos, Francisco Ortegón Gallego. The evolution thermistor problem with degenerate thermal conductivity. Communications on Pure and Applied Analysis, 2002, 1 (3) : 313-325. doi: 10.3934/cpaa.2002.1.313 [7] María Teresa González Montesinos, Francisco Ortegón Gallego. The thermistor problem with degenerate thermal conductivity and metallic conduction. Conference Publications, 2007, 2007 (Special) : 446-455. doi: 10.3934/proc.2007.2007.446 [8] Wei Lv, Ruirui Sui. Optimality of piecewise thermal conductivity in a snow-ice thermodynamic system. Numerical Algebra, Control and Optimization, 2015, 5 (1) : 47-57. doi: 10.3934/naco.2015.5.47 [9] Lili Du, Mingshu Fan. Thermal runaway for a nonlinear diffusion model in thermal electricity. Discrete and Continuous Dynamical Systems, 2013, 33 (6) : 2349-2368. doi: 10.3934/dcds.2013.33.2349 [10] Eduard Feireisl, Josef Málek, Antonín Novotný. Navier's slip and incompressible limits in domains with variable bottoms. Discrete and Continuous Dynamical Systems - S, 2008, 1 (3) : 427-460. doi: 10.3934/dcdss.2008.1.427 [11] Ali Akgül. Analysis and new applications of fractal fractional differential equations with power law kernel. Discrete and Continuous Dynamical Systems - S, 2021, 14 (10) : 3401-3417. doi: 10.3934/dcdss.2020423 [12] Carlos Montalto, Alexandru Tamasan. Stability in conductivity imaging from partial measurements of one interior current. Inverse Problems and Imaging, 2017, 11 (2) : 339-353. doi: 10.3934/ipi.2017016 [13] M. Eller, Roberto Triggiani. Exact/approximate controllability of thermoelastic plates with variable thermal coefficients. Discrete and Continuous Dynamical Systems, 2001, 7 (2) : 283-302. doi: 10.3934/dcds.2001.7.283 [14] Elena Bonetti, Pierluigi Colli, Mauro Fabrizio, Gianni Gilardi. Modelling and long-time behaviour for phase transitions with entropy balance and thermal memory conductivity. Discrete and Continuous Dynamical Systems - B, 2006, 6 (5) : 1001-1026. doi: 10.3934/dcdsb.2006.6.1001 [15] Adriana C. Briozzo, María F. Natale, Domingo A. Tarzia. The Stefan problem with temperature-dependent thermal conductivity and a convective term with a convective condition at the fixed face. Communications on Pure and Applied Analysis, 2010, 9 (5) : 1209-1220. doi: 10.3934/cpaa.2010.9.1209 [16] Anna Marciniak-Czochra, Andro Mikelić. A nonlinear effective slip interface law for transport phenomena between a fracture flow and a porous medium. Discrete and Continuous Dynamical Systems - S, 2014, 7 (5) : 1065-1077. doi: 10.3934/dcdss.2014.7.1065 [17] Jing Li, Panos Stinis. Model reduction for a power grid model. Journal of Computational Dynamics, 2022, 9 (1) : 1-26. doi: 10.3934/jcd.2021019 [18] Yu-Zhu Wang, Weibing Zuo. On the blow-up criterion of smooth solutions for Hall-magnetohydrodynamics system with partial viscosity. Communications on Pure and Applied Analysis, 2014, 13 (3) : 1327-1336. doi: 10.3934/cpaa.2014.13.1327 [19] Md. Golam Hafez, Sayed Allamah Iqbal, Asaduzzaman, Zakia Hammouch. Dynamical behaviors and oblique resonant nonlinear waves with dual-power law nonlinearity and conformable temporal evolution. Discrete and Continuous Dynamical Systems - S, 2021, 14 (7) : 2245-2260. doi: 10.3934/dcdss.2021058 [20] Ebenezer Bonyah, Fatmawati. An analysis of tuberculosis model with exponential decay law operator. Discrete and Continuous Dynamical Systems - S, 2021, 14 (7) : 2101-2117. doi: 10.3934/dcdss.2021057

2021 Impact Factor: 1.865