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Nanoscience & Nanotechnology-Asia


ISSN (Print): 2210-6812
ISSN (Online): 2210-6820

Research Article

Boundary Layer Flow and Cattaneo-Christov Heat Flux of a Nonlinear Stretching Sheet with a Suspended CNT

Author(s): S. Shakunthala* and M.M. Nandeppanavar

Volume 9, Issue 4, 2019

Page: [494 - 503] Pages: 10

DOI: 10.2174/2210681208666180821142231

Price: $65


Background: In this article the Boundary layer flow and Cattaneo-Christov Heat flux of nonlinear stretching sheet in a suspended carbon nanotube is analyzed.

Methods: The governing classical PDE’s are changing into ODE’s using the similarity transformation method. This boundary value problem is solved by using numerical method known as Runge-Kutta fourth order method with effective shooting technique. Presently in this analysis , the flow, velocity and heat transfer characteristics for different heat transferphysical parameters such as nanofluid (ϕ), suction parameter (N>0), heat flux parameter (β) and Prandtl number (Pr) are studied for two cases i.e., single Wall Carbon Nanotube (SWCNT) and Multiwall Carbon Nanotube (MWCNT) respectively.

Results: Our results are in good agreement within a limiting condition comparing with previously published results. This study signifies that practical applications in science and engineering fields for example in functional ceramics, nano metals for energy and environmental applications.

Conclusion: A theoretical study of boundary layer flow and Catteneo-Christove heat flux is carried out. In this study some of the important findings are collected as follows:

1. The result of nanoparticle volume fraction f and suction parameter N shows that, as increasing f it increases the flow, velocity and temperature while as increasing N which increases the flow and temperature but decreases the velocity at boundary layer.

2. A comparison result is plotted which is an excellent agreement with previously published results.

3. As increasing the Prandtl number and relaxation time of heat flux parameter in the thermal boundary layer which decreases the temperature of thermal boundary layer.

4. Effect of relaxation time of heat flux is same for both local skin friction and local nusselt number i.e. increasing.

Keywords: Boundary layer flow, Cattaneo-Christov heat flux, suction parameter, CNT, SWCNT, MWCNT, numerical method, convective boundary condition.

Graphical Abstract
Belmiloudi, A. Parameter identification problems and analysis of the impact of porous media in biofluid heat transfer in biological tissues during thermal therapy. Nonlinear Anal. Real World Appl., 2010, 11, 1345-1363.
Singh, P.; Tomer, N.S.; Kumar, S.; Sinha, D. Effect of radiation and porosity parameter on magneto hydrodynamic flow due to stretching sheet in porous media. Thermal. Sci., 2011, 15(2), 517-526.
Abel, M.S. Kumar, K.A. Kumar, R.R. MHD Flow, and heat transfer with effects of Buoyancy, viscous and joules dissipation over a nonlinear vertical stretching Porous sheet with partial slip. Engineering, 2011, 3, 285-291.
Sahoo, S.N. Dash, G.C. Heat and Mass transfer of MHD convective boundary layer flow past a stretching porous wall embedded in a Porous Medium. J. Eng. Thermophys., 2012, 21(3), 181-102.
Mukhopadhyay, S. Analysis of boundary layer flow over a porous nonlinearly stretching sheet with partial slip at the boundary. Alex. Eng. J., 2013, 52, 563-569.
Mandal, I.C.; Mukhopadhyay, S. Heat transfer analysis for fluid flow over an exponentially stretching porous sheet with surface heat flux in porous medium. Ain Shams Eng. J., 2013, 4, 103-110.
Singh, A.K. Madhab, B. MHD Free convective heat and mass transfer of fluid flow past a moving variable surface in porous media. IJETT, 2013, 4(4), 1151-1157.
Singh, V. Agarwal, S. MHD flow and heat transfer for maxwell fluid over an exponential stretching sheet with variable thermal conductivity in porous medium. Thermal. Sci., 2014, 18(2), 599-615.
Sinha, A.; Misra, J.C. Mixed convection hydromagnetic flow with heat generation thermophoresis and mass transfer over an inclined nonlinear porous shrinking sheet: A numerical approach. J. Mech., 2014, 30, 491-503.
Manjunatha, P.T.; Gireesha, B.J.; Kumara, B.C.P. Thermal analysis of conducting dusty fluid flow in a porous medium over a stretching cylinder in the presence of non-uniform source/sink. Int. J. Mech. Mater. Eng, 2014, 1, 13.
Hunegnaw, D. Kishan.N. Unsteady MHD heat and mass transfer flow over stretching sheet in Porous medium with variable properties considering viscous dissipation and chemical reaction. Am. Chem. Sci. J., 2014, 4(6), 901-917.
Malik, R.; Khan, M.; Mushtaq, M. Cattaneo-Christov heat flux model for Sisko fluid flow past a permeable non-linearly stretching cylinder. J. Mol. Liq., 2016, 222, 430-434.
Hayat, T. Qayyum, S. Imtiaz, M. Alsaedi, A. Impact of Cattaneo-Christov heat flux in jeffrey fluid flow with homogeneous-heterogeneous reactions. Plos One, 2016, 11(2) e0148662
Malik, M.Y. Khan, M. Salahuddin, T. Khan, I. Variable viscosity and MHD flow in Casson fluid with Cattaneo-Christov heat flux model: Using Keller box method. Int. J. Eng. Sci. Technol., 2016, 19, 1985-1992.
Kudenatti, R.B.; Kirsur, S.R.; Nargund, A.L.; Bujurke, N.M. Similarity solutions of the MHD boundary layer flow past a constant wedge within porous media. Math. Probl. Engin., 2017, 1428137, 11.
Hussain, S. Finite element solution for MHD flow of Nanofluids with Heat and Mass transfer through a Porous media with thermal radiation, viscous dissipation and chemical reaction effects. Adv. Appl. Math. Mech., 2017, 9(4), 904-923.
Makinde, O.D. Mishra, S.R. Chemically reacting MHD mixed convection variable viscosity blasius flow embedded in a porous medium. D D Forum, 2017, 374, 83-91.
Shah, R.A. Abbas, T. Idrees, M. Ullah, M. MHD Carreau fluid slip flow over a porous stretching sheet with viscous dissipation and variable thermal conductivity. Bound. Value Probl., 2017, 2017, 94.
Kundu, P.K. Chakraborty, T.; Das, K. Framing the Cattaneo–Christov heat flux phenomena on CNT- based maxwell nanofluid along stretching sheet with multiple Slips. Arab. J. Sci. Eng., 2018, 43(3), 1177-1188.
Mahantesha, 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. J. Inform. Med, 2017, 9, 26-34.
Akbar, N.S.; Khan, Z.H.; Nadeem, S. The combined effect of slip and convective boundary conditions on stagnation-point flow of CNT suspended nanofluid over a stretching sheet. J. Mol. Liq., 2014, 196, 21-25.
Gorder, R.A.V.; Vajravelu, K. A note on flow geometries and the similarity solutions of the boundary layer equations for a nonlinearly stretching sheet. Arch. Appl. Mech., 2010, 80(11), 1329-1332.
Shirvan, K.M.; Ellahi, R.; Mamourian, M.; Moghiman, M. Effects of wavy surface characteristics on natural convection heat transfer in a cosine corrugated square cavity filled with nanofluid. Int. J. Heat Mass Transf., 2017, 107, 1110-1118.
Ellahi, R.; Tariq, M.H.; Hassan, M.; Vafai, K. On boundary layer nano-ferroliquid flow under the influence of low oscillating stretchable rotating disk. J. Mol. Liq., 2017, 229, 339-345.
Shirvan, K.M.; Mamourian, M.; Mirzakhanlari, S.; Ellahi, R. Numerical investigation of heat exchanger effectiveness in a double pipe heat exchanger filled with nanofluid: A sensitivity analysis by response surface methodology. Powder Technol., 2017, 313, 99-111.
Esfahani, J.A.; Akbarzadeh, M.; Rashidi, S.; Rosen, M.A.; Ellahi, R. Influences of wavy wall and nanoparticles on entropy generation over heat exchanger plat. Int. J. Heat Mass Transf., 2017, 109, 1162-1171.
Rashidi, S.; Esfahani, J.A.; Ellahi, R. Convective heat transfer and particle motion in an obstructed duct with two side by side obstacles by means of DPM model. Appl. Sci., 2017, 7, 431.
Hassan, M.; Zeeshan, A.; Majeed, A.; Ellahi, R. Particle shape effects on ferrofuids flow and heat transfer under influence of low oscillating magnetic field. J. Magnet. Magnet. Mater., 2017, 443, 36-44.
Rashidi, S.; Akar, S.; Bovand, M.; Ellahi, R. Volume of fluid model to simulate the nanofluid flow and entropy generation in a single slope solar still. Renew. Energy, 2018, 115, 400-410.
Ijaz, N.; Zeeshan, A.; Bhatti, M.M.; Ellahi, R. Analytical study on liquid-solid particles interaction in the presence of heat and mass transfer through a wavy channel. J. Mol. Liq., 2018, 250, 80-87.
Zeeshan, A.; Shehzad, N.; Ellahi, R. Analysis of activation energy in Couette-Poiseuile flow of nanofluid in the presence of chemical reaction and convective boundary conditions. Results Phys, 2018, 8, 502-512.
Ellahi, R. Special issue on recent developments of nanofluids. Appl. Sci., 2018, 8, 192.
Dogonchi, A.S.; Ganji, D.D. Study of nanofluid flow and heat transfer between non-parallel stretching walls considering Brownian motion. J. Taiwan Inst. Chem. Eng, 2016, 69, 1-13.
Dogonchi, A.S.; Ganji, D.D. Investigation of heat transfer for cooling turbine disks with a non-Newtonian fluid flow using DRA. Case Stud. Therm. Eng, 2015, 6, 40-51.
Dogonchi, A.S.; Ganji, D.D. Impact of Cattaneo-Christov heat flux on MHD nanofluid flow and heat transfer between parallel plates considering thermal radiation effect. J. Taiwan Inst. Chem. Eng, 2017, 80, 1-12.
Dogonchi, A.S.; Divsalar, K.; Ganji, D.D. Flow and heat transfer of MHD nanofluid between parallel plates in the presence of thermal radiation. Comput. Methods Appl. Mech. Engrg., 2016, 310, 58-76.
Dogonchi, A.S.; Hatami, M.; Domairry, G. Motion analysis of a spherical solid particle in plane Couette Newtonian fluid flow. Powder Technol., 2015, 274, 186-192.
Dogonchi, A.S.; Hatami, M.; Hosseinzadeh, K.; Domairry, G. Non-spherical particles sedimentation in an incompressible Newtonian medium by Padé approximation. Powder Technol., 2015, 278, 248-256.
Dogonchi, A.S.; Chamkha, A.J.; Ganji, D.D. A numerical investigation of magneto-hydrodynamic natural convection of Cu–water nanofluid in a wavy cavity using CVFEM. J. Thermal. Anal. Calorimet., 2018, 12, 319-332.
Dogonchi, A.S.; Ganji, D.D. Analytical solution and heat transfer of two-phase nanofluid flow between non-parallel walls considering Joule heating effect. Powder Technol., 2017, 318, 390-400.
Dogonchi, A.S.; Ganji, D.D. Thermal radiation effect on the nano-fluid buoyancy flow and heat transfer over a stretching sheet considering Brownian motion. J. Mol. Liq., 2016, 223, 512-527.
Dogonchi, A.S.; Ganji, D.D. Investigation of MHD nanofluid flow and heat transfer in a stretching/shrinking convergent/divergent channel considering thermal radiation. J. Mol. Liq., 2016, 220, 592-603.
Dogonchi, A.S.; Ganji, D.D. Convection–radiation heat transfer study of moving fin with temperature-dependent thermal conductivity, heat transfer coefficient and heat generation. Appl. Therm. Eng., 2016, 103, 705-712.
Dogonchi, A.S.; Ganji, D.D. Effect of Cattaneo-Christov heat flux on buoyancy MHD nanofluid flow and heat transfer over a stretching sheet in the presence of Joule heating and thermal radiation impacts. Indian J. Phys., 2018, 92, 757-766.
Dogonchi, A.S.; Alizadeh, M.; Ganji, D.D. Investigation of MHD Go-water nanofluid flow and heat transfer in a porous channel in the presence of thermal radiation effect. Adv. Powder Technol., 2017, 28, 1815-1825.
Mahantesh, M.N. Gorla, G.S.R.; Shakunthala, S. MHD blasius flow and heat transfer of a flat plate in the presence of suspended carbon nano-fluids. J. Nanomater. Nanoeng. Nanosys., 2017, 232(1), 31-40.
Mahantesh, M.N.; Shakunthala, S. Flow and heat transfer of carbon nanofluids over a vertical plate. Front. Heat Mass Transf. (FHMT),, 2017, 9, 27.
Kays, W.; Crawford, M. Convective Heat and Mass Transfer; McGraw Hill, 1980.
Mahantesh, M.N.; Shakunthala, S. Heat transfer analysis of stagnation point flow over a stretching cylinder in a suspension of carbon nanotube. J. Nanofluids, 2016, 6, 1173-1180.

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