Second-Order Slip Effect on MHD Flow and Radiative Heat Transfer through Porous Medium due to an Exponentially Stretching Sheet
DOI:
https://doi.org/10.48048/tis.2022.5612Keywords:
Exponentially stretching sheet, MHD flow, Second-order slip condition, Heat transferAbstract
The magnetohydrodynamic (MHD) boundary layer flow and radiative heat transfer with second-order slip condition are investigated in this paper. The fluid flow is considered towards an exponentially stretching sheet. The effect of magnetic field and thermal conductivity are taken into account. The obtained nonlinear mathematical expression of the flow are transformed into ordinary differential equations by similarity transformation. The coupled higher order nonlinear ordinary differential equations are solved numerically. The solution for velocity and temperature profile against the first and second-order slip parameters are analyzed. Significant changes are observed in skin friction coefficient and Local Nusselt number due to the magnetic parameter. The characteristics of the flow are discussed through graphs for different pertinent parameters. The results designate that the Local Nusselt number reduces with the increased value of magnetic parameter but opposite behavior is observed for the skin friction coefficient. The rate of heat transfer decreases with higher value of Prandtl number and enhances for Radiation parameter.
HIGHLIGHTS
- Phenomenon of an exponentially stretching sheet with thermal conductivity also incorporate in fluid flow
- Behavior of magnetic parameter (M) and Radiation parameter (R) are analyzed
- Highly nonlinear mathematical equations are solved numerically
- Variation of velocity profile obtained for the first and second order slip parameters
GRAPHICAL ABSTRACT
Downloads
References
LJ Crane. Flow past a stretching plate. ZAAM J. Appl. Math. Phys. 1970; 21, 645-7.
W Ibrahim. Magnetohydrodynamics (MHD) flow of a tangent hyperbolic fluid with nanoparticles past a stretching sheet with second order slip and convective boundary condition. Results Phys. 2017; 7, 3723-31.
M Irfan and MA Farooq. Thermophoretic MHD free stream flow with variable internal heat generation/ absorption and variable liquid characteristics in a permeable medium over a radiative exponentially stretching sheet. J. Mater. Res. Tech. 2020; 9, 4855-66.
A Ishak. MHD boundary layer flow due to an exponentially stretching sheet with radiation effect. Sains Malaysiana 2011; 40, 391-5.
A Majeed, FM Noori, A Zeeshan, T Mahmood, SU Rehman and I Khan. Analysis of activation energy in magnetohydrodynamic flow with chemical reaction and second order momentum slip model. Case Stud. Therm. Eng. 2018; 12, 765-73.
MM Nandeppanavar, K Vajravelu, MS Abel and MN Siddalingapp. Second order slip flow and heat transfer over a stretching sheet with non-linear Navier boundary condition. Int. J. Therm. Sci. 2012; 58, 143-50.
RD Ene and V Marinca. Approximate solutions for steady boundary layer MHD viscous flow and radiative heat transfer over an exponentially porous stretching sheet. Appl. Math. Comput. 2015; 269, 389-401.
R Kumar, S Sood, SA Shehzad and M Sheikholeslami. Numerical modeling of time-dependent bio-convective stagnation flow of a nanofluid in slip regime. Results Phys. 2017; 7, 3325-32.
K Bhattacharyya, S Mukhopadhyay and GC Layek. Slip effects on an unsteady boundary layer stagnation-point flow and heat transfer towards a stretching sheet. Chin. Phys. Lett. 2011; 28, 094702.
K Bhattacharyya and GC Layek. Slip effect on diffusion of chemically reactive species in boundary layer flow over a vertical stretching sheet with suction or blowing. Chem. Eng. Comm. 2011; 198, 1354-65.
Aurangzaib, MS Uddin, K Bhattacharyya and S Shafie. Micropolar fluid flow and heat transfer over an exponentially permeable shrinking sheet. Propul. Power Res. 2016; 5, 310-7.
K Bhattacharyya, MS Uddin and GC Layek. Exact solution for thermal boundary layer in Casson fluid flow over permeable shrinking sheet with variable wall temperature and thermal radiation. Alexandria Eng. J. 2016; 55, 1703-12.
S Mukhopadhyay. Slip effects on MHD boundary layer flow over an exponentially stretching sheet with suction/blowing and thermal radiation. Ain Shams Eng. J. 2013; 4, 485-91.
I Waini, A Ishak and I Pop. Mixed convection flow over an exponentially stretching/shrinking vertical surface in a hybrid nanofluid. Alexandria Eng. J. 2020; 59, 1881-91.
S Nadeem, MN Khan and N Abbas. Transportation of slip effects on nanomaterial micropolar fluid flow over exponentially stretching. Alexandria Eng. J. 2020; 59, 3443-50.
NN Reddy, VS Rao and BR Reddy. Chemical reaction impact on MHD natural convection flow through porous medium past an exponentially stretching sheet in presence of heat source/sink and viscous dissipation. Case Stud. Therm. Eng. 2021; 25, 100879.
F Mabood, A Shafiq, T Hayat and S Abelman. Radiation effects on stagnation point flow with melting heat transfer and second order slip. Results Phys. 2017; 7, 31-42.
MM Nandeppanavar, S Vaishali, MC Kemparaju and N Raveendra. Theoretical analysis of thermal characteristics of Casson nano fluid flow past an exponential stretching sheet in Darcy porous media. Case Stud. Therm. Eng. 2020; 21, 100717.
K Bhattacharyya and GC Layek. Chemically reactive solute distribution in MHD boundary layer flow over a permeable stretching sheet with suction or blowing. Chem. Eng. Comm. 2010; 197, 1527-40.
K Bhattacharyya, S Mukhopadhyay and GC Layek. Unsteady MHD boundary layer flow with diffusion and first-order chemical reaction over a permeable stretching sheet with suction or blowing. Chem. Eng. Comm. 2013; 200, 379-97.
K Bhattacharyya, T Hayat and A Alsaedi. Exact solution for boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet. ZAMM J. Appl. Math. Mech. 2014; 94, 522-8.
IC Mandal and S Mukhopadhyay. Nonlinear convection in micropolar fluid flow past an exponentially stretching sheet in an exponentially moving stream with thermal radiation. Mech. Adv. Mate. Struct. 2019; 26, 2040-6.
F Mabood and K Das. Melting heat transfer on hydromagnetic flow of a nanofluid over a stretching sheet with radiation and second-order slip. Eur. Phys. J. Plus 2016; 131, 3.
S Ghosh and S Mukhopadhyay. Flow and heat transfer of nanofluid over an exponentially shrinking porous sheet with heat and mass fluxes. Propul. Power Res. 2018; 7, 268-75.
SK Adegbie, OK Koriko and IL Animasaun. Melting heat transfer effects on stagnation point flow of micropolar fluid with variable dynamic viscosity and thermal conductivity at constant vortex viscosity. J. Nigerian Math. Soc. 2016; 35, 34-47.
M Sheikholeslami and DD Ganji. Nanofluid convective heat transfer using semi analytical and numerical approaches: A review. J. Taiwan Inst. Chem. Eng. 2016; 65, 43-77.
K Bhattacharyya and GC Layek. Magnetohydrodynamic boundary layer flow of nanofluid over an exponentially stretching permeable sheet. Phys. Res. Int. 2014; 2014, 592536.
I Ullah, K Bhattacharyya, S shafie and I Khan. Unsteady MHD mixed convection slip flow of Casson fluid over nonlinearly stretching sheet embedded in a porous medium with chemical reaction, thermal radiation, heat generation/absorption and convective boundary conditions. Plos One 2016; 11, e0165348.
GS Seth, AK Singha, MS Mandal, A Banerjee and K Bhattacharyya. MHD stagnation-point flow and heat transfer past a non-isothermal shrinking/stretching sheet in porous medium with heat sink or source effect. Int. J. Mech. Sci. 2017; 134, 98-111.
K Bhattacharyya, S Mukhopadhyay and GC Layek. Reactive solute transfer in magnetohydrodynamic boundary layer stagnation-point flow over a stretching sheet with suction/blowing. Chem. Eng. Comm. 2012; 199, 368-83.
B Mandal, K Bhattacharyya, A Banerjee, AK Verma and AK Gautam. MHD mixed convection on an inclined stretching plate in Darcy porous medium with Soret effect and variable surface conditions. J. Nonlinear Eng. 2020; 9, 457-69.
A Zeeshan, N Shehzad and R Ellahi. Analysis of activation energy in Couette-Poiseuille flow of nanofluid in the presence of chemical reaction and convective boundary conditions. Results Phys. 2018; 8, 502-12.
S Xun, J Zhao, L Zheng and X Zhang. Bioconvection in rotating system immersed in nanofluid with temperature dependent viscosity and thermal conductivity. Int. J. Heat Mass Tran. 2017; 111, 1001-6.
CSK Raju, N Sandeep, V Sugunamma, MJ Babu and JVR Reddy. Heat and mass transfer in magnetohydrodynamic Casson fluid over an exponentially permeable stretching surface. Eng. Sci. Tech. Int. J. 2016; 19, 45-52.
I Tlili, MM Bhatti, SM Hamad, AA Barzinjy, M Sheikholeslami and A Shafee. Macroscopic modeling for convection of Hybrid nanofluid with magnetic effects. Stat. Mech. Appl. 2019; 534, 122136.
A Shahzad, R Ali, M Kamran, SUD Khan, SUD Khan and A Farooq. Axisymmetric flow with heat transfer over exponentially stretching sheet: A computational approach. Stat. Mech. Appl. 2020; 554, 124242.
F Mabood, WA Khan and AIM Ismail. MHD flow over exponential radiating stretching sheet using homotopy analysis method. J. King Saud Univ. Eng. Sci. 2017; 29, 68-74.
D Pal and G Mandal. Double diffusive magnetohydrodynamic heat and mass transfer of nanofluids over a nonlinear stretching/shrinking sheet with viscous-Ohmic dissipation and thermal radiation. Propul. Power Res. 2017; 6, 58-69.
MM Bhatti, T Abbas and MM Rashidi. A new numerical simulation of MHD stagnation-point flow over a permeable stretching/shrinking sheet in porous media with heat transfer. Iranian J. Sci. Tech. Trans. A Sci. 2017; 41, 779-85.
NNW Khalili, AA Samson, ASA Aziz and ZM Ali. Chemical reaction and radiation effects on MHD flow past an exponentially stretching sheet with heat sink. J. Phys. Conf. Ser. 2017; 890, 012025.
T Sajid, M Sagheer, S Hissain and M Bilal. Darcy-Forchheimer flow of Maxwell nanofluid flow with nonlinear thermal radiation and activation energy. AIP Adv. 2018; 8, 035102.
RK Kumar, GV Kumar, CSK Raju, SA Shehzad and SVK Varma. Analysis of Arrhenius activation energy in magnetohydrodynamic Carreau fluid flow through improved theory of heat and binary chemical reaction. J. Phys. Comm. 2018; 2, 035004.
G Sandhya, G Sarojamma, PVS Narayana and B Venkateswarlu. Buoyancy forces and activation energy on the MHD radiative flow over an exponential stretching sheet with second-order slip. Heat Tran. 2020; 50, 784-800.
A Ishak. MHD boundary layer flow due to an exponentially stretching sheet with radiation effect. Sains Malaysiana 2011; 40, 391-5.
K Bhattacharyya. Boundary layer stagnation-point flow of Casson fluid and heat transfer towards a shrinking/stretching sheet. Front. Heat Mass Tran. 2013; 4, 023003.
S Mukhopadhyay, K Bhattacharyya and T Hayat. Exact solutions for the flow of Casson fluid over a stretching surface with transpiration and heat transfer effects. Chin. Phys. B 2013; 22, 114701.
Downloads
Published
Issue
Section
License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.



