The unified impact of thermal radiation and heat source on unsteady flow of tangent hyperbolic nanofluid through a permeable shrinking sheet

Sakiadis, 1961, Boundary layer behavior on continuous solid surface on a continuous flat surface. I: the boundary layer on a continuous at surface, AIChE J., 7, 26, 10.1002/aic.690070108 Crane, 1970, Flow past a stretching plate, Z. Angew. Math. Phys., 21, 645, 10.1007/BF01587695 Wang, 2002, Flow due to a stretching boundary with partial slip: an exact solution of the Navier Stokes equations, Chem. Eng. Sci., 57, 3745, 10.1016/S0009-2509(02)00267-1 Miklavčič, 2006, Viscous flow due to a shrinking sheet, Q. Appl. Math, 64, 283, 10.1090/S0033-569X-06-01002-5 Fang, 2009, Viscous flow over an unsteady shrinking sheet with mass transfer, Chin. Phys. Lett., 26, 2 Fang, 2010, Thermal boundary layers over a shrinking sheet: an analytical solution, Acta Mech., 209, 325, 10.1007/s00707-009-0183-2 Fang, 2012, Boundary layer flow over a stretching sheet with variable thickness, Appl. Math. Comput., 218, 7241, 10.1016/j.amc.2011.12.094 Bhattacharyya, 2014, Soret and Dufour effects on convective heat and mass transfer in the stagnation point flow towards a shrinking surface, Physica Scripta, 89, 1, 10.1088/0031-8949/89/9/095203 Akbar, 2013, Numerical solutions of magnetohydrodynamic boundary layer flow of tangent hyperbolic fluid towards a stretching sheet, Indian J. Phys., 87, 1121, 10.1007/s12648-013-0339-8 Naseer, 2014, The boundary layer flow of tangent hyperbolic fluid over a vertical exponentially stretching cylinder, Alex. Eng. J., 53, 747, 10.1016/j.aej.2014.05.001 Kumar, 2014, Effect of slip on peristaltic pumping of a hyperbolic tangent fluid in an inclined asymmetric channel, Adv. Appl. Sci. Res., 5, 91 Malik, 2015, MHD flow of tangent hyperbolic fluid over a stretching cylinder:using Keller box method, J. Mag. Mag. Mater., 395, 271, 10.1016/j.jmmm.2015.07.097 Akram, 2015, Effect of partial slip on the peristaltic transport of a hyperbolic tangent fluid model in an asymmetric channel, Computat. Mathem. Mathem. Phys., 55, 1899, 10.1134/S0965542515110147 Rehman, 2017, Mutual effects of thermal radiations and thermal stratification on tangent hyperbolic fluid flow yields by both cylindrical and flat surfaces, Case Stu. Therm. Eng., 10, 244, 10.1016/j.csite.2017.07.003 Wang, 2010, Application of nanofluids: current and future, Adv. Mech. Eng., 10.1155, 519659, 10.1155/2010/519659 Buongiorno, 2006, Convective transport in nanofluids, J. Heat Transf., 128, 240, 10.1115/1.2150834 Khan, 2018, Salient aspect of entropy generation optimization in mixed convection nanomaterial flow, Int. J. Heat Mass Transf., 126, 1337, 10.1016/j.ijheatmasstransfer.2018.05.168 Rehman, 2017, MHD flow of carbon in micropolar nanofluid with convective heat transfer in the rotating frame, J. Mol. Liq., 231, 353, 10.1016/j.molliq.2017.02.022 Khan, 2017, Chemically reactive flow of upper-convective maxwell fluid with Cattaneo-Christor heat flux model, J. Braz. Soc. Mech. Sci. Eng., 39, 4571, 10.1007/s40430-017-0915-5 Riaz, 2021, Thermal analysis of peristaltic flow of nanosized particles within a curved channel with second-order partial slip and porous medium, J. Therm. Anal. Calorim., 143, 1997, 10.1007/s10973-020-09454-9 Riaz, 2022, A numerical analysis for the transport of modified hybrid nanofluids containing various nanoparticles with mixed convection applications in a vertical cylinder, Front. Phys., 10, 1018148, 10.3389/fphy.2022.1018148 Dharmaiah, 2022, Influence of magneto hydrodynamics (MHD) nonlinear radiation on micropolar nanofluid flow over a stretching surface: revised Buongiorno’s nanofluid model, J. Nanofluids, 11, 1009, 10.1166/jon.2022.1890 Jamaludin, 2019, Mixed convection stagnation-point flow of a nanofluid past a permeable stretching/shrinking sheet in the presence of thermal radiation and heat source/sink, Energies, 12, 788, 10.3390/en12050788 Kamal, 2019, Stability analysis of MHD stagnation point flow towards a permeable stretching/shrinking sheet in a nanofluid with chemical reaction effect, Saing Malaysiana, 48, 243, 10.17576/jsm-2019-4801-28 Patel, 2019, MHD flow of micropolar nanofluid over a stretching/shrinking sheet considering radiation, Int. Comm. Heat Mass Transf., 108, 104322, 10.1016/j.icheatmasstransfer.2019.104322 Renuka, 2021, Unsteady separated stagnation point flow of nanofluid past a moving flat surface in the presence of Buongiorno’s model, J. Appl. Comput. Mech., 7, 1283 Mburu, 2021, A numerical study of entropy generation on Oldroyd-B nanofluid flow past a Riga plate, J. Therm. Eng., 7, 845, 10.18186/thermal.930653 Nayak, 2021, Three dimensional rotating flow of an Oldroyd-B nanofluid with relaxation - retardation viscous dissipation, J. Nanofluids, 10, 408, 10.1166/jon.2021.1795 Khan, 2017, Nanomaterial based flow of Prandtl-Eyring (non-Newtonian) fluid using Brownian and thermophoretic diffusion with entropy generation, Comput. Methods Programs Biomed., 180, 105017, 10.1016/j.cmpb.2019.105017 Rashid, 2019, Entropy generation in flow of ferromagnetic liquid with non-linear radiation and slip condition, J. Mol. Liquids, 276, 441, 10.1016/j.molliq.2018.11.148 Gopalkrishna, 2022, Impact of Joule heating and nonlinear thermal radiation on the flow of Casson nanofluid with entropy generation, Int. J. Amb. Energy, 43 Khan, 2017, Boundary layer flow of MHD tangent hyperbolic nanofluid over a stretching sheet: a numerical investigation, Results Phys., 7, 2837, 10.1016/j.rinp.2017.07.061 Ibrahim, 2017, Magnetohydrodynamic (MHD) flow of a tangent hyperbolic fluid with nanoparticle past a stretching sheet with second order slip and convective boundary condition, Results Phys., 7, 3723, 10.1016/j.rinp.2017.09.041 Saidulu, 2019, Radiation effect on MHD flow of a tangent hyperbolic nanofluid over an inclined exponentially stretching sheet, Int. J. Fluid Mech. Res., 46, 277, 10.1615/InterJFluidMechRes.2018025858 Shahzad, 2019, MHD tangent hyperbolic nanofluid with chemical reaction, viscous dissipation and joule heating effects, AIP Adv., 9, 25007, 10.1063/1.5054798 Gharami, 2020, MHD effect on unsteady flow of tangent hyperbolic nano-fluid past a moving cylinder with chemical reaction, SN Appl. Sci., 2, 1256, 10.1007/s42452-020-3048-x Shafiq, 2021, Statistical modeling for bioconvective tangent hyperbolic nanofluid towards stretching surface with zero mass flux condition, Sci. Rep., 11, 13869, 10.1038/s41598-021-93329-y Ahmad, 2022, Thermal and entropy generation analysis of magnetohydrodynamic tangent hyperbolic slip flow towards a stretching sheet, J. Process Mech. Eng., 236 Hassan, 2022, Thermodynamic analysis of a tangent hyperbolic hydromagnetic heat generating fluid in quadratic Boussinesq approximation, J. Compt. Math. Data Sci., 4, 100058, 10.1016/j.jcmds.2022.100058 Khan, 2018, Entropy generation in radiative motion of tangent hyperbolic nanofluid in presence of activation energy and nonlinear mixed convection, Int. J. Heat Mass Transf., 126, 1337 Khan, 2018, Entropy generation optimization and activation energy in nonlinear mixed convection flow of a tangent hyperbolic nanofluid, Eur. J. Phy. Plus, 133, 329, 10.1140/epjp/i2018-12093-y Sultana, 2022, Hydromagnetic slip flow and heat transfer treatment of maxwell fluid with hybrid nanostructure: law Prandtl number, Int. J. Amb. Energy Gope, 2023, Hydro-thermo-fluidic aspects of Oldroyd B fluid with hybrid nanostructure subject to low and moderate Prandtl number, Multidiscip. Model. Mater.Struct., 10.1108/MMMS-09-2022-0200 Akbar, 2012, Peristaltic flow of a tangent hyperbolic fluid in an inclined asymmetric channel with slip and heat transfer, Prog. Comput. Fluid Dyn., 12, 363, 10.1504/PCFD.2012.049100 Nadeem, 2010, Series solution for the peristaltic flow of a tangent hyperbolic fluid in a uniform inclined tube, Zeitschrift fur Naturforschung, 65a, 887, 10.1515/zna-2010-1101 Khan, 2010, Boundary layer flow of a nanofluid past a stretching sheet, Int. J. Heat Mass Transf., 53, 2477, 10.1016/j.ijheatmasstransfer.2010.01.032 Kuznetsov, 2010, Natural convective boundary layer flow of a nanofluid past a vertical plate, Int. J. Therm. Sci., 49, 243, 10.1016/j.ijthermalsci.2009.07.015 Hayat, 2016, Characteristics of magnetic field and melting heat transfer in stagnation-point flow of tangent hyperbolic liquids, J. Magn. Magn. Mater., 405, 97, 10.1016/j.jmmm.2015.10.080 Kebebe, 2020, Heat and mass transfer analysis in unsteady flow of tangent hyperbolic nanofluid over a moving wedge with buoyancy and dissipation effects, Heliyon, 6, e03776, 10.1016/j.heliyon.2020.e03776 Mahdy, 2018, Unsteady MHD boundary layer flow of tangent hyperbolic two phase nanofluid of moving stretched porous wedge, Int. J. Num. Methods Heat Fluid Flow, 10.1108/HFF-12-2017-0499 Vajravelu, 2004, Hydromagnetic flow of a second grade fluid over a stretching sheet, Appl. Math. Comput., 148, 783, 10.1016/S0096-3003(02)00942-6 Cortell, 2007, Viscous flow and heat transfer over a nonlinearly stretching sheet, Appl. Math. Comput., 184, 864, 10.1016/j.amc.2006.06.077 Weidman, 2006, The effect of transpiration on self similar boundary layer flow over moving surfaces, Int. J. Eng. Sci., 44, 730, 10.1016/j.ijengsci.2006.04.005 Merkin, 1986, On dual solutions occurring in mixed convection in a porous medium, J. Eng. Math., 20, 171, 10.1007/BF00042775 Shampine, 2005, Solving hyperbolic PDEs in MATLAB, Appl. Num. Anal. Comput. Math., 2, 346, 10.1002/anac.200510025 Jaluria, 2003 Hayat, 2017, Non-Darcy Forchheimer flow of ferromagnetic second grade fluid, Results Phys., 7, 3419, 10.1016/j.rinp.2017.08.041 Javed, 2018, Axisymmetric flow of Casson fluid by a swirling cylinder, Results Phys., 9, 1250, 10.1016/j.rinp.2018.04.015 Khan, 2018, VIV study of an elastically mounted cylinder having low mass-damping ratio using RANS model, Int. J. Heat Mass Transf., 121, 309, 10.1016/j.ijheatmasstransfer.2017.12.109 Hayat, 2018, Magnetohydrodynamic (MHD) flow of nanofluid with double stratification and slip conditions, Phys. Chem. Liq., 56, 189, 10.1080/00319104.2017.1317778 Rosca, 2015, Unsteady boundary layer flow over a permeable curved stretching/shrinking surface, Eur. J. Mech. - B/Fluids, 51, 61, 10.1016/j.euromechflu.2015.01.001