Abstract
In current communication, we opted four constant (hyperbolic-tangent) liquid model highlighting shear thinning attributes. Consideration of this model together with MHD (magneto-hydrodynamic) is of prodigious importance owing to diverse industrial utilizations. Besides, MHD has several usages in heat exchangers fabrication, space vehicle strength, thermal fortification, polymer technology, power generators, petroleum industry, crude oil purification and fluid dews sprigs. Such implications motivated us to endeavor further towards hydromagnetic characteristics under convective and stratified constraints. Heat sink or source and radiation aspects elaborate heat transportation mechanism. Non-linear PDEs are transfigured to ODEs via implementation of transformation procedure. Homotopy method is chosen for simulations. Attributes of dimensionless factors are highlighted through graphs. We found lower velocity subject to higher Hartman number estimations.
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References
Abbas MA, Bai YQ, Bhatti MM, Rashidi MM (2016) Three dimensional peristaltic flow of hyperbolic tangent fluid in non-uniform channel having flexible walls. Alexandria Eng J 55:653–662
Akbar NS, Nadeem S, Haq RU, Khan ZH (2013) Numerical solutions of magnetohydrodynamic boundary layer flow of tangent hyperbolic fluid towards a stretching sheet. Indian J Physics 87:1121–1124
Aly EH (2016) Existence of the multiple exact solutions for nanofluid flow over a stretching/shrinking sheet embedded in a porous medium at the presence of magnetic field with electrical conductivity and thermal radiation effects. Powder Technol 301:760–781
Anjum A, Mir NA, Farooq M, Ahmad S, Rafiq N (2019) Optimization of entropy generation in thermally stratified polystyrene-water/kerosene nanofluid flow with convective boundary condition. Eur Phys J Plus 134:176
Anjum A, Mir NA, Farooq M, Ijaz Khan M, Hayat T (2018) Influence of thermal stratification and slip conditions on stagnation point flow towards variable thicked Riga plate. Results in Physics 9:1021–1030
Eid MR, Mahny KL (2017) Unsteady MHD heat and mass transfer of a non-Newtonian nanofluid flow of a two-phase model over a permeable stretching wall with heat generation/absorption. Adv Powder Technol 28:3063–3073
Farooq S, Ijaz Khan M, Hayat T, Waqas M, Alsaedi A (2019) Theoretical investigation of peristalsis transport in flow of hyperbolic tangent fluid with slip effects and chemical reaction. J Molecular Liquids 285:314–322
Farooq M, Mansoor Z, Khan MI, Hayat T, Anjum A, Mir NA (2018) Thermally stratified squeezed flow between two vertical Riga plates with no slip conditions. Eur Phys J Plus 133:152
Ghadikolaei SS, Hosseinzadeh Kh, Yassari M, Sadeghi H, Ganji DD (2017) Boundary layer analysis of micropolar dusty fluid with TiO2 nanoparticles in a porous medium under the effect of magnetic field and thermal radiation over a stretching sheet. J Molecular Liquids 244:374–389
Gulzar MM, Waqas M, Asghar Z, Ali S (2019) Rheology of mixed convective Casson nanofluid in a convectively heated stratified medium. Appl Nanosci. https://doi.org/10.1007/s13204-019-01166-3
Hayat T, Hussain Z, Farooq M, Alsaedi A, Obaid M (2014) Thermally stratified stagnation point flow of an Oldroyd-B fluid. Int J Nonlinear Sci Numer Simul 15:77–86
Hayat T, Khan MI, Waqas M, Alsaedi A (2017) On the performance of heat absorption/generation and thermal stratification in mixed convective flow of an Oldroyd-B fluid. Nuclear Eng Technol 49:1645–1653
Hayat T, Qayyum S, Ahmad B, Waqas M (2016) Radiative flow of a tangent hyperbolic fluid with convective conditions and chemical reaction. Eur Phys J Plus 131:422
Hayat T, Waqas M, Alsaedi A, Bashir G, Alzahrani F (2017) Magnetohydrodynamic (MHD) stretched flow of tangent hyperbolic nanoliquid with variable thickness. J Molecular Liquids 229:178–184
Hayat T, Waqas M, Shehzad SA, Alsaedi A (2014) Effects of Joule heating and thermophoresis on stretched flow with convective boundary conditions. Scientia Iranica 21:682–692
Hayat T, Waqas M, Shehzad SA, Alsaedi A (2016) On 2D stratified flow of an Oldroyd-B fluid with chemical reaction: an application of non-Fourier heat flux theory. J Molec Liquids 223:566–571
Hayat T, Waqas M, Shehzad SA, Alsaedi A (2016a) Chemically reactive flow of third grade fluid by an exponentially convected stretching sheet. J Molecular Liquids 223:853–860
Ibrahim W (2015) Nonlinear radiative heat transfer in magnetohydrodynamic (MHD) stagnation point flow of nanofluid past a stretching sheet with convective boundary condition. Propuls Power Res 4:230–239
Ijaz Khan M, Khan MWA, Alsaedi A, Hayat T, Imran Khan M (2020) Entropy generation optimization in flow of non-Newtonian nanomaterial with binary chemical reaction and Arrhenius activation energy, Physica A: Statistical Mechanics and its Applications 538:122806
Javed M, Farooq M, Ahmad S, Anjum A (2018) Melting heat transfer with radiative effects and homogeneous-heterogeneous reaction in thermally stratified stagnation flow embedded in porous medium. J Central South University 25:2701–2711
Kumar G, Manjunatha S, Gireesha BJ, Abbasi FM, Shehzad SA (2019) Numerical illustrations of 3D tangent hyperbolic liquid flow past a bidirectional moving sheet with convective heat transfer at the boundary. Heat Transfer Asian Res. https://doi.org/10.1002/htj.21462
Liao S (2012) Homotopic analysis method in nonlinear differential equations. Springer, Heidelberg
M. Waqas, M. Ijaz Khan, T. Hayat, M. M. Gulzar and A. Alsaedi, Transportation of radiative energy in viscoelastic nanofluid considering buoyancy forces and convective conditions, Chaos, Solitons & Fractals 130 (2020) 109415.
Mansour MA, El-Anssary NF, Aly AM (2008) Effects of chemical reaction and thermal stratification on MHD free convective heat and mass transfer over a vertical stretching surface embedded in a porous media considering Soret and Dufour numbers. Chem Eng J 145:340–345
Nayak MK (2017) MHD 3D flow and heat transfer analysis of nanofluid by shrinking surface inspired by thermal radiation and viscous dissipation. Int J Mechan Sci 124–125:185–193
Omowaye AJ, Fagbade AI, Ajayi AO (2015) Dufour and soret effects on steady MHD convective flow of a fluid in a porous medium with temperature dependent viscosity: Homotopy analysis approach. J Nigerian Mathemat Soc 34:343–360
Qayyum S, Hayat T, Shehzad SA, Alsaedi A (2018) Mixed convection and heat generation/absorption aspects in MHD flow of tangent-hyperbolic nanoliquid with Newtonian heat/mass transfer. Rad Phys Chem 144:396–404
Rehman KU, Khan AA, Malik MY, Ali U, Naseer M (2017) Numerical analysis subject to double stratification and chemically reactive species on Williamson dual convection fluid flow yield by an inclined stretching cylindrical surface. Chinese J Physics 55:1637–1652
Rehman KU, Malik AA, Malik MY, Saba NU (2017) Mutual effects of thermal radiations and thermal stratification on tangent hyperbolic fluid flow yields by both cylindrical and flat surfaces. Case Stud Therm Eng 10:244–254
Rehman KU, Qaiser A, Malik MY, Ali U (2017) Numerical communication for MHD thermally stratified dual convection flow of Casson fluid yields by stretching cylinder. Chinese J Physics 55:1605–1614
Shirkhani R, Hoshyar HA, Rahimipetroudi I, Akhavan H, Ganji DD (2018) Unsteady time-dependent incompressible Newtonian fluid flow between two parallel plates by homotopy analysis method (HAM), homotopy perturbation method (HPM) and collocation method (CM). Propul Power Res 7:247–256
T. Hayat, Salman Ahmad, M. Ijaz Khan, A. Alsaedi and M. Waqas, Investigation of second grade fluid through temperature dependent thermal conductivity and non-Fourier heat flux, Results in Physics 9 (2018) 871-878.
Waqas M (2019) Simulation of revised nanofluid model in the stagnation region of cross fluid by expanding-contracting cylinder. Int J Numer Methods Heat Fluid Flow 30:2193–2205
Waqas M (2020) A mathematical and computational framework for heat transfer analysis of ferromagnetic non-Newtonian liquid subjected to heterogeneous and homogeneous reactions. J Magnet Magnetic Mater 493:165646
Waqas M, Bashir G, Hayat T, Alsaedi A (2019) On non-Fourier flux in nonlinear stretching flow of hyperbolic tangent material. Neural Comp Appl 31:597–605
Waqas M, Farooq M, Khan MI, Alsaedi A, Hayat T, Yasmeen T (2016) Magnetohydrodynamic (MHD) mixed convection flow of micropolar liquid due to nonlinear stretched sheet with convective condition. Int J Heat Mass Transfer 102:766–772
Waqas M, Gulzar MM, Dogonchi AS, Javed MA, Khan WA (2019) Darcy-Forchheimer stratified flow of viscoelastic nanofluid subjected to convective conditions. Appl Nanosci 9:2031–2037
Waqas M, Hayat T, Alsaedi A (2019) A theoretical analysis of SWCNT-MWCNT and H2O nanofluids considering Darcy-Forchheimer relation. Appl Nanosci 9:1183–1191
Waqas M, Hayat T, Shehzad SA, Alsaedi A (2018) Transport of magnetohydrodynamic nanomaterial in a stratified medium considering gyrotactic microorganisms. Physica B 529:33–40
Zehra N, Kousar KU (2019) Rehman (2019) Pressure dependent viscosity subject to Poiseuille and Couette flows via Tangent hyperbolic model. Physica A: Statistical Mechanics and its Applications 527:121332
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Gulzar, M.M., Aslam, A., Waqas, M. et al. A nonlinear mathematical analysis for magneto-hyperbolic-tangent liquid featuring simultaneous aspects of magnetic field, heat source and thermal stratification. Appl Nanosci 10, 4513–4518 (2020). https://doi.org/10.1007/s13204-020-01483-y
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DOI: https://doi.org/10.1007/s13204-020-01483-y