Unsteady Flow of an MHD Tangent Hyperbolic Nanofluid Over a Stretching Sheet


  • Muhammad Asif Jamal Department of Basic Science Usman Institute of technology university, Karachi, Pakistan
  • M. Faizan Department of Basic Science Usman Institute of technology university, Karachi, Pakistan
  • Ahmed Farid Department of Basic Science Usman Institute of technology university, Karachi, Pakistan
  • Fozia Shaikh Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76090, Sindh, Pakistan;
  • Fozia hanif Department of Mathematical Science, Pakistan, 75300




Abstract The recent article addresses the unsteady flow of MHD incompressible tangent hyperbolic fluid with Nanofluid particles in the direction of a stretching surface. Nano-fluid is related to thermo-phoretic and Brownian movement. With proper help through the transformation procedure, the set of non-linear (PDEs) is re-framed into (ODEs). The initiate expressions of momentum, temperature field, and nano-particle concentration are composed into groups of nonlinear equations. That consequential terminology is computed shooting system. The impact of fundamental parameters on the flow field, thermal circulation, and meditation is described. Moreover, the flow field behavior due to the Wall friction, local Nusselt, and Sherwood numbers are examined. This study is significant as this transformation determined the shooting technique’s numerical result and ensured the physical parameters’ behavior graphically. The results show that the velocity field diminishes by escalating the Weissenberg (We) figure and power-law index (n), while thermal and concentration fields remain to detect elevating at similar parameters. Furthermore, the computed result is compared with existing literature and gets accuracy.


Abbas, M. A., Bai, Y., Bhatti, M. and Rashidi, M. [2016], ‘Three dimensional peristaltic flow of hyperbolic tangent fluid in non-uniform channel having flexible walls’, Alexandria Engineering Journal 55(1), 653–662.

Akbar, N. S., Ebaid, A. and Khan, Z. [2015], ‘Numerical analysis of magnetic field effects on eyringpowell fluid flow towards a stretching sheet’, Journal of magnetism and Magnetic Materials 382, 355–358.

Akbar, N. S., Nadeem, S., Haq, R. U. and Khan, Z. [2013], ‘Numerical solutions of magnetohydrodynamic boundary layer flow of tangent hyperbolic fluid towards a stretching sheet’, Indian journal of Physics 87(11), 1121–1124.

Ashorynejad, H., Sheikholeslami, M., Pop, I. and Ganji, D. [2013], ‘Nanofluid flow and heat transfer due to a stretching cylinder in the presence of magnetic field’, Heat and Mass Transfer 49(3), 427–436.

Buongiorno, J. [2006], ‘Convective transport in nanofluids’.

Chakrabarti, A. and Gupta, A. [1979], ‘Hydromagnetic flow and heat transfer over a stretching sheet’, Quarterly of Applied Mathematics 37(1), 73–78.

Chamkha, A., Aly, A. and Mansour, M. [2010], ‘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), 846–858.

Chamkha, A. J., Aly, A. M. and Al-Mudhaf, H. [2011], ‘Laminar mhd mixed convection flow of a nanofluid

along a stretching permeable surface in the presence of heat generation or absorption effects’, International Journal of Microscale and Nanoscale Thermal and Fluid Transport Phenomena 2(1), 51–70.

Chamkha, A. J. and Khaled, A.-R. A. [2000], ‘Similarity solutions for hydromagnetic mixed convection heat and mass transfer for hiemenz flow through porous media’, International Journal of Numerical Methods for Heat & Fluid Flow.

Choi, S. U. and Eastman, J. A. [1995], Enhancing thermal conductivity of fluids with nanoparticles,

Technical report, Argonne National Lab.(ANL), Argonne, IL (United States).

Haq, R. U., Shahzad, F. and Al-Mdallal, Q. M. [2017], ‘Mhd pulsatile flow of engine oil based carbon nanotubes between two concentric cylinders’, Results in Physics 7, 57–68.

Hayat, T., Khan, M. I., Waqas, M. and Alsaedi, A. [2017], ‘Mathematical modeling of non-newtonian fluid with chemical aspects: a new formulation and results by numerical technique’, Colloids and Surfaces A: Physicochemical and Engineering Aspects 518, 263–272.

Hayat, T., Qayyum, S., Alsaedi, A. and Ahmad, B. [2017], ‘Magnetohydrodynamic (mhd) nonlinear convective flow of walters-b nanofluid over a nonlinear stretching sheet with variable thickness’, International Journal of Heat and Mass Transfer 110, 506–514.

Khan, M. I., Waqas, M., Hayat, T. and Alsaedi, A. [2017], ‘A comparative study of casson fluid with homogeneous-heterogeneous reactions’, Journal of colloid and interface science 498, 85–90.

Khan, M., Malik, M., Salahuddin, T. and Khan, I. [2016], ‘Heat transfer squeezed flow of carreau fluid over a sensor surface with variable thermal conductivity: a numerical study’, Results in physics 6, 940– 945.

Khan, M., Manzur, M. and ur Rahman, M. [2017], ‘On axisymmetric flow and heat transfer of cross fluid over a radially stretching sheet’, Results in physics 7, 3767–3772.

Khedr, M.-E., Chamkha, A. and Bayomi, M. [2009], ‘Mhd flow of a micropolar fluid past a stretched permeable surface with heat generation or absorption’, Nonlinear Analysis: Modelling and Control

(1), 27–40.

Kumaran, V., Banerjee, A., Kumar, A. V. and Vajravelu, K. [2009], ‘Mhd flow past a stretching permeable sheet’, Applied mathematics and computation 210(1), 26–32.

Lee, S., Choi, S.-S., Li, S., and Eastman, J. [1999], ‘Measuring thermal conductivity of fluids containing oxide nanoparticles’.

Madhu, M., Kishan, N. and Chamkha, A. J. [2017], ‘Unsteady flow of a maxwell nanofluid over a stretching surface in the presence of magnetohydrodynamic and thermal radiation effects’, Propulsion and

Power research 6(1), 31–40.

Magyari, E. and Chamkha, A. [2008], ‘Exact analytical results for the thermosolutal mhd marangoni boundary layers’, International Journal of Thermal Sciences 47(7), 848–857.

Malik, M., Jamil, H., Salahuddin, T., Bilal, S., Rehman, K. and Mustafa, Z. [2016], ‘Mixed convection dissipative viscous fluid flow over a rotating cone by way of variable viscosity and thermal conductivity’, Results in physics 6, 1126–1135.

Malik, M., Khan, M., Salahuddin, T. and Khan, I. [2016], ‘Variable viscosity and mhd flow in casson fluid with cattaneo–christov heat flux model: Using keller box method’, Engineering Science and Technology, an International Journal 19(4), 1985–1992.

Malik, M., Salahuddin, T., Hussain, A. and Bilal, S. [2015], ‘Mhd flow of tangent hyperbolic fluid over a stretching cylinder: using keller box method’, Journal of magnetism and magnetic materials 395, 271–276.

Masuda, H., Ebata, A. and Teramae, K. [1993], ‘Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles. dispersion of al2o3, sio2 and tio2 ultra-fine particles’.

Memon, K., Siddiqui, A., Shah, S. F. and Ahmad, S. [2014], ‘Unsteady drainage of the power law fluid model down a vertical cylinder’, J. Appl. Environ. Biol. Sci 4(9S), 309–319.

Mukhopadhyay, S., Ranjan De, P. and Layek, G. [2013], ‘Heat transfer characteristics for the maxwell fluid flow past an unsteady stretching permeable surface embedded in a porous medium with thermal radiation’, Journal of Applied Mechanics and Technical Physics 54(3), 385–396.

Nadeem, S. and Maraj, E. [2013], ‘The mathematical analysis for peristaltic flow of hyperbolic tangent fluid in a curved channel’, Communications in theoretical physics 59(6), 729.

Pavlov, K. [1974], ‘Magnetohydrodynamic flow of an incompressible viscous fluid caused by deformation of a plane surface’, Magnitnaya Gidrodinamika 4(1), 146–147.

Pryazhnikov, M., Minakov, A., Rudyak, V. Y. and Guzei, D. [2017], ‘Thermal conductivity measurements of nanofluids’, International Journal of Heat and Mass Transfer 104, 1275–1282.

Rahman, M., Al-Lawatia, M., Eltayeb, I. and Al-Salti, N. [2012], ‘Hydromagnetic slip flow of water based nanofluids past a wedge with convective surface in the presence of heat generation (or) absorption’, International Journal of Thermal Sciences 57, 172–182.

Rassoulinejad-Mousavi, S., Abbasbandy, S. and Alsulami, H. [2014], ‘Analytical flow study of a conducting maxwell fluid through a porous saturated channel at various wall boundary conditions’, The

European Physical Journal Plus 129(8), 1–10.

Salahuddin, T., Khan, I., Malik, M., Khan, M., Hussain, A. and Awais, M. [2017], ‘Internal friction between fluid particles of mhd tangent hyperbolic fluid with heat generation: Using coefficients improved by cash and karp’, The European Physical Journal Plus 132(5), 1–10.

Salahuddin, T., Malik, M., Hussain, A., Awais, M., Khan, I. and Khan, M. [2017], ‘Analysis of tangent hyperbolic nanofluid impinging on a stretching cylinder near the stagnation point’, Results in Physics

, 426–434.

Shah, S. M., Memon, K., Shah, S. F., Sheikh, A. H., Ghoto, A. A. and Siddiqui, A. [2019], ‘Exact solution for ptt fluid on a vertical moving belt for lift with slip condition’, Indian Journal of Science and Technology 12, 30.

Shahzad, A. and Ali, R. [2012], ‘Approximate analytic solution for magneto-hydrodynamic flow of a non-newtonian fluid over a vertical stretching sheet’, Can J Appl Sci 2(1), 202–215.

Shahzad, F., Haq, R. U. and Al-Mdallal, Q. M. [2016], ‘Water driven cu nanoparticles between two concentric ducts with oscillatory pressure gradient’, Journal of Molecular Liquids 224, 322–332.

Suresh, S., Venkitaraj, K., Selvakumar, P. and Chandrasekar, M. [2011], ‘Synthesis of al2o3–cu/water hybrid nanofluids using two step method and its thermo physical properties’, Colloids and Surfaces A: Physicochemical and Engineering Aspects 388(1-3), 41–48.

Tiwari, R. K. and Das, M. K. [2007], ‘Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids’, International Journal of heat and Mass transfer 50(9-10), 2002–2018.

Trisaksri, V. and Wongwises, S. [2007], ‘Critical review of heat transfer characteristics of nanofluids’, Renewable and sustainable energy reviews 11(3), 512–523.

Ul Haq, R., Rajotia, D. and Noor, N. F. M. [2016], ‘Thermophysical effects of water driven copper nanoparticles on mhd axisymmetric permeable shrinking sheet: dual-nature study’, The European

Physical Journal E 39(3), 1–12.

Ullah, Z. and Zaman, G. [2017], ‘Lie group analysis of magnetohydrodynamic tangent hyperbolic fluid flow towards a stretching sheet with slip conditions’, Heliyon 3(11), e00443.

Waqas, M., Hayat, T., Farooq, M., Shehzad, S. and Alsaedi, A. [2016], ‘Cattaneo-christov heat flux

model for flow of variable thermal conductivity generalized burgers fluid’, Journal of Molecular Liquids 220, 642–648.

Xuan, Y. and Roetzel, W. [2000], ‘Conceptions for heat transfer correlation of nanofluids’, International Journal of heat and Mass transfer 43(19), 3701–3707.

Zaib, A., Bhattacharyya, K., Uddin, M., Shafie, S. et al. [2016], ‘Dual solutions of non-newtonian casson fluid flow and heat transfer over an exponentially permeable shrinking sheet with viscous dissipation’, Modelling and simulation in engineering 2016.




How to Cite

Jamal, M. A., Faizan, M., Farid, A., Shaikh, F., & hanif, F. (2022). Unsteady Flow of an MHD Tangent Hyperbolic Nanofluid Over a Stretching Sheet. VFAST Transactions on Mathematics, 10(1), 40–56. https://doi.org/10.21015/vtm.v10i1.1215