Melting Heat Transfer in Magnetohydrodynamic Carreau Fluid over a Thermally Stratified Parabolic Surface

Abstract:

In this paper, we theoretically analyzed the effects of non-uniform heat source/sink on the magnetohydrodynamic dissipative flow of a Carreau fluid towards a thermally stratified melting surface of the paraboloid of revolution. Exponential heat source along with the temperature dependent thermal conductivity and viscosity are taken into account. The representing differential conditions are changed into an arrangement of non-straight coupled ODE’s and solved by employing the R-K with shooting system. Numerical arrangements are obtained from the flow, temperature profiles of various parametric values and after that domino effect are exhibited graphically and also a friction factor and local Sherwood number of various physical parameters are demonstrated graphically and in tabular form. Boosting values of the Weissenberg number increase both the velocity and thermal profiles of Carreau fluid. Rising values of velocity power law index parameter depreciate both the flow and local Sherwood number.

• Periodical: Defect and Diffusion Forum (Volume 388)
• Pages: 246-264
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.388.246
• Online since: October 2018
• Authors: G. Kumaran, Pallava Lakshminarayana, Bala Anki Reddy, N. Sandeep*
• Keywords: Carreau Fluid, Magnetohydrodynamic (MHD), Melting Surface, Non-Uniform Heat Source/Sink, Viscous Dissipation

References

[1] S. Ahmed, J. Zueco and Luis M. Lopez-Gonzalez, Effects of chemical reaction, heat and mass transfer and viscous dissipation over a MHD flow in a vertical porous wall using perturbation method, International Journal of Heat and Mass Transfer, 104 (2017).

DOI: 10.1016/j.ijheatmasstransfer.2016.07.076

[2] C. Israel-Cookey, A.Ogulu and V. B. Omubo-Pepple, Influence of viscous dissipation and radiation on unsteady MHD free-convection flow past an infinite heated vertical plate in a porous medium with time depedent suction, International Journal of Heat and Mass Transfer, 46 (2003).

DOI: 10.1016/s0017-9310(02)00544-6

[3] A. Mahdy, Unsteady MHD slip flow of a non-Newtonian Casson fluid due to stretching sheet with suction or blowing effect, Journal of Applied Fluid Mechanics, 9(2) (2016) 785-793.

DOI: 10.18869/acadpub.jafm.68.225.24687

[4] G. Mahanta and S. Shaw, 3D Casson fluid flow past a porous linearly stretching sheet with convective boundary condition, Alexandria Engineering Joural, 54(2015) 653-659.

DOI: 10.1016/j.aej.2015.04.014

[5] S. Mukhopadhyay, P. Ranjan De and K. Bhattacharyya, Casson fluid flow over an unsteady stretching surface, Ain Shams Engineering Journal, 4 (2013) 933-938.

DOI: 10.1016/j.asej.2013.04.004

[6] S. Pramanik, Casson fluid flow and heat transfer past an exponentially porous stretching surface in the presence of thermal radiation, Ain Shams Engineering Journal, 5 (2014) 205-212.

DOI: 10.1016/j.asej.2013.05.003

[7] M. M. Rashidi, S. Bagheri, E. Momoniat and N. Freidoonimehr, Entropy analysis of convective MHD flow of third grade non-Newtonian fluid over a stretching sheet Ain Shams Engineering Journal. http://dx.doi.org/10.101 6/j.asej.2015.08.012.

DOI: 10.1016/j.asej.2015.08.012

[8] B. Ramandevi, J.V. Ramana Reddy, V. Sugunamma and N. Sandeep Combined influence of viscous dissipation and non-uniform heat source/sink on MHD non-Newtonian fluid flow with Cattaneo-Christov heat flux, Alexandria Engineering Journal, Doi.org/10.1016/j.aej.2017.01.026.

DOI: 10.1016/j.aej.2017.01.026

[9] I. Rashid, R. U. Haq and Q. M. Al-Mdallal, Aligned magnetic field effects on water based melallic nanoparticles over a stretchinng sheet with PST and thermal radiation effects, Physica E, 89 (2017) 33-42.

DOI: 10.1016/j.physe.2017.01.029

[10] M. Abd El-Aziz, Dual solutions in hydromagnetic stagnation point flow and heat transfer towards a stretching/shrinking sheet with non-uniform heat source/sink and variable surface heat flux, Journal of the Egyptian Mathematical society, 24 (2016).

DOI: 10.1016/j.joems.2015.09.004

[11] T. Hayat, S. Qayyum, A. Alsaedi and A. Shafiq, Inclined magnetic field and heat source/sink aspects in flow of nanofluid with nonlinear thermal radiation, International Journal Heat and Mass Transfer, 103 (2016) 99-107.

DOI: 10.1016/j.ijheatmasstransfer.2016.06.055

[12] M. Subhas Abel and N. Mahesha, Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal condutivity, non uniform heat source and radiation, Applied Mathematical modelling, 32(2008) 1965-(1983).

DOI: 10.1016/j.apm.2007.06.038

[13] F. Mabood, S. M. Ibrahim, M.M. Rashidi, M. S. Shadloo and G. Lorenzini, Non-uniform heat source/sink and Soret effects on MHD non-Darcian convetive flow past a stretching sheet in a micropolar fluid with radiation, International Journal of Heat and Mass Transfer, 93(2016).

DOI: 10.1016/j.ijheatmasstransfer.2015.10.014

[14] M. Khan and M. Azam, Unsteady heat and mass transfer mechanisms in MHD Carreau nanofluid flow, Journal of Molecular. Liquids. 225 (2017) 554-562.

DOI: 10.1016/j.molliq.2016.11.107

[15] M. Khan, M. Azam and A. Munir, On unsteady Falkner-Skan flow of MHD Carreau nanofluid past a static/moving wedege with convective surface condition, Journal of Molecular Liquids. 2330 (2017) 48-58.

DOI: 10.1016/j.molliq.2016.12.097

[16] T. Hayat, S. Farooq, A. Alsaedi and B. Ahmad, Numerical analysis for radial MHD and mixed convection effects in peristalsis of non-Newtonian nanomaterial with zero mass flux conditions, Results in physics, http://dx.doi.org/10.1016/j.rinp.2016.12.048.

DOI: 10.1016/j.rinp.2016.12.048

[17] C. Sulochana, G.P. Ashwinkumar and N. Sandeep, Transpiration effects on stagnation-point flow of a Carreau nano fluid in the presence of thermophorsis and Brownian motion, Alexandria Engineering. Journal, 55 (2016) 1151-1157.

DOI: 10.1016/j.aej.2016.03.031

[18] C.S.K. Raju and N. Sandeep, unsteady three- dimensional flow of Casson-Carreau fluids past a stretching surface, Alexandria Engineering. Journal, 55 (2016) 1115-1126.

DOI: 10.1016/j.aej.2016.03.023

[19] A. Khalid, I. Khan, A. Khan and S. Shafie, Unsteady MHD free convection flow of Casson fluid past over an oscillating plate embedded in a porous medium, Engineering Science. and Technology International Journal, 18 (2015) 309-317.

DOI: 10.1016/j.jestch.2014.12.006

[20] S. Nadeem, Arshad Riaz, R. Ellahi, and N. S Akbar, Series solution of unsteady peristaltic flow of a Carreau fluid in eccentric cylinders.  Ain Shams Engineering Journal, 5(1) (2014) 293-304.

DOI: 10.1016/j.asej.2013.09.005

[21] R. Ellahi, Arshad Riaz, Sohail Nadeem, and Mohamed Ali, Peristaltic flow of Carreau fluid in a rectangular duct through a porous medium, Mathematical Problems in Engineering 2012.

DOI: 10.1155/2012/329639

[22] M.J. Uddin, A. Beg, N. Amin, Hydromagnetic transport phenomena from a stretching or shrinking nonlinear nanomaterial sheet with Navier slip and convective heating: a model for bio-nano-materials processing, Journal of Magnetism Magnetic Mater, 368 (2014).

DOI: 10.1016/j.jmmm.2014.05.041

[23] R.U. Haq, S. Nadeem, Z.H. Khan, N.F.M. Noor, MHD squeezed flow of water functionalized metallic nanoparticles over a sensor surface, Physica E, 73 (2015) 45–53.

DOI: 10.1016/j.physe.2015.05.007

[24] M .K. Nayak, G. C. Dash, and L. P. Singh, Heat and mass transfer effects on MHD viscoelastic fluid over a stretching sheet through porous medium in presence of chemical reaction. Propulsion and Power Research, 5(1) (2016) 70-80.

DOI: 10.1016/j.jppr.2016.01.006

[25] M. Kar S.N. Sahoo P.K. Rath G.C. Rath, Heatandmass transfer effects on a dissipative and radiative viscoelastic MHD flow over a stretching porous sheet, Arabian Journal Science Engineering, 39 (5) (2014) 3393–3401.

DOI: 10.1007/s13369-014-0991-0

[26] J.C. Arnold A.A. Asir,S.Somasundaram,T.Christopher, Heat transfer in a viscoelastic boundary layer flow over a stretching sheet, International Journal of Heat Mass and Transfer, 53 (2010)1112– 1118.

DOI: 10.1016/j.ijheatmasstransfer.2009.10.046

[27] N. Sandeep, C. Sulochana, C.S.K. Raju, M. Jayachandra Babu, Unsteady boundary layer flow of thermophoretic MHD nanofluid past a stretching sheet with space and time dependent internal heat source/sink, Application and Applied Mathematics: An International Journal, 10(1) (2015).

DOI: 10.1166/jon.2015.1181

[28] M. Sathish Kumar, N. Sandeep, and B. Rushi Kumar, Free convective heat transfer of mhd dissipative Carreau nanofluid flow over a stretching sheet, Frontiers in Heat and Mass Transfer, 8 (2017).

DOI: 10.5098/hmt.8.13

[29] T. Hayat, Sadia Asad, M. Mustafa and Alsaedi, Boundary layer flow of Carreau fluid over a convectively heated stretching sheet, Applied Mathematics and Computation, 246 (2014) 12-22.

DOI: 10.1016/j.amc.2014.07.083

[30] C. Sulochana, G.P. Ashwinkumar and N. Sandeep, Transpiration effects on stagnation-point flow of a Carreau nano fluid in the presence of thermophorsis and Brownian motion, Alexandria Engineering Journal, 55 (2016) 1151-1157.

DOI: 10.1016/j.aej.2016.03.031

[31] R. Mehmood, S. Nadeem, S. Saleem and N. Sher Akber, Flow and Heat Transfer analysis of a Jeffery Nano fluid impinging obliquely over a stretched plate. Journal of the Taiwan Institute of Chemical Engineers. 74 (2017) 49-58.

DOI: 10.1016/j.jtice.2017.02.001

[32] T. Hayat, S. Makhdoom, M. Awais, S. Saleem and M. M. Rashidi, Axisymmetric Powell Eyring fluid flow with convective boundary condition: An optimal analysis, Applied Mathematics and Mechanics (English Edition) 37(7) (2016) 919-928.

DOI: 10.1007/s10483-016-2093-9

[33] M. Awais, T. Hayat, S. Irum and S. Saleem, Dual solutions for nonlinear flow using Lie group analysis, PlosONE10(11): e0142732. doi:10.1371/ journal.pone.0142732.

DOI: 10.1371/journal.pone.0142732

[34] S. Nadeem, A. U. khan and S. Saleem, A comparative analysis on different nanofluid models for the oscillatory stagnation point flow, The European Physical Journal Plus (2016) 131:261.

DOI: 10.1140/epjp/i2016-16261-9

[35] S.P. Anjali Devi, M.Prakesh, Temperature dependent viscosity and thermal conductivity effects on hydromagnetic flow over a slandering stretching sheet, Journal of the Nigerian Mathematical Science. (2015).

DOI: 10.1016/j.jnnms.2015.07.002

[36] I.L. Animasaun, N. Sandeep, Buoyancy induced model for the flow of 36 nm alumina-water nanofluid along upper horizontal surface of paraboloid of revolution with variable thermal conductivity and viscosity, Powder Technology, 301 (2016) 858-867.

DOI: 10.1016/j.powtec.2016.07.023

[37] I. L. Animasaun, Double diffusive unsteady convective micropolar flow past a vertical porous plate moving through binary mixture using modified Boussinesq approximation, Ain Shams Engineering Journal, 7( 2) (2015) 755–765.

DOI: 10.1016/j.asej.2015.06.010

[38] A. J. Omowaye and I. L. Animasaun, Upper-convected maxwell fluid flow with variable thermo-physical properties over a melting surface situated in hot environment subject to thermal stratification, Journal of Applied Fluid Mechanics, 9(4) (2016).

DOI: 10.18869/acadpub.jafm.68.235.24939