Non-linear Radiation and Navier-slip effects on UCM Nanofluid ‎Flow past a Stretching Sheet under Lorentzian Force

Document Type : Research Paper


1 Department of Mathematics, SVEC, Tirupati-517502, India

2 Department of Mathematics, SAS, VIT University, Vellore, T.N., India‎

3 Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj, Uttar Pradesh- 211004, India

4 Department of Aeronautics and Astronautics, Air Force Institute of Technology, Wright Patterson Air Force Base, Dayton, Ohio 45433, USA

5 Department of Mathematics, SV University, Tirupati, India


In the present article, the novel contributions are modelling of Upper convected Maxwell nanoflow under Lorentzian influence over a stretching surface and investigating it using bvp4c procedure with MATLAB software. The boundary is set fixed with axial slip. Non-linear energy distribution is incorporated. Similarity variables are utilized to transmute non-linear PDEs of the basic fluid model to coupled system of ODEs. Computed numerical results are better compared with the past literature work to evidence its efficacy. The nanoflow momentum, energy, species diffusion are visualized graphically and analyzing the performance of proficient physical quantities on shear stress, energy dispersion coefficient, mass diffusion coefficient scatter of the system are seen through tables. Presence of magnetic field reduces friction at the wall and acts as a cooling agent.Navier slip increases the friction factor near the wall. Non-linear radiation transfers more heat from the system. Energy transfer coefficient is high in linear thermal rather than non-linear thermal distribution.


Main Subjects

‎[1]‎ Harris, J., Rheology and Non-Newtonian Flow, Longman, London, 28, 1977.‎
‎[2]‎ Mustafa, M., Cattaneo-Christov heat flux model for rotating flow and heat transfer of upper-convected ‎Maxwell fluid, AIP Advances, 5, 2015, 047109.‎ ‎
‎[3]‎ Shah, S., Hussain, S., Sagheer, M., MHD effects and heat transfer for the UCM fluid along with Joule ‎heating and thermal radiation using Cattaneo-Christov heat flux model , AIP Advances, 6, 2016, 085103.‎
‎[4]‎ Mahanthesh, B., Gireesha, B.J., Raju, C.S.K., Cattaneo-Christov heat flux on UCM nanofluid flow across a melting surface with double stratification and exponential space dependent internal heat source, Informatics in Medicine Unlocked, 9, 2017, 26-34.‎
‎[5]‎ Ijaz Khan, M., Tasawar Hayat, M.W., Imran Khan, M., Alsaedi, A., ‎Chemically reactive flow of upper-convected Maxwell fluid with Cattaneo–Christov heat flux model, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39(11), 2017, 4571–4578.‎
‎[6]‎ Mushtaq, A., Mustafa, M., Hayat, T., Alsaedi, A., Buoyancy effects in stagnation-point ‎flow of Maxwell fluid utilizing non-Fourier heat flux approach, PLoS One, 13(5), 2018, e0192685.‎
‎[7]‎ Bhaskar Reddy, N., Poornima, T., Sreenivasulu, P., Influence of Variable Thermal Conductivity on MHD ‎Boundary Layer Slip Flow of Ethylene-Glycol Based Cu Nanofluids over a Stretching Sheet with Convective Boundary ‎Condition, International Journal of Engineering Mathematics, 2014, 905158.‎
‎[8]‎ Das, A.K., Chatterjee, S., Analysis of thermophoresis and Brownian motion effect in heat ‎transfer for nanofluid immersed distribution transformer, Electrical Engineering, 100(3), 2018, 1963–1974. ‎
‎[9]‎ Ghalambaz, M., Mehryan, S.A.M., Zahmatkesh, I., Chamkha, A.J., Free convection heat transfer ‎analysis of a suspension of nano–encapsulated phase change materials (NEPCMs) in an inclined porous cavity, ‎International Journal of Thermal Sciences, 157, 2020, 106503. ‎
‎[10] Ghalambaz, M., Mehryan, S.A.M., Mozaffari, M., Hashem Zadeh, S.M., Saffari ‎Pour, M., Study of thermal and hydrodynamic characteristics of water-nano-encapsulated phase change particles ‎suspension in an annulus of a porous eccentric horizontal cylinder, International Journal of Heat and Mass Transfer, ‎‎156, 2020, 119792.‎ ‎
‎[11]‎ Alfven, H., Existence of electromagnetic-hydrodynamic waves, Nature, 150, 1942, 405.‎
‎[12]‎ Bhaskar Reddy, N., Poornima, T., Sreenivasulu, P., Radiative heat transfer effect on MHD slip flow of ‎Dissipating Nanofluid past an exponential stretching porous sheet, International Journal of Pure and Applied Mathematics,109(9), 2016, 134 – 142.‎
‎[13]‎ Waini, I., Zainal, N.A., Safwa Khashi'ie, N., Aligned Magnetic Field Effects on Flow and ‎Heat Transfer of the Upper-Convected Maxwell Fluid over a Stretching/Shrinking Sheet, MATEC Web of Conference, ‎‎97, 01078, 2017.‎
‎[14]‎ Tamoor, M., MHD convective boundary layer slip flow and heat transfer over nonlinearly stretching ‎cylinder embedded in a thermally stratified medium, Results in Physics, 7, 2017, 4247-4252.‎
‎[15]‎ Nayak, M.K., Shaw, S., Chamkha, A.J., Impact of Variable Magnetic Field and Convective Boundary ‎Condition on a Stretched 3D Radiative Flow of Cu-H2O Nanofluid, AMSE JOURNALS-AMSE IIETA Series: Modelling B, 86(3), 2018, 658-678.‎
‎[16]‎ Takhar, H.S., Chamkha, A.J., Nath, G., Unsteady three-dimensional MHD-boundary-layer flow due to the ‎impulsive motion of a stretching surface, Acta Mechanica, 146, 2001, 59–71.‎
‎[17]‎ Takhar, H.S., Chamkha, A.J., Nath, G., Unsteady flow and heat transfer on a semi-infinite flat plate with an ‎aligned magnetic field, International Journal of Engineering Science, 37(13), 1999, 1723-1736.. ‎
‎[18]‎ Veera Krishna, M., Chamkha, A.J., Hall and ion slip effects on MHD rotating boundary layer flow of nanofluid ‎past an infinite vertical plate embedded in a porous medium, Results in Physics, 15, 2019, 102652.‎‎
‎[19]‎ Thameem Basha, H., Sivaraj, R., Subramanyam Reddy, A., Chamkha, A.J., SWCNH/diamond-ethylene ‎glycol nanofluid flow over a wedge, plate and stagnation point with induced magnetic field and nonlinear radiation – ‎solar energy application, European Physics Journal Special Topics, 228, 2019, 2531–2551.
‎[20]‎ Kumar, B., Seth, G.S., Nandkeolyar, R., Chamkha, A.J., Outlining the impact of induced magnetic field and ‎thermal radiation on magneto-convection flow of dissipative fluid, International Journal of Thermal Sciences, ‎‎146, 2019, 106101.‎
‎[21]‎ Gorla, R., Chamkha, A.J., Natural Convective Boundary Layer Flow Over a Nonisothermal Vertical Plate ‎Embedded in a Porous Medium Saturated With a Nanofluid, Nanoscale and Microscale Thermophysical Engineering, ‎‎15, 2011, 81-94.‎
‎[22]‎ Ganesh Kumar, K., Gnaneswara Reddy, M., Sudharani, M.V.V.N.L., Shehzad, S.A., Chamkha, A.J., Cattaneo–‎Christov heat diffusion phenomenon in Reiner–Philippoff fluid through a transverse magnetic field, Physica A: Statistical Mechanics and its Applications, 541, 2020, 123330.
‎[23]‎ Ali, L., Liu, X., Bagh, A., Finite Element Analysis of Variable Viscosity Impact on MHD Flow and Heat ‎Transfer of Nanofluid Using the Cattaneo–Christov Model, Coatings, 2020, 10, 395.‎‎
‎[24]‎ Benkhedda, M., Boufendi, T., Tayebi, T., Chamkha, A.J., Convective heat transfer performance of hybrid ‎nanofluid in a horizontal pipe considering nanoparticles shapes effect, Journal of Thermal analysis and Calorimetry, 140, 2020, 411–425.
‎[25] Chamkha, A.J., Aly, A.M., Mansour, M.A., Similarity solution for unsteady heat and mass transfer from a ‎stretching surface embedded in a ‎porous medium with suction/injection and chemical reaction effects, Chemical Engineering Communications, 197(6), 2010, 846-858.‎
‎[26] Archana, M., Gireesha, B.J., Porika Venkatesh, Gnaneswara Reddy, M., Influence of Nonlinear Thermal Radiation ‎and Magnetic Field on Three-Dimensional Flow of a Maxwell Nanofluid, Journal of Nanofluids, 6(2), 2017, 1-11.‎
‎[27] Khan, M., Irfan, M., Khan, W.A., Impact of nonlinear thermal radiation and gyrotactic microorganisms on the ‎Magneto-Burgers nanofluid, International Journal of Mechanical Sciences, 130, 2017, 375-382.‎
‎[28] Awais, M., Hayat, T., Muqaddass, N., Ali, A., Awan, S.E., Nanoparticles and nonlinear thermal ‎radiation properties in the rheology of polymeric ‎material, Results in Physics, 8, 2018, 1038-1045.‎
‎[29] Lu, D., Ramzan, M., Noor ul Huda, Chung, J.D., Farooq, U., Nonlinear radiation effect on MHD Carreau ‎nanofluid flow over a radially stretching surface with zero mass flux at the surface, Scientific Reports, 8 , 2018, 3709. ‎
‎[30] Shoaib, Md., Raja, M.A.Z, Sabir, M.T., Islam, S., Shah, Zahir, Kumam, P., Alrabaiah, H., Numerical investigation ‎for rotating flow of MHD hybrid nanofluid with thermal radiation over a stretching sheet, Scientific Reports, 10, 2020, 18533.‎
‎[31] Anwar, T., Kumam, P., Watthayu, W., An exact analysis of unsteady MHD free convection flow of some ‎nanofluids with ramped wall velocity and ramped wall temperature accounting heat radiation and injection/consumption, Scientific Reports, 10, 2020, 17830.