Optimization of Heat Transfer Properties of Nanofluid Flow Over a Shrinking Surface Through Mathematical Modeling

A. Bhandari 1  and R.K. Pavan Kumar Pannala 1
  • 1 University of Petroleum and Energy Studies (UPES), Department of Mathematics, School of Engineering, Dehradun, India

Abstract

In the current study, a three dimensional incompressible magnetohydrodynamic (MHD) nanofluid flow over a shrinking surface with associated thermal buoyancy, thermal radiation, and heating absorption effects, as well as viscous dissipation have been investigated. The model has been represented in a set of partial differential equations and is transformed using suitable similarity transformations which are then solved by using the finite element method through COMSOL. The results for velocity and temperature profiles are provided for various values of the shrinking parameter, Biot’s number, heat generation/absorption parameter, thermal Grashof number, nanoparticle volume fraction, permeability parameter, magnetic parameter and radiation parameter.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] Mahalakshmi, Thangavelu, Nagarajan Nithyadevi, Hakan F. Oztop and Nidal Abu-Hamdeh (2018): MHD mixed convective heat transfer in a lid-driven enclosure filled with Ag-water nanofluid with center heater. − International Journal of Mechanical Sciences, vol.142, pp.407-419.

  • [2] Nayak M.K. (2017): MHD 3D flow and heat transfer analysis of nanofluid by shrinking surface inspired by thermal radiation and viscous dissipation. − International Journal of Mechanical Sciences, vol.124, pp.185-193.

  • [3] Hayat, Tasawar, Maria Imtiaz and Ahmed Alsaedi (2015): MHD 3D flow of nanofluid in presence of convective conditions. − Journal of Molecular Liquids, vol.212, pp.203-208.

  • [4] Elazem, Nader Y. Abd and Abdelhalim Ebaid (2017): Effects of partial slip boundary condition and radiation on the heat and mass transfer of MHD-nanofluid flow. − Indian Journal of Physics, 91.12, pp.1599-1608.

  • [5] Bhargava, Rama and Mania Goyal (2015): An efficient hybrid approach for simulating MHD nanofluid flow over a permeable stretching sheet. − Mathematical Analysis and its Applications, Springer, New Delhi, pp.701-714.

  • [6] Tamim, Hossein, Saeed Dinarvand, Reza Hosseini and Pop I. (2014): MHD mixed convection stagnation-point flow of a nanofluid over a vertical permeable surface: a comprehensive report of dual solutions. − Heat and Mass Transfer, 50.5, pp.639-650.

  • [7] Hayat T., Rashid M., Imtiaz M. and Alsaedi A. (2017): MHD effects on a thermo-solutal stratified nanofluid flow on an exponentially radiating stretching sheet. − Journal of Applied Mechanics and Technical Physics, 58.2, pp.214-223.

  • [8] Kumar R., Raju C.S.K., Sekhar K.R. and Reddy G.V. (2017): Three dimensional MHD ferrous nanofluid flow over a sheet of variable thickness in slip flow regime. − Journal of Mechanics, pp.1-12.

  • [9] Vajravelu K. and Prasad K.V. (2012): Heat transfer phenomena in a moving nanofluid over a horizontal surface. − Journal of Mechanics, 28.3, pp.579-588.

  • [10] Biswas, Rajib and Sarder Firoz Ahmmed (2018): Effects of hall current and chemical reaction on magnetohydrodynamics unsteady heat and mass transfer of Casson nanofluid flow through a vertical plate. − Journal of Heat Transfer, 140.9, 092402.

  • [11] Hayat, Tasawar, Arsalan Aziz, Taseer Muhammad, and Ahmed Alsaedi. (2017): Three-dimensional flow of nanofluid with heat and mass flux boundary conditions. − Chinese Journal of Physics, 55.4, pp.1495-1510.

  • [12] Sudhagar, Palani, Peri K. Kameswaran and B. Rushi Kumar (2017): Magnetohydrodynamics mixed convection flow of a nanofluid in an isothermal vertical cone. − Journal of Heat Transfer, 139.3.

  • [13] Das K., Pinaki Ranjan Duari and Kundu P.K. (2016): Effects of magnetic field on an unsteady mixed convection flow of nanofluids containing spherical and cylindrical nanoparticles. − Journal of Heat Transfer, 138.6, 061901.

  • [14] Nandkeolyar, Raj, Peri K. Kameswaran, Sachin Shaw and Precious Sibanda (2014): Heat transfer on nanofluid flow with homogeneous–heterogeneous reactions and internal heat generation. − Journal of Heat Transfer, 136.12, 122001.

  • [15] Nandkeolyar R., Motsa S.S. and Sibanda P. (2013): Viscous and Joule heating in the stagnation point nanofluid flow through a stretching sheet with homogenous–heterogeneous reactions and nonlinear convection. − Journal of Nanotechnology in Engineering and Medicine, 4.4, 041002.

  • [16] Mustafa M., S. Hina, T. Hayat and A. Alsaedi (2013): Slip effects on the peristaltic motion of nanofluid in a channel with wall properties. − Journal of Heat Transfer, 135.4, 041701.

  • [17] Hayat T., Numra Gull M. Farooq and B. Ahmad (2015): Thermal radiation effect in MHD flow of Powell-Eyring nanofluid induced by a stretching cylinder. − Journal of Aerospace Engineering, 29.1, 04015011.

  • [18] Hayat, Tasawar, Taseer Muhammad, Sabir Ali Shehzad and Ahmed Alsaedi. (2015): Three-dimensional flow of Jeffrey nanofluid with a new mass flux condition. − Journal of Aerospace Engineering, 29.2, 04015054.

  • [19] Ramzan M., Bilal M., Jae Dong Chung, Dian Chen Lu and Farooq U. (2017): Impact of generalized Fourier’s and Fick’s laws on MHD 3D second grade nanofluid flow with variable thermal conductivity and convective heat and mass conditions. − Physics of Fluids, 29.9, 093102.

  • [20] Chamkha A.J., Rashad A.M., Mansour M.A., Armaghani T. and Ghalambaz M. (2017): Effects of heat sink and source and entropy generation on MHD mixed convection of a Cu-water nanofluid in a lid-driven square porous enclosure with partial slip. − Physics of Fluids, 29.5, 052001.

  • [21] Mohebbi, Rasul, Mohsen Izadi and Chamkha Ali J. (2017): Heat source location and natural convection in a C-shaped enclosure saturated by a nanofluid. − Physics of Fluids, 29.12, 122009.

  • [22] Reddy, B. Siva Kumar, M. Veera Krishna, KV Surya Narayana Rao, and R. Bhuvana Vijaya. (2018): HAM Solutions on MHD flow of nano-fluid through saturated porous medium with Hall effects. − Materials Today: Proceedings, 5.1, pp.120-131.

  • [23] Ibrahim, Wubshet (2017): Magnetohydrodynamic (MHD) boundary layer stagnation point flow and heat transfer of a nanofluid past a stretching sheet with melting. − Propulsion and Power Research, 6.3, pp.214-222.

  • [24] Mahalakshmi, Thangavelu, Nagarajan Nithyadevi, Hakan F. Oztop, and Nidal Abu-Hamdeh. (2018): MHD mixed convective heat transfer in a lid-driven enclosure filled with Ag-water nanofluid with center heater. − International Journal of Mechanical Sciences, vol.142, pp.407-419.

  • [25] Ramzan, Muhammad, Hina Gul and Seifedine Kadry (2019): Onset of Cattaneo-Christov heat flux and thermal stratification in ethylene-glycol based nanofluid flow containing carbon nanotubes in a rotating frame. − IEEE Access, vol.7, pp.146190-146197.

  • [26] Khan, Umair, Shafiq Ahmad, Muhammad Ramzan, Muhammad Suleman, Dianchen Lu and Saba Inam. (2019): Numerical simulation of Darcy–Forchheimer 3D unsteady nanofluid flow comprising carbon nanotubes with Cattaneo–Christov heat flux and velocity and thermal slip conditions. − Processes, 7.10, 687.

  • [27] Li, Zhixiong, Ahmad Shafee, R. Kandasamy, M. Ramzan, and Qasem M. Al-Mdallal (2019): Nanoparticle transportation through a permeable duct with Joule heating influence. − Microsystem Technologies, 25.9, pp.3571-3580.

  • [28] Ramzan, Muhammad, Mutaz Mohammad and Fares Howari (2019): Magnetized suspended carbon nanotubes based nanofluid flow with bio-convection and entropy generation past a vertical cone. − Scientificreports, 9.1, pp.1-15.

  • [29] Ramzan, Muhammad, Mutaz Mohammad, Fares Howari, and Jae Dong Chung. (2019): Entropy analysis of carbon nanotubes based nanofluid flow past a vertical cone with thermal radiation. − Entropy, 21.7, 642.

  • [30] Alebraheem, Jawdat and Ramzan M. (2019): Flow of nanofluid with Cattaneo–Christov heat flux model. − Applied Nanoscience, pp.1-11.

  • [31] Farooq U., Lu D.C., Munir S., Suleman M. and Ramzan M. (2019): Flow of rheological nanofluid over a static wedge. − Journal of Nanofluids, 8.6, pp.1362-1366.

  • [32] Li, Zhixiong, M. Ramzan, Ahmad Shafee, S. Saleem, Qasem M. Al-Mdallal and Ali J. Chamkha. (2019): Numerical approach for nanofluid transportation due to electric force in a porous enclosure. − Microsystem Technologies, 25.6, pp.2501-2514.

  • [33] Bilal M. and Ramzan M. (2019): Hall current effect on unsteady rotational flow of carbon nanotubes with dust particles and nonlinear thermal radiation in Darcy–Forchheimer porous media. − Journal of Thermal Analysis and Calorimetry, vol.138, pp.3127-3137.

  • [34] Farooq, Umer, Dianchen Lu, Shahzad Munir, Muhammad Ramzan, Muhammad Suleman and Shahid Hussain (2019): MHD flow of Maxwell fluid with nanomaterials due to an exponentially stretching surface. − Scientific Reports 9.1, 7312.

  • [35] Lu, Dianchen, Muhammad Ramzan, Mutaz Mohammad, Fares Howari and Jae Dong Chung. (2019): A thin film flow of nanofluid comprising carbon nanotubes influenced by Cattaneo-Christov heat flux and entropy generation. − Coatings, 9.5, 296.

  • [36] Suleman, Muhammad, Muhammad Ramzan, Shafiq Ahmad, and Dianchen Lu. (2019): Numerical simulation for homogeneous–heterogeneous reactions and Newtonian heating in the silver-water nanofluid flow past a nonlinear stretched cylinder. − Physica Scripta, 94.8, 085702.

  • [37] Lu, Dianchen, Zhixiong Li, M. Ramzan, Ahmad Shafee, and Jae Dong Chung. (2019): Unsteady squeezing carbon nanotubes based nano-liquid flow with Cattaneo–Christov heat flux and homogeneous–heterogeneous reactions. − Applied Nanoscience, 9.2, pp.169-178.

  • [38] Suleman, Muhammad, Muhammad Ramzan, Shafiq Ahmad, Dianchen Lu, Taseer Muhammad and Jae Dong Chung (2019): A numerical simulation of silver–water nanofluid flow with impacts of Newtonian heating and homogeneous–heterogeneous reactions past a nonlinear stretched cylinder. − Symmetry, 11.2, 295.

  • [39] Ramzan, Muhammad, Mohsen Sheikholeslami, Maria Saeed and Jae Dong Chung (2019): On the convective heat and zero nanoparticle mass flux conditions in the flow of 3D MHD couple stress nanofluid over an exponentially stretched surface. − Scientific Reports 9.1, 562.

  • [40] Li, Zhixiong, Sheikholeslami M., Ahmad Shafee, Ramzan M., Kandasamy R. and Qasem M. Al-Mdallal (2019): Influence of adding nanoparticles on solidification in a heat storage system considering radiation effect. − Journal of Molecular Liquids, vol.273, pp.589-605.

  • [41] Sheikholeslami M., Ahmad Shafee, M. Ramzan and Zhixiong Li (2018): Investigation of Lorentz forces and radiation impacts on nanofluid treatment in a porous semi annulus via Darcy law. − Journal of MolecularLiquids, vol.272, pp.8-14.

  • [42] Suleman, Muhammad, Muhammad Ramzan, Madiha Zulfiqar, Muhammad Bilal, Ahmad Shafee, Jae Dong Chung, Dianchen Lu and Umer Farooq (2018): Entropy analysis of 3D non-Newtonian MHD nanofluid flow with nonlinear thermal radiation past over exponential stretched surface. − Entropy, 20.12, 930.

  • [43] Hsiao and Kai-Long (2017): To promote radiation electrical MHD activation energy thermal extrusion manufacturing system efficiency by using Carreau-nanofluid with parameters control method. − Energy, vol.130, pp.486-499.

  • [44] Hsiao and Kai-Long (2017): Combined electrical MHD heat transfer thermal extrusion system using Maxwell fluid with radiative and viscous dissipation effects. − Applied Thermal Engineering, vol.112, pp.1281-1288.

  • [45] Hsiao and Kai-Long (2017): Micropolar nanofluid flow with MHD and viscous dissipation effects towards a stretching sheet with multimedia feature. − International Journal of Heat and Mass Transfer, vol.112, pp.983-990.

  • [46] Hsiao and Kai-Long (2016): Stagnation electrical MHD nanofluid mixed convection with slip boundary on a stretching sheet. − Applied Thermal Engineering, vol.98, pp.850-861.

OPEN ACCESS

Journal + Issues

Search