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Three Dimensional MHD Ferrous Nanofluid Flow Over a Sheet of Variable Thickness in Slip Flow Regime

Published online by Cambridge University Press:  04 December 2017

R. Kumar ,
C. S. K. Raju ,
K. R. Sekhar  and
G. V. Reddy
R. Kumar*
Affiliation:
Department of Mathematics Central University of Himachal Pradesh Dharamshala, India
C. S. K. Raju
Affiliation:
GITAM School of Technology GITAM University Bangalore, India
K. R. Sekhar
Affiliation:
Department of Mathematics Sri Venkateswara University Tirupathi, India
G. V. Reddy
Affiliation:
Department of Mathematics Sri Venkateswara University Tirupathi, India
*
*Corresponding author (rakesh.lect@gmail.com)
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Abstract

In the present paper, we analyzed the effects of magnetic field on the three dimensional flow of a nanofluid having the suspension of ferrous nano-particles within the framework of a non-uniformly thicked sheet in a slip flow regime. The sheet of variable thickness is assumed to be stretched in horizontal and transverse directions. The effects of thermophoretic forces and Brownian motion have also been incorporated into the governing equations. The RK-Fehlberg-integration scheme with shooting technique is employed to resolve the altered governing non-linear differential equations. Velocity, temperature and concentration profiles are presented and discussed for two cases namely uniform thickness stretching sheet UTSS (n = 1) and variable thickness stretching sheet VTSS (n ≠ 1), and skin friction coefficient, reduced Nusselt number and Sherwood number are computed and analyzed through tables. The results reveal that heat and mass transfer processes over slendering sheet matches with those over a flat sheet in the presence of slip flow regime.

Keywords

Variable thicknessSlip flowFerrous nano-particlesRK-Fehlberg-integration scheme
Type
Research Article
Information
Journal of Mechanics , Volume 35 , Issue 2 , April 2019 , pp. 255 - 266
Copyright
© The Society of Theoretical and Applied Mechanics 2017 

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References

REFERENCES

Choi, S. U. S. and Eastman, J. A., “Enhancing Thermal Conductivity of Fluids with Nanoparticles,” ASME International Mechanical Engineering Congress & Exposition, San Francisco, CA, U.S., pp. 12–17 (1995).Google Scholar
Mustafa, M., Mushtaq, A., Hayat, T. and Alsaedi, A., “Rotating Flow of Magnetite-Water Nanofluid over a Stretching Surface Inspired by Non-Linear Thermal Radiation,” PLOS ONE, 11, e01149304 (2016).Google Scholar
Sandeep, N., Raju, C. S. K., Sulochana, C. and Sugunamma, V., “Effects of Aligned Magnetic Field and Radiation on the Flow of Ferrofluids over a Flat Plate with Non-Uniform Heat Source/Sink,” International Journal of Science and Engineering, 8, pp. 151–158 (2015).Google Scholar
Raju, C. S. K., Sandeep, N., Jayachandra Babu, M. and Ramana Reddy, J. V., “Stagnation Point Flow of a Ferrofluid Towards a Stretching Sheet,” Journal of Nanofluids, 5, pp. 245–252 (2016).Google Scholar
Raju, C. S. K., Sandeep, N., Jayachandra Babu, M. and Sugunamma, V., “Dual Solutions for Three-Dimensional MHD Flow of a Nanofluid over a Nonlinearly Permeable Stretching Sheet,” Alexandria Engineering Journal, 55, pp. 151–162 (2016).Google Scholar
Hayat, T., Abbas, Z., Pop, I. and Asghar, S., “Effects of Radiation and Magnetic Field on the Mixed Convection Stagnation Point Flow over a Vertical Stretching Sheet in a Porous Medium,” International Journal of Heat and Mass Transfer, 53, pp. 466–474 (2010).Google Scholar
Malvandi, A., Hedayati, F. and Ganji, D. D., “Slip Effects on Unsteady Stagnation Point Flow of a Nanofluid over a Stretching Sheet,” Powder Technology, 253, pp. 377–384 (2014).Google Scholar
Kumar, R. and Sood, S., “Effect of Quadratic Density Variation on Mixed Convection Stagnation Point Heat Transfer and MHD Fluid Flow in Porous Medium Towards a Permeable Shrinking Sheet,” Journal of Porous Media, 19, pp. 1083–1097 (2016).Google Scholar
Kumar, R. and Sood, S., “Interaction of Magnetic Field and Nonlinear Convection in the Stagnation Point Flow over a Shrinking Sheet,” Journal of Engineering, Article ID 675252 (2016).Google Scholar
Kumar, R. and Sood, S., “Combined Influence of Fluctuations in the Temperature and Stretching Velocity of the Sheet on MHD Flow of Cu-Water Nanofluid through Totating Porous Medium with Cubic Autocatalysis Chemical Reaction,” Journal of Molecular Liquids, 237, pp. 347–360 (2017).Google Scholar
Kumar, R., Sood, S., Sheikholeslami, M. and Shehzad, S. A., “Nonlinear Thermal Radiation and Cubic Autocatalysis Chemical Reaction Effects on the Flow of Stretched Nanofluid under Rotational Oscillations,” Journal of Colloid and Interface Science, 505, pp. 253–265 (2017).Google Scholar
Buongiorno, J., “Convective Transport in Nanofluids,” Journal of Heat Transfer, 128, pp. 240–250 (2006).Google Scholar
Nield, D. A. and Kuznetsov, A. V., “The Cheng-Minkowycz Problem for Natural Convective Boundary Layer Flow in a Porous Medium Saturated by a Nanofluid,” International Journal of Heat and Mass Transfer, 52, pp. 5792–5795 (2009).Google Scholar
Khan, J. A., Mustafa, M., Hayat, T. and Alsaedi, A., “Three Dimensional Flow of Nanofluid over a Non-Linearly Stretching Sheet: an Application to Solar Energy,” International Journal of Heat and Mass Transfer, 86, pp. 158–164 (2015).Google Scholar
Sekhar, K. R., Reddy, G. V. and Varma, S. V. K., “Mixed Convection Couette Flow of a Nanofluid through a Vertical Channel,” Elixir International Journal, 99, pp. 43237–43241 (2016).Google Scholar
Falana, A., Ojewale, O. A. and Adeboje, T. B., “Effect of Brownian Motion and Thermophoresis on a Nonlinearly Stretching Permeable Sheet in a Nanofluid,” Advances in Nanoparticles, 5, pp. 123–134 (2016).Google Scholar
Raju, C. S. K. and Sandeep, N., “Unsteady Casson Nanofluid Flow over a Rotating Cone in a Rotating Frame Filled with Ferrous Nanoparticles: A Numerical Study,” Journal of Magnetism & Magnetic Materials, 421, pp. 216–224 (2017).Google Scholar
Grosan, T. and Pop, I., “Fully Developed Mixed Convection in a Vertical Channel Filled by a Nanofluid,” Journal Heat Transfer, 134, 082501 (2012).Google Scholar
Fani, B., Kalteh, M. and Abbassi, A., “Investigating the Effect of Brownian Motion and Viscous Dissipation on the Nano-Fluid Heat Transfer in a Trapezoidal Microchannel Heat Sink,” Advanced Powder Technology, 26, pp. 83–90 (2015).Google Scholar
Haq, R. U. I., Khan, Z. H. and Khan, W. A., “Thermo Physical Effects of Carbon Nanotubes on MHD Flow over a Stretching Surface,” Physica E: Low-Dimensional Systems and Nanostructures, 63, pp. 215–222 (2014).Google Scholar
Raju, C. S. K., Sandeep, N. and Sugunamma, V., “Unsteady Magneto-Nanofluid Flow Caused by a Rotating Cone with Temperature Dependent Viscosity: A Surgical Implant Application,” Journal of Molecular Liquids, 222, pp. 1183–1191 (2016).Google Scholar
Fang, T., Zhang, J. and Zhang, Y., “Boundary Layer Flow over a Stretching Sheet with Variable Thickness,” Applied Mathematics and Computation, 218, pp. 7241–52 (2012).Google Scholar
Sulochana, C. and Sandeep, N., “Dual Solutions for Radiative MHD Forced Convective Flow of a Nanofluid over a Slendering Stretching Sheet in Porous Medium,” Journal of Naval Architecture and Marine Engineering, 12, pp. 115–124 (2015).Google Scholar
Babu, M. J. and Sandeep, N., “MHD Non-Newtonian Fluid Flow over a Slandering Stretching Sheet in the Presence of Cross Diffusion Effects,” Alexandria Engineering Journal, 55, pp. 2193–2201 (2016).Google Scholar
Anjali Devi, S. P. and Prakash, M., “Thermal Radiation Effects on Hydrodynamic Flow over a Slendering Stretching Sheet,” Journal of The Brazilian Society of Mechanical Sciences and Engineering, 38, pp. 423–431 (2016).Google Scholar
Hayat, T., Abbas, T., Ayub, M., Farooq, M. and Alsaedi, A., “Flow of Nanofluid Due to Convectively Heated Riga Plate with Variable Thickness,” Journal of Molecular Liquids, 222, pp. 854–862 (2016).Google Scholar
Hayat, T., Ullah, I., Alsaedi, A. and Farooq, M., “MHD Flow of Powell-Eyring Nanofluid over a Non-Linear Stretching Sheet with Variable Thickness,” Results in Physics, 7, pp. 189–196 (2017).Google Scholar
Anjali Devi, S. P. and Prakash, M., “Slip Flow Effects over Hydromagnetic Forced Convective Flow over a Slendering Stretching Sheet,” Journal of Applied Fluid Mechanics, 9, pp. 683–692 (2016).Google Scholar
Reddy, J. V. R., Sugunamma, V. and Sandeep, N., “Effects of Frictional Heating on Radiative Ferro-Fluid Flow over a Slendering Stretching Sheet with Aligned Magnetic Field,” The European Physical Journal Plus, 132 (2017).Google Scholar
Prasad, K. V., Vajravelu, K., Vaidya, H. and Van Gorder, R. A., “MHD Flow and Heat Transfer in a Nanofluid over a Slender Elastic Sheet with Variable Thickness,” Results in Physics, 7, pp. 1462–1474 (2017).Google Scholar
Reddy, S. C., Naikoti, K. and Rashidi, M. M., “MHD Flow and Heat Transfer Characteristics of Williamson Nanofluid over a Stretching Sheet with Variable Thickness and Variable Thermal Conductivity,” Transactions of A. Razmadze Mathematical Institute, 171, pp. 195–211 (2017).Google Scholar
Hayat, T., Muhammad, K., Farooq, M. and Alsaedi, A., “Melting Heat Transfer in Stagnation Point Flow of Carbon Nanotubes Towards Variable Thickness Surface,” AIP ADVANCES, 6, 015214 (2016).Google Scholar
Khader, M. and Megahed, A. M., “Numerical Solution for Boundary Layer Flow Due to a Nonlinearly Stretching Sheet with Variable Thickness and Slip Velocity,” The European Physical Journal Plus, 128, pp. 100–108 (2013).Google Scholar