Abstract
This paper mainly focuses on the impacts of slip conditions on the two-dimensional unsteady mixed convection flow of electrical magnetohydrodynamic nanofluid over a stretching sheet in the presence of thermal radiation, viscous dissipation, and chemical reaction. The synchronized impacts of electric and magnetic fields on the momentum and energy fields using Buongiorno nanofluid model were introduced to enhance thermal conductivity and hence create more pathways to heat transfer performance of nanofluid. The highly nonlinear couple systems of partial differential equations were modeled as a set of nonlinear ordinary differential equations by using suitably defined transformations which are then solved by implicit finite difference scheme known as Keller box method. It was established that velocity has a direct opposite relationship with electric and magnetic fields. The velocity, temperature, and concentration profiles caused intense decay to velocity slip, thermal slip, and solutal slip, with permeability condition. Magnetic field enhances the nanofluid temperature intensely with impermeable medium resulting in a decrease in heat transfer rate from the surface. The heat convection current is strengthened by viscous dissipation and radiative heat transfer prevailing impermeability, which leads to a reduction in heat transfer rate. Comparisons with previously published works seen in the literature were made, and the result was found to be in excellent agreement.
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Abbreviations
- a :
-
Constant
- \(b\) :
-
Stretching sheet constant
- \(B_{0}\) :
-
Magnetic field factor
- \(c_{\text{f}}\) :
-
Skin friction coefficient
- \(D_{\text{B}}\) :
-
Brownian diffusion coefficient
- \(D_{\text{T}}\) :
-
Thermophoresis diffusion coefficient
- \(E_{0}\) :
-
Electric field factor
- \(Ec\) :
-
Eckert number
- \(f^{\prime }\) :
-
Dimensionless velocity
- \(J\) :
-
Joule current
- \(k\) :
-
Thermal conductivity
- \(M\) :
-
Magnetic field parameter
- \(Rd\) :
-
Radiation parameter
- \(Nb\) :
-
Brownian motion parameter
- \(Nt\) :
-
Thermophoresis parameter
- \(Nu\) :
-
Local Nusselt number
- \(p\) :
-
Fluid pressure
- \(Pr\) :
-
Prandtl number
- \(q_{\text{r}}\) :
-
Radiative heat flux
- \(Re\) :
-
Local Reynolds number
- s :
-
Suction/injection
- \(Sc\) :
-
Schmidt number
- \(Sh\) :
-
Local Sherwood number
- \(T\) :
-
Temperature of the fluid
- \(T_{\text{w}}\) :
-
Constant temperature at the wall
- \(T_{\infty }\) :
-
Ambient temperature
- \(u,v\) :
-
Velocity component along x- and y-direction
- \(v_{\text{w}}\) :
-
Wall mass transfer
- \(V\) :
-
Fluid velocity
- \(\alpha\) :
-
Thermal diffusivity
- \(\sigma\) :
-
Electrical conductivity
- \(\sigma *\) :
-
Stefan–Boltzmann constant
- \(\eta\) :
-
Dimensionless similarity variable
- \(\mu\) :
-
Dynamic viscosity of the fluid
- \(\upsilon\) :
-
Kinematic viscosity of the fluid
- \(\left( \rho \right)_{\text{f}}\) :
-
Density of the fluid
- \(\left( {\rho c} \right)_{\text{f}}\) :
-
Heat capacity of the fluid
- \(\left( {\rho c} \right)_{\text{p}}\) :
-
Effective heat capacity of a nanoparticle
- \(\psi\) :
-
Stream function
- \(\sigma\) :
-
Electrical conductivity
- \(\varphi_{\text{w}}\) :
-
Nanoparticle volume fraction at the surface
- \(\varphi_{\infty }\) :
-
Nanoparticle volume fraction at large values of \(y\)
- \(\theta\) :
-
Dimensionless temperature
- \(\phi\) :
-
Dimensionless concentration
- \(\tau\) :
-
Ratio between the effective heat transfer capacity and the heat capacity of the fluid
- \(\lambda\) :
-
Mixed convection parameter
- \(\gamma\) :
-
Chemical reaction
- \(\infty\) :
-
Condition at the free stream
- \({\text{w}}\) :
-
Condition at the surface
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Acknowledgements
The authors would like to acknowledge Ministry of Higher Education and Research Management Centre, UTM, for the financial support through HIR grant vote No. Q.J130000.2409.04G43, COE grant vote No. Q.J130000.2409.03G96, and vote No. 19H00 for this research. Also, Y.S. Daniel thankfully acknowledges financial support from TETFUND through Kaduna State University, Nigeria.
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Daniel, Y.S., Aziz, Z.A., Ismail, Z. et al. Slip role for unsteady MHD mixed convection of nanofluid over stretching sheet with thermal radiation and electric field. Indian J Phys 94, 195–207 (2020). https://doi.org/10.1007/s12648-019-01474-y
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DOI: https://doi.org/10.1007/s12648-019-01474-y