This paper deals with an unsteady magnetohydrodynamic two-dimensional second-grade fluid flow towards a permeable exponentially stretching surface with heterogeneous–homogeneous reactions. The nonuniform heat source/sink, thermal slip, and thermal radiation effect are also considered to analyze the thermal attributes. The modeled equations of motions are converted into nonlinear ordinary differential equations (ODEs) by suitable transformations. A MATLAB Bvp4c approach is employed for the numerical solution of ODEs. The outcomes of various parameters are scrutinized by graphs. The quantities of interests such as Nusselt number and the skin friction are presented and discussed. The resistance effects take place due to higher estimations of second-grade parameter, as a result, the velocity field declines. The temperature field raises with the increment of radiation parameter. The concentration of nanoparticles decaying when heterogeneous-homogeneous reactions become larger. Moreover, from the tabulated data, it is noticed the growing estimations of K and M boosts the coefficient of skin friction.
ErdoǧanMEImrakCE. Effects of the side walls on the unsteady flow of a second-grade fluid in a duct of uniform cross-section. Int J Non-Linear Mech2004; 39: 1379–1384.
2.
HayatTWangYHutterK. Hall effects on the unsteady hydromagnetic oscillatory flow of a second-grade fluid. Int J Non-Linear Mech2004; 39: 1027–1037.
3.
FetecauCFetecauC. Starting solutions for some unsteady unidirectional flows of a second-grade fluid. Int. J. Eng. Sci2005; 43: 781–789.
4.
HayatTNadeemSAsgharS, et al.Effects of Hall current on unsteady flow of a second-grade fluid in a rotating system. Chem. Eng. Commun2005; 192: 1272–1284.
5.
ErdoǧanMEİmrakCE. On the comparison of two different solutions in the form of series of the governing equation of an unsteady flow of a second-grade fluid. Int J Non-Linear Mech2005; 40: 545–550.
6.
KhanMNadeemSHayatT, et al.Unsteady motions of a generalized second-grade fluid. Math. comput. Model2005; 41: 629–637.
7.
AbbasZHayatTSajidM, et al.Unsteady flow of a second-grade fluid film over an unsteady stretching sheet. Math. comput. Model2008; 48: 518–526.
8.
NazarMFetecauCAwanAU. A note on the unsteady flow of a generalized second-grade fluid through a circular cylinder subject to a time dependent shear stress. Nonlinear Anal. Real World Appl2010; 11: 2207–2214.
9.
AhmadI. On unsteady boundary layer flow of a second grade fluid over a stretching sheet. Adv. Theor. Appl. Mech2013; 6: 95–105.
10.
KhanAANaeemSEllahiR, et al.Dufour and soret effects on darcy-forchheimer flow of second-grade fluid with the variable magnetic field and thermal conductivity. INT J NUMER METHOD H2020; 30: 4331–4347.
11.
KrishnaMVAhamadNAChamkhaAJ. Hall and ion slip impacts on unsteady MHD convective rotating flow of heat generating/absorbing second grade fluid. Alex. Eng. J2021; 60: 845–858.
12.
AliLKhanNSAliR, et al.Novel insights into the computational techniques in unsteady MHD second-grade fluid dynamics with oscillatory boundary conditions. J Heat Transfer2021; 50: 2502–2524.
13.
MerkinJH. A model for isothermal homogeneous-heterogeneous reactions in boundary-layer flow. Math. comput. model1996; 24: 125–136.
14.
BachokNIshakAPopI. On the stagnation-point flow towards a stretching sheet with homogeneous–heterogeneous reactions effects. Commun Nonlinear Sci Numer Simul COMMUN NONLINEAR SCI2011; 16: 4296–4302.
15.
KhanWAPopIM. Effects of homogeneous–heterogeneous reactions on the viscoelastic fluid toward a stretching sheet. J Heat Transfer2012; 134: 064506.
16.
KameswaranPKShawSSibandaPVSN, et al.Homogeneous–heterogeneous reactions in a nanofluid flow due to a porous stretching sheet. Int. J. Heat Mass Transf2013; 57: 465–472.
17.
KhanMIQayyumSHayatT, et al.Entropy optimization in flow of williamson nanofluid in the presence of chemical reaction and joule heating. Int. J. Heat Mass Transf2019; 133: 959–967.
18.
KhanMIKhanMWAAhmadS, et al.Transportation of homogeneous–heterogeneous reactions in flow of sutterby fluid confined between two co-axially rotating disks. Phy. Scr2020; 95: 055211.
19.
GireeshaBJSowmyaGKhanMI, et al.Flow of hybrid nanofluid across a permeable longitudinal moving fin along with thermal radiation and natural convection. Comput. Methods Programs Biomed.2020; 185: 105166.
20.
KhanMIAlzahraniFHobinyA, et al.Modeling of cattaneo-christov double diffusions (CCDD) in williamson nanomaterial slip flow subject to porous medium. J. Mater. Res. Technol2020; 9: 6172–6177.
21.
SaifRSMuhammadTSadiaH, et al.Boundary layer flow due to a nonlinear stretching curved surface with convective boundary condition and homogeneous-heterogeneous reactions. Phys. A: Stat. Mech. Appl2020; 551: 123996.
22.
HashmiMSAl-KhaledKKhanN, et al.Buoyancy driven mixed convection flow of magnetized maxell fluid with homogeneous-heterogeneous reactions with convective boundary conditions. Results Phys2020; 19: 103379.
23.
MishraSRMathurPAliHM. Analysis of homogeneous–heterogeneous reactions in a micropolar nanofluid past a nonlinear stretching surface: semi-analytical approach. J. Therm. Anal. Calorim2021; 144: 1–11.
24.
AbelMSSiddheshwarPGNandeppanavarMM. Heat transfer in a viscoelastic boundary layer flow over a stretching sheet with viscous dissipation and non-uniform heat source. Int. J. Heat Mass Transf2007; 50: 960–966.
25.
AbelMSMaheshaN. Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity, non-uniform heat source and radiation. Appl. Math. Model2008; 32: 1965–1983.
26.
TsaiRHuangKHHuangJS. Flow and heat transfer over an unsteady stretching surface with non-uniform heat source. Int. J. Heat Mass Transf2008; 35: 1340–1343.
27.
AbelMSDattiPSMaheshaN. Flow and heat transfer in a power-law fluid over a stretching sheet with variable thermal conductivity and non-uniform heat source. Int. J. Heat Mass Transf2009; 52: 2902–2913.
28.
PalDMondalH. Effect of variable viscosity on MHD non-darcy mixed convective heat transfer over a stretching sheet embedded in a porous medium with non-uniform heat source/sink. Commun Nonlinear Sci Numer Simul COMMUN NONLINEAR SCI2010; 15: 1553–1564.
29.
NandeppanavarMMAbelMSTawadeJ. Heat transfer in a Walter's Liquid B fluid over an impermeable stretching sheet with non-uniform heat source/sink and elastic deformation. Commun Nonlinear Sci Numer Simul COMMUN NONLINEAR SCI2010; 15: 1791–1802.
30.
KhanMIAlzahraniFHobinyA, et al.Fully developed second order velocity slip darcy-forchheimer flow by a variable thicked surface of disk with entropy generation. Int. Commun. Heat Mass Transf2020; 117: 104778.
31.
KhanMIAlzahraniF. Nonlinear dissipative slip flow of jeffrey nanomaterial towards a curved surface with entropy generation and activation energy. Math Comput Simul MATH COMPUT SIMULAT2021; 185: 47–61.
32.
DadheechAParmarAOlkhaA. Inclined MHD and radiative Maxwell slip fluid flow and heat transfer due to permeable melting surface with a Non-linear heat source. Int. J. Appl. Comput. Math2021; 7: 1–17.
33.
SitholeHMondalHSibandaP. Entropy generation in a second grade magnetohydrodynamic nanofluid flow over a convectively heated stretching sheet with nonlinear thermal radiation and viscous dissipation. Results Phys2018; 9: 1077–1085.
