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**Exploration of heat and mass transfer in the convective slip flow of non-Newtonian Casson fluid.**
*(English)*
Zbl 1445.76006

Casson fluid is a kind of shear-thinning fluid with yield stress. The authors explore plane convective flow of such fluid through a porous plane with heat source. Additionally, chemical reaction takes place while the fluid flows through the membrane. The problem is solved by finite difference method; more precisely, the Crank-Nicolson scheme is applied. The discretization of governing equations leads to a linear equations system that is solved in MATLAB. Then the authors study how the solution depends on such non-dimensional parameters as Grashof, Schmidt, Biot numbers and so on.

Reviewer: Aleksey Syromyasov (Saransk)

### MSC:

76A05 | Non-Newtonian fluids |

76S05 | Flows in porous media; filtration; seepage |

76R10 | Free convection |

76V05 | Reaction effects in flows |

76M20 | Finite difference methods applied to problems in fluid mechanics |

80A19 | Diffusive and convective heat and mass transfer, heat flow |

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\textit{A. Parmar} and \textit{S. Jain}, Int. J. Appl. Comput. Math. 4, No. 2, Paper No. 67, 13 p. (2018; Zbl 1445.76006)

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### References:

[1] | Gireesha, BJ; Mahanthesh, B; Rashidi, MM, MHD boundary layer heat and mass transfer of a chemically reacting Casson fluid over a permeable stretching surface with non-uniform heat source/sink, Int. J. Ind. Math., 7, 247-260, (2015) |

[2] | Raju, CSK; Sandeep, N, Unsteady three-dimensional flow of Casson-carreau fluids past a stretching surface, Alex. Eng. J., 55, 1115-1126, (2016) |

[3] | Raju, CSK; Sandeep, N; Sugunamma, V; Jayachandrababu, M; Ramanareddy, JV, Heat and mass transfer in magnetohydrodynamic Casson fluid over an exponentially permeable stretching surface, Eng. Sci. Technol. Int., 19, 45-52, (2016) |

[4] | Benazir, AJ; Sivaraj, R; Makinde, OD, Unsteady MHD Casson fluid flow over a vertical cone and flat plate with nonuniform heat source/sink, Int. J. Eng. Res. Afr., 21, 69-83, (2015) |

[5] | Khan, SI; Khan, U; Ahmed, N; Jan, SU; Waheed, A; Din, STM, Effects of viscous dissipation and convective boundary conditions on Blasius and sakiadis problems for Casson fluid, Natl. Acad. Sci. Lett., 38, 247-250, (2015) |

[6] | Hussain, T; Shehzad, SA; Alsaedi, A; Hayat, T; Ramzan, M, Flow of Casson nanofluid with viscous dissipation and convective conditions: a mathematical model, J. Cent. South Univ., 22, 1132-1140, (2015) |

[7] | Mahanta, G; Shaw, S, Mixed convection stagnation point flow of Casson fluid with convective boundary conditions, IJIRSET, 4, 2347-6710, (2015) |

[8] | Arthur, EM; Seini, IY; Bortteir, LB, Analysis of Casson fluid flow over a vertical porous surface with chemical reaction in the presence of magnetic field, J. Appl. Math. Phys., 3, 713-723, (2015) |

[9] | Megahed, AM, Effect of slip velocity on Casson thin film flow and heat transfer due to unsteady stretching sheet in presence of variable heat flux and viscous dissipation, Appl. Math. Mech. Engl. Ed., 36, 1273-1284, (2015) · Zbl 1326.76008 |

[10] | Megahed, AM, MHD viscous Casson fluid flow and heat transfer with second-order slip velocity and thermal slip over a permeable stretching sheet in the presence of internal heat generation/absorption and thermal radiation, Eur. Phys. J. Plus, 130, 81, (2015) |

[11] | Kataria, HR; Patel, HR, Radiation and chemical reaction effects on MHD Casson fluid flow past an oscillating vertical plate embedded in porous medium, Alex. Eng. J., 55, 583-595, (2016) |

[12] | Ullah, I; Khan, I; Shafie, S, Hydromagnetic Falkner-Skan flow of Casson fluid past a moving wedge with heat transfer, Alex. Eng. J., 55, 2139-2148, (2016) |

[13] | Animasaun, IL; Sandeep, N; Koriko, OK, Modified kinematic viscosity model for 3D-Casson fluid flow within boundary layer formed on a surface at absolute zero, J. Mol. Liq., 221, 1197-1206, (2016) |

[14] | Animasaun, IL, Casson fluid flow with variable viscosity and thermal conductivity along exponentially stretching sheet embedded in a thermally stratified medium with exponentially heat generation, J. Heat Mass Transf. Res. (JHMTR), 2, 63-78, (2015) |

[15] | Animasaun, IL, Effects of thermophoresis, variable viscosity and thermal conductivity on free convective heat and mass transfer of non-Darcian MHD dissipative Casson fluid flow with suction and nth order of chemical reaction, J. Niger. Math. Soc., 34, 11-31, (2015) · Zbl 1349.76883 |

[16] | Makinde, OD; Animasaun, IL, Bioconvection in MHD nanofluid flow with nonlinear thermal radiation and quartic autocatalysis chemical reaction past an upper surface of a paraboloid of revolution, Int. J. Therm. Sci., 109, 159-171, (2016) |

[17] | Makinde, OD; Animasaun, IL, Thermophoresis and Brownian motion effects on MHD bioconvection of nanofluid with nonlinear thermal radiation and quartic chemical reaction past an upper horizontal surface of a paraboloid of revolution, J. Mol. Liq., 221, 733-743, (2016) |

[18] | Shaw, S; Mahanta, G; Sibanda, P, Non-linear thermal convection in a Casson fluid flow over a horizontal plate with convective boundary condition, Alex. Eng. J., 55, 1295-1304, (2016) |

[19] | Sulochana, C; Ashwinkumar, GP; Sandeep, N, Similarity solution of 3D Casson nanofluid flow over a stretching sheet with convective boundary conditions, J. Niger. Math. Soc., 35, 128-141, (2016) · Zbl 1349.76909 |

[20] | Malik, MY; Khan, M; Salahuddin, T; Khan, I, Variable viscosity and MHD flow in Casson fluid with Cattaneo-Christov heat flux model: using Keller box method, Eng. Sci. Technol. Int. J., 19, 1985-1992, (2016) |

[21] | Bhattacharyya, K; Uddin, MS; Layek, GC, Exact solution for thermal boundary layer in Casson fluid flow over permeable shrinking sheet with variable wall temperature and thermal radiation, Alex. Eng. J., 55, 1703-1712, (2016) |

[22] | Raju, CSK; Sandeepa, N; Saleem, S, Effects of induced magnetic field and homogeneous-heterogeneous reactions on stagnation flow of a Casson fluid, Eng. Sci. Technol. Int. J., 19, 875-887, (2016) |

[23] | Bala, P; Reddy, A, Magneto hydrodynamic flow of a Casson fluid over an exponentially inclined permeable stretching surface with thermal radiation and chemical reaction, Ain Shams Eng. J., 7, 593-602, (2016) |

[24] | Mukhopadhyay, S, Casson fluid flow and heat transfer over a nonlinearly stretching surface, Chin. Phys., 22, 7, (2013) |

[25] | Makinde, OD, Heat and mass transfer by MHD mixed convection stagnation point flow toward a vertical plate embedded in a highly porous medium with radiation and internal heat generation, Meccanica, 47, 1173-1184, (2012) · Zbl 1293.76173 |

[26] | Das, K; Sharma, RP; Sarkar, A, Heat and mass transfer of a second-grade magneto-hydrodynamic fluid over a convectively heated stretching sheet, J. Comput. Des. Eng., 3, 330-336, (2016) |

[27] | Chauhan, DS; Agrawal, R, MHD flow through a porous medium adjacent to a stretching sheet: numerical and an approximate solution, Eur. Phys. J. Plus, 126, 47, (2011) |

[28] | Chauhan, DS; Rastogi, P, Heat transfer and entropy generation in MHD flow through a porous medium past a stretching sheet, Int. J. Energy Technol., 3, 1-13, (2011) |

[29] | Chauhan D.S., Agrawal R.: MHD flow and heat transfer in a channel bounded by a shrinking sheet and a porous medium bed: homotopy analysis method. ISRN Thermodyn. Article ID 291270, 10 (2013). http://dx.doi.org/10.1155/2013/291270. |

[30] | Layek, GC; Mukhopadhyay, S; Samad, SKA, Study of MHD boundary layer flow over a heated stretching sheet with variable viscosity, Int. J. Heat Mass Transf., 48, 4460-4466, (2005) · Zbl 1189.76787 |

[31] | Animasaun, IL; Aluko, OB, Analysis on variable fluid viscosity of non-Darcian flow over a moving vertical plate in a porous medium with suction and viscous dissipation, Int. Organ. Sci. Res. (J. Eng.), 04, 18-32, (2014) |

[32] | Animasaun, IL; Oyem, AO, Effect of variable viscosity, dufour, soret and thermal conductivity on free convective heat and mass transfer of non-Darcian flow past porous flat surface, Am. J. Comput. Math., 4, 357-365, (2014) |

[33] | Jain, S., Kumar, V., Bohra, S.: Entropy generation for MHD radiative compressible fluid flow in a channel partially filled with porous medium. Glob. Stoch. Anal. SI:13-31 (2017). http://www.mukpublications.com/resources/Ch_2_F |

[34] | Jain, S., Choudhary, R.: Soret and Dufour effects on MHD fluid flow due to moving permeable cylinder with radiation. Glob. Stoch. Anal. SI:75-84 (2017). http://www.mukpublications.com/resources/Ch_8_F |

[35] | Jain, S; Choudhary, R, Effects of MHD on boundary layer flow in porous medium due to exponentially shrinking sheet with slip, Procedia Eng., 127, 1203-1210, (2015) |

[36] | Jain, S., Parmar, A.: Comparative study of flow and heat transfer behavior of Newtonian and non-Newtonian fluids over a permeable stretching surface. Glob. Stoch. Anal. SI:41-50 (2017). http://www.mukpublications.com/resources/Ch_4_F |

[37] | Jain, S, Temperature distribution in a viscous fluid flow through a channel bounded by a porous medium and a stretching sheet, J. Rajasthan Acad. Phys. Sci., 4, 477-482, (2006) · Zbl 1155.76402 |

[38] | Parmar, A, MHD Falkner-Skan flow of Casson fluid flow and heat transfer with variable property past a moving wedge, Int. J. Appl. Comput. Math., (2017) |

[39] | Parmar, A, Unsteady convective boundary layer flow for MHD williamson fluid over an inclined porous stretching sheet with non-linear radiation and heat source, Int. J. Appl. Comput. Math., (2017) |

[40] | Jain, S; Bohra, S, Heat and mass transfer over a three-dimensional inclined non-linear stretching sheet with convective boundary conditions, Indian J. Pure Appl. Phys., 55, 847-856, (2017) |

[41] | Gaffar, SA; Prasad, VR; Vijaya, B; Beg, OA, Mixed convection flow of magnetic viscoelastic polymer from a non-isothermal wedge with Biot number effects, Int. J. Eng. Math., 287623, 15, (2015) · Zbl 1381.76401 |

[42] | Ayano, MS; Demeke, NT, Slip effect on MHD chemically reacting convictive boundary layer flow with heat absorption, J. Eng., 2689493, 9, (2016) |

[43] | Ahmed, AA, The influence of slip boundary condition on Casson nanofluid flow over a stretching sheet in the presence of viscous dissipation and chemical reaction, Math. Probl. Eng., 3804751, 12, (2017) |

[44] | Ajayi, TM; Omowaye, AJ; Animasau, IL, Viscous dissipation effects on the motion of Casson fluid over an upper horizontal thermally stratified melting surface of a paraboloid of revolution: boundary layer analysis, J. Appl. Math., 1697135, 13, (2017) |

[45] | Krishnaiah, M; Rajendar, P; Laxmi, TV; Reddy, MCK, Influence of non-uniform heat source/sink on stagnation point flow of a MHD Casson nanofluid flow over an exponentially stretching surface, Glob. J. Pure Appl. Math., 13, 7009-7033, (2017) |

[46] | Seth, GS; Sarkar, S; Chamkha, AJ, Unsteady hydromagnetic flow past a moving vertical plate with convective surface boundary condition, J. Appl. Fluid Mech., 9, 1877-1886, (2016) |

[47] | Pandya, N; Shukla, AK, Effect of radiation and chemical reaction on an unsteady walter’s-B viscoelastic MHD flow past a vertical porous plate, Int. J. Adv. Appl. Math. Mech., 3, 19-26, (2016) · Zbl 1367.76066 |

[48] | Prakash, J; Prasad, PD; Kiran Kumar, RVMSS; Varma, SVK, Diffusion-thermo effects on MHD free convective radiative and chemically reactive boundary layer flow through a porous medium over a vertical plate, JCARME, 5, 111-126, (2016) |

[49] | Reddy, GS; Kumar, SG; Reddy, SK; Prasad, PD; Varma, SVK, MHD free convective radiative and chemically reactive flow over a vertical porous surface in the presence of diffusion-thermo effect, Int. J. Adv. Eng. Res. Sci. (IJAERS), 4, 65-78, (2017) |

[50] | Hayat, T; Mabood, F; Imtiaz, M; Alsaedi, A, Unsteady convective boundary layer flow of Maxwell fluid with nonlinear thermal radiation: a numerical study, IJNSNS, 17, 221-229, (2016) · Zbl 1401.76098 |

[51] | Kim, YJ, Unsteady MHD convective heat transfer past a semi-infinite vertical moving plate with variable suction, Int. J. Eng. Sci., 38, 833-845, (2000) · Zbl 1210.76219 |

[52] | Pal, D; Talukdar, B, Perturbation analysis of unsteady magneto hydro-dynamic convective heat and mass transfer in a boundary layer slip flow past a vertical permeable plate with thermal radiation and chemical reaction, Commun. Nonlinear Sci. Numer. Simul., 15, 1813-1830, (2010) · Zbl 1222.76114 |

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