A significant study on flow analysis of viscoelastic fluid with variable thermo-physical properties. (English) Zbl 1540.76007
Summary: Due to large amount of engineering applications, the flow of viscoelastic fluid due to stretched surfaces has turned out to be very famous among the challenging research field of fluid mechanics. Therefore, the main idea of this paper is to classify the instantaneous significances of thermo-physical parameters on the flow of an electrically conducting second grade fluid flow caused by stretched needle. Flow is generated due to a needle which is stretched vertically. The dimensionless transformations are used to change the leading partial differential equations including energy, mass and momentum conservation into ordinary differential form. The newly formed equations along with boundary constraints are solved by employing built in Bvp4c Matlab package. Moreover, the solutions for dimensionless concentration, fluid velocity and energy distributions are analyzed graphically. The thermo-physical embedded parameters controlling the mass, flow and heat transfer characteristics are the magnetic parameter, variable thickness parameter, second grade fluid parameter, small parameter, variable diffusivity parameter and Prandtl number.
Keywords:
moving thin needle; second grade fluid; mixed convection flow; variable viscosity; variable thermal conductivity; variable diffusion coefficient; Bvp4cReferences:
| [1] | Ahmad, N., Visco-elastic boundary layer flow past a stretching plate and heat transfer with variable thermal conductivity, World J. Mech., 1, 15-20 (2011) |
| [2] | Ahmad, Rida; Mustaf, M.; Hina, S., Buongiorno’s model for fluid flow around a moving thin needle in a flowing nano fluid: A numerical study, Chinese J. Phys., 55, 1264-1274 (2017) |
| [3] | Ali, F.; Imtiaz, A.; Khan, W. A.; Khan, I.; Badruddin, I. A., Effects of MHD and porosity on entropy generation in two incompressible Newtonian fluids over a thin needle in a parallel free stream, Sci. Rep., 10, Article 22305 pp. (2020) |
| [4] | F. Ali, M. Saqib, I. Khan, N.A. Sheikh, Application of Caputo-Fabrizio derivatives to MHD free convection flow of generalized Walters’-B fluid model, Eur. Phys. J. Plus 131 (10) 377. |
| [5] | F. Ali, N.A. Sheikh, I. Khan, M. Saqib, Magnetic field effect on blood flow of Casson fluid in axisymmetric cylindrical tube: A fractional model, J. Magn. Magn. Mater. 423 327-336. |
| [6] | F. Ali, N.A. Sheikh, I. Khan, M. Saqib, Impact of Lorentz forces on \(\text{Fe}_3 \text{O}_4\)-water ferrofluid entropy and energy treatment within a permeable semi annulus, Journal of cleaner production, 221 885-898. |
| [7] | Anand, V. W.J.; Ganesh, S.; Ismail, Md.; Kirubhashankar, C. K., Unsteady MHD dusty fluid flow of an exponentially stretching sheat with heat source through porous medium, Appl. Math. Sci., 9, 2083-2090 (2015) |
| [8] | Anjali Devi, S. P.; Prakash, M., Temperature dependent viscosity and thermal conductivity effects on hydromagnetic flow over a slendering stretching sheet, J. Nigerian Math. Soc., 34, 318-330 (2015) · Zbl 1349.76889 |
| [9] | Asghar, S.; Hayat, T.; Ariel, P. D., Unsteady couette flows in second grade fluid with variable material properties, J. Nonlinear Sci. Numer. Simul., 14, 154-159 (2009) · Zbl 1221.76013 |
| [10] | Babu, M. J.; Sandeep, N.; Ali, N. E.; Nuhait, Abdullah O., Magnetohydrodynamic dissipative flow across the slandering stretching sheet with temperature dependent variable viscosity, Results Phys., 7, 1801-1807 (2017) |
| [11] | Bandelli, R.; Rajagopal, K. R., Start-up flows of second grade fluids in domains with one finite dimension, Int. J. Non-Linear Mech., 30, 817-839 (1995) · Zbl 0866.76004 |
| [12] | bandelli, R.; Rajagopal, K. R.; Galdi, G. P., Some unsteady motion of fluid of second grade, Arch. Mech., 47, 661-676 (1995) · Zbl 0835.76002 |
| [13] | Bilal, M.; Sagheer, M.; Hussain, S., Numerical study of magnetohydrodynamics and thermal radiation on williamson nanofluid flow over a stretching cylinder with variable thermal conductivity, Alex. Eng. J., 57, 3281-3289 (2018) |
| [14] | Dadapat, B. S.; Gupta, A. S., Flow and heat transfer in the viscoelastic fluid over a stretching sheet, Int. J. Non-Linear Mech., 24, 215-219 (1989) · Zbl 0693.76015 |
| [15] | Elbashbeshy, E. M.A., Free convection flow with variable viscosity and thermal diffusivity along the vertical plate in the presence of the magnetic field, Internat. J. Engrg. Sci., 38, 207-213 (2000) · Zbl 1210.76214 |
| [16] | Ellahi, R.; Riaz, Arshad, Analytical solutions for MHD flow in a third-grade fluid with variable viscosity, Math. Comput. Modelling, 52, 1783-1793 (2010) · Zbl 1205.76296 |
| [17] | Fectecau, C., Starting solution for the motion of second grade fluid due to longitudinal and torsional oscillation of a circular cylinder, Internat. J. Engrg. Sci., 44, 788-796 (2006) · Zbl 1213.76014 |
| [18] | Ghadikolaeia, S. S.; Hosseinzadehb, Kh.; Yassaria, M.; Sadeghia, H.; Ganjib, D. D., Analytical and numerical solution of non-Newtonian second-grade fluid flow on a stretching sheet, Therm. Sci. Eng. Progress, 5, 309-316 (2018) |
| [19] | Gitima, P., Effect of variable viscosity and thermal conductivity of micropolar fluid in a porous channel in presence of magnetic field, Int. J. Basic Sci. Soc. Sci., 1, 69-77 (2012) |
| [20] | Grosan, T.; Pop, I., Forced convection boundary layer flow past non isothermal thin needles in nanofluids, J. Heat Transfer, 133 (2011) · Zbl 1219.80044 |
| [21] | Gul, T.; Khan, M. A.; Noman, W.; Khan, I.; Alkanhal, T. A.; Tlili, I., Fractional order forced convection carbon nanotube nanofluid flow passing over a thin needle, Symmetry, 11, 312 (2019) · Zbl 1423.82049 |
| [22] | A. Gul, I. Khan, S. Shafie, A. Khalid, A. Khan, Heat transfer in MHD mixed convection flow of a ferrofluid along a vertical channel, PloS One 10 (11) e0141213. |
| [23] | Hakeem, A. E.; El Misiery, A. E.M.; El Shamy, I. I., Effect of endoscope and variable viscosity on peristaltic motion, Appl. Math. Comput., 158, 497-511 (2004) · Zbl 1098.76080 |
| [24] | Hakeem, A. K.A.; Ganesh, N.; Ganga, B., Effect of heat radiation in a Walter’sB fluid over a stretching sheet with non-uniform heat source/sink and elastic deformation, J. King Saud Univ., Eng. Sci., 26, 168-175 (2014) · Zbl 1336.35292 |
| [25] | Hayat, T.; Anwar, M. S.; Farooq, M.; Alsaedi, A., Mixed convection flow of viscoelastic fluid by a stretching cylinder with heat transfer, PLoS One, 10 (2015) |
| [26] | Hayat, T.; Khan, M.; Ayub, M., Some analytical solutions for second grade fluid flows for cylindrical geometries, Math. Comput. Modelling, 43, 16-29 (2006) · Zbl 1090.76006 |
| [27] | Hossain, M. A.; Khanafer, K.; Vafai, K., The effect of radiation on free convection flow of fluid with variable viscosity from a porous verticleplate, Int. J. Therm. Sci., 40, 115-124 (2001) |
| [28] | A. Hussain, M.Z. Salleh, I. Khan, S. Shafie, Convection heat transfer in micropolar nanofluids with oxide nanoparticles in water, kerosene and engine oil, J. Mol. Liq. 229, 482-488. |
| [29] | Ismail, Z.; Hussain, A.; Khan, I.; Hussain, A. G.; Shafie, S., Unsteady boundary layer MHD free convection flow in a porous medium with constant mass diffusion and Newtonian heating, Eur. Phys. J. Plus, 129, 46 (2014) |
| [30] | Jamil, M.; Fetecau, C., Some exact solution of rotating flows of a generalized Burger fluid in cylindrical domain, J. Non-Newton. Fluid Mech., 165, 1700-1712 (2010) · Zbl 1274.76365 |
| [31] | A. Khalid, I. Khan, S. Shafie, Exact solutions for free convection flow of nanofluids with ramped wall temperature, Eur. Phys. J. Plus 130 (4) 57. · Zbl 1356.35179 |
| [32] | Khan, Y.; Wu, Q.; Faraz, N.; Yildirim, A., The effects of variable viscosity and thermal conductivity on a thin film flow over a shrinking/stretching sheet, Comput. Math. Appl., 61, 3391-3399 (2011) · Zbl 1222.76014 |
| [33] | U. Khan, A. Zaib, I. Khan, D. Baleanue, E.S.M. Sherif, Comparative investigation on MHD nonlinear radiative flow through a moving thin needle comprising two hybridized AA7075 and AA7072 alloys nanomaterials through binary chemical reaction with activation energy. |
| [34] | U. Khan, A. Zaib, I. Khan, K.S. Nisar, Dual solutions of nanomaterial flow comprising titanium alloy \(( \text{Ti}_6 \text{Al}_4 \text{V} )\) suspended in Williamson fluid through a thin moving needle with nonlinear thermal radiation: Stability scrutinization, Sci. Rep. |
| [35] | K.G. Kumar, Scrutinization of 3D flow and nonlinear radiative heat transfer of non-Newtonian nanoparticles over an exponentially sheet, Internat. J. Numer. Methods Heat Fluid Flow. |
| [36] | K.G. Kumar, Exploration of flow and heat transfer of non-Newtonian nanofluid over a stretching sheet by considering slip factor, Internat. J. Numer. Methods Heat Fluid Flow 0961-5539. |
| [37] | Kumar, K. G.; Gireesha, B. J.; Manjunatha, S.; Rudraswamy, N. G., Effect of nonlinear thermal radiation on double-diffusive mixed convection boundary layer flow of viscoelastic nanofluid over a stretching sheet, Mater. Eng., 12-18 (2017) |
| [38] | Kumar, K. G.; Hani, E. H.B.; Assad, M. E.H.; Gorji, M. R.; Nadeem, S., A novel approach for investigation of heat transfer enhancement with ferromagnetic hybrid nanofluid by considering solar radiation, Microsyst. Technol., 27, 97-104 (2021) |
| [39] | Kumari, M.; Nath, G., Mixed convection boundary layer flow over a thin vertical cylinder with localized injection/suction and cooling/heating, Int. J. Heat Mass Transfer, 47, 969-976 (2004) · Zbl 1058.76061 |
| [40] | Lee, L. L., Boundary layer over a thin needle, Phys. Fluids, 10, 820-822 (1967) · Zbl 0158.23204 |
| [41] | Lin, Y.; Zheng, L.; Ma, L., Heat transfer characteristics of thin power-law liquid films over horizontal stretching sheet with internal heating and variable thermal coefficient, Appl. Math. Mech. Engl. Ed., 37, 1587-1596 (2016) · Zbl 1374.76013 |
| [42] | Magnetohydrodynamic flow and heat transfer of a hybrid nanofluid over a rotating disk by considering Arrhenius energy. · Zbl 1521.76913 |
| [43] | Malik, M. Y.; Jamil, Hamayoun; Salahuddin, T.; Bilal, S.; Rahman, K. U.; Mustafa, Zubair, Mixed convection viscous dissipative fluid over a rotating cone by way of variable viscosity and thermal conductivity, Results Phys., 6, 1126-1135 (2016) |
| [44] | Mukhopadhyay, S.; Mandal, I. C., Boundary layer flow and heat transfer of a Casson fluid past a symmetric porous wedge with surface heat flux, J. Heat Transfer Asian Res., 42, 665-675 (2013) |
| [45] | Narain, J. P.; Uberoi, M. S., Forced heat transfer over a thin needles, J. Heat Transfer, 94, 240-242 (1972) |
| [46] | Pantokratoras, A., Results on the variable viscosity on flow and heat transfer to a continuous moving plate, Internat. J. Engrg. Sci., 42, 1891-1896 (2004) · Zbl 1211.76043 |
| [47] | Pantokratoras, A., Study of MHD boundary layer flow over a heated stretching sheet with variable viscosity: A numerical reinvestigation, Int. J. Heat Mass Transfer, 51, 104-110 (2008) · Zbl 1140.80354 |
| [48] | Qureshi, Imran Haider; Nawaz, M.; Rana, Shafia; Zubair, T., Galerkin finite element study on the effects of variable thermal conductivity and variable mass diffusion conductance on heat and mass transfer, Commun. Theor. Phys., 70, 49-59 (2018) |
| [49] | Raju, S. S.; Kumar, K. G.; Gorji, M. R.; Khan, I., Darcy-Forchheimer flow and heat transfer augmentation of a viscoelastic fluid over an incessant moving needle in the presence of viscous dissipation, Microsyst. Technol., 25, 3399-3405 (2019) |
| [50] | Rashidi, M. M.; Hayat, T.; Keimanesh, M.; Yousefian, H., A study on heat transfer in a second grade fluid through a porous medium with the modified differential transform, J. Heat Transfer Asian Res., 42, 31-45 (2013) |
| [51] | Reddy, M. G., Unsteady radiative-convective boundary layer flow of a Casson fluid with variable thermal conductivity, J. Eng. Sci. Thermophy., 88, 240-251 (2015) |
| [52] | Sakiadis, B. C., Boundary layer behavior on continuous solid flat surfaces, AIChE J., 7, 26-28 (1961) |
| [53] | Salahuddin, T.; Arshad, M.; Siddique, N.; Alqahtani, A. S.; Malik, M. Y., Thermophysical properties and internal energy change in Casson fluid flow along with activation energy, Ain Shams Eng. J. (2020) |
| [54] | Salahuddin, T.; Siddique, N.; Arshad, M., Insight into the dynamics of the non-Newtonian Casson fluid on a horizontal object with variable thickness, Math. Comput. Simulation, 177, 211-231 (2020) · Zbl 1510.76016 |
| [55] | Salahuddin, T.; Siddique, N.; Arshad, M., Insight into the dynamics of the non-Newtonian Casson fluid on a horizontal object with variable thickness, Math. Comput. Simulation, 177, 211-231 (2020) · Zbl 1510.76016 |
| [56] | Seddeek, M. A., The effect of variable viscosity on hydromagnetic flow and heat transfer past a continuously moving porous boundary with radiation, Int. Commun. Heat Mass Transfer, 27, 1037-1046 (2000) |
| [57] | Seshadri, R.; Munjam, S. R., The study of heat and mass transfer in a viscoelastic fluid due to a continuous stretching surface using homotopy analysis method, J. Appl. Anal. Comput., 4, 389-403 (2014) · Zbl 1306.76035 |
| [58] | N.A. Shah, I. Khan, Heat transfer analysis in a second grade fluid over and oscillating vertical plate using fractional Caputo-Fabrizio derivatives, Eur. Phys. J. C 76 (7) 362. |
| [59] | N.A. Sheikh, F. Ali, M. Saqib, I. Khan, S.A.A. Jan, A.S. Alshomrani, M.S. Alghamdi, Comparison and analysis of the Atangana-Baleanu and Caputo-Fabrizio fractional derivatives for generalized Casson fluid model with heat generation and chemical reaction, Results Phys. 7 789-800. |
| [60] | Soid, Siti Khuzaimah; Ishak, Anuar; Pop, Ioan, Boundary layer past continuously moving thinneedle in a nanofluid, Appl. Therm. Eng., 14, 58-64 (2017) |
| [61] | Tanveer, Anum; Salahuddin, T.; Khan, Mumtaz; Alshomranid, Ali Saleh; Malik, M. Y., The assessment of nanofluid in a Von Karman flow with temperature relied viscosity, Results Phys., 9, 916-922 (2018) |
| [62] | Yurusoy, M.; Pakdermirli, M., Approximate analytic solution of third grade fluid in a pipe, Int. J. Non-Linear Mech., 37, 187-195 (2002) · Zbl 1116.76314 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
