Melting Heat Transfer and Radiation Effects on Jeffrey Fluid Flow over a Continuously Moving Surface with a Parallel Free Stream

Document Type: Research Paper

Authors

1 Department of Mathematics, SAS, VIT, Vellore – 632 014, T.N, India

2 Department of Mathematics, Sree Vidyanikethan Engineering College, Tirupati-517 102, A.P, India

Abstract

This article is proposed to address the melting heat transfer of a Jeffrey fluid in Blasius and Sakiadis flow caused due to a moving surface. Thermal radiation and a constant free stream are considered in this mathematical model. The non-linear coupled dimensionless equations from the governing equations are attained by employing appropriate similarity transformations. The resulting dimensionless equations are solved by implementing RKF method. The impact of sundry emerging parameters on different flow fields are interpreted with the help of figures and tables. For augmented values of Deborah number, the velocity profile diminishes in the case of Blasius flow and the reverse behavior in the Sakiadis flow is observed. Moreover, the velocity of non-Newtonian liquid in case of Blasius flow is superior to that of the Sakiadis flow. The present work is demonstrated by matching with the computational results in the literature and found to be outstanding agreement.

Keywords

Main Subjects

[1] Turkyilmazoglu, M., Analytical solutions to mixed convection MHD fluid flow induced by a nonlinearly deforming permeable surface, Communications in Nonlinear Science and Numerical Simulation 63 (2018) 373–379.

[2] Khan, W.A., Alshomrani, A.S., Alzahrani, A.K., Khan, M., Irfan, M., Impact of autocatalysis chemical reaction on nonlinear radiative heat transfer of unsteady three-dimensional Eyring–Powell magneto-nanofluid flow, Pramana 91(63) (2018) 1-9.

[3] Farooq, M., Khan, M.I.,  Waqas, M., Hayat, T., Alsaedi, A., Khan, M.I., MHD stagnation point flow of viscoelastic nanofluid with non-linear radiation effects, J. Mol. Liq. 221 (2016) 1097-1103.

[4] Hayat, T., Khan, M.I., Waqas, M., Alsaedi, A., Yasmeen, T., Diffusion of chemically reactive species in third grade flow over an exponentially stretching sheet considering magnetic field effects, Chinese J. Chem. Eng. 25(3) (2017) 257-263.

[5] Azeem Khan, W., Khan, M., Malik, R., Three-dimensional flow of an Oldroyd-B nanofluid towards stretching surface with heat generation/absorption, Plos One 9(8) (2014) 105107.

[6] Sohail, A., Shah, S.I.A., Khan, W.A., Khan, M. Thermally radiative convective flow of magnetic nanomaterial: A revised model, Results in Physics 7 (2017) 2439–2444.

[7] Athirah, N., Zin, M., Khan, I.,  Shafie, S., Saleh, A., Analysis of heat transfer for unsteady MHD free convection flow of rotating Jeffrey nanofluid saturated in a porous medium, Results in Physics 7 (2017) 288–309.

[8] Hayat, T., Waqas, M., Khan, M.I., Alsaedi, A., Impacts of constructive and destructive chemical reactions in magnetohydrodynamic (MHD) flow of Jeffrey liquid due to nonlinear radially stretched surface, J. Mol. Liq. 225 (2017) 302–310.

[9] Zeeshan, A., Majeed, A., Heat transfer analysis of Jeffery fluid flow over a stretching sheet with suction/injection and magnetic dipole effect, Alexandria Eng. J. 55(3) (2016) 2171–2181.

[10] Turkyilmazoglu, M., Magnetic Field and Slip Effects on the Flow and Heat Transfer of Stagnation Point Jeffrey Fluid over Deformable Surfaces, Z. Naturforsch. A 71(6) (2016) 549-556.

[11] Harish Babu, D., Satya Narayana, P.V., Joule heating effects on MHD mixed convection of a Jeffrey fluid over a stretching sheet with power law heat flux:a numerical study, J. Mag. Magn. Mat. 412 (2016) 185-193.

[12] Satya Narayana, P.V., Harish Babu, D., Numerical study of MHD heat and mass transfer Jeffrey fluid over a stretching sheet with chemical reaction and radiation, J. Taiwan Inst. of Chem. Engg. 59 (2016) 18-25.

[13] Blasius, H., Grenzschichten in Flussigkeitenmitkleiner reibun, Zeitschrift für angewandte Mathematik und Physik 56 (1908) 1–37.

[14] Sakiadis, B.C., Boundary-layer behaviour on continuous solid surfaces, boundary layer equations for 2-dimensional and axisymmetric flow, Am. Inst. Chem. Eng. J. 7 (1961) 26–28.

[15] Afzal, N., Badaruddin, A., Elgarvi, A.A., Momentum and transport on a continuous flat surface moving in a parallel stream, Int. J. Heat Mass Transfer 36 (1993) 3399–3403.

[16] Bataller, R. C., Radiation effects for the Blasius and Sakiadis flows with a convective surface boundary condition, Appl. Math. Comput. 206(2) (2008) 832–840.

[17] Olanrewaju, P.O., Adeeyo, O.A., Agboola, O.O., Bishop, S.A., Buoyancy and thermal radiation effects for the Blasius and Sakiadis flows with a convective surface boundary condition, J. Energy, Heat & Mass Transf. 33(3) (2011) 211-232.

[18] Hady, F.M., Eid, M.R., Ahmed, M.A., The Blasius and Sakiadis flow in a nanofluid through a porous medium in the presence of thermal radiation under a convective surface boundary condition, Int. J. Eng. Innov. Technol. 3(3) (2013) 225–234.

[19] Hayat, T., Iqbal, Z., Mustafa, M., Obaidat, S., Flow and heat transfer of Jeffrey fluid over a continuously moving surface with a parallel free stream, J. Heat Transf. 134(1) (2012) 11701-7.

[20] Jalil, M., Asghar, S., Imran, S.M., Self similar solutions for the flow and heat transfer of Powell-Eyring fluid over a moving surface in a parallel free stream, Int. J. Heat Mass Transf. 65 (2013) 73–79.

[21] Anjali Devi, S.P., Suriyakumar, P., Effect of magnetic field on Blasius and Sakiadis flow of nanofluids past an inclined plate, J. Taibah Univ. Sci.11(6) (2017) 1275-1288.

[22] Mustafa, M., Khan, J.A., Hayat, T., Alsaedi, A., Sakiadis flow of Maxwell fluid considering magnetic field and convective boundary conditions, AIP Adv. 5(2) (2015) 1-9.

[23] Ramesh, G.K., Gireesha, B.J., Gorla, R.S.R., Study on Sakiadis and Blasius flows of Williamson fluid with convective boundary condition, Nonlinear Eng. 4(4) (2015) 215–221.

[24] Pantokratoras, A., Non-similar Blasius and Sakiadis flow of a non-Newtonian Carreau fluid, J. Taiwan Inst. Chem. Eng. 56 (2015) 1–5.

[25] Sekhar, K.R., Reddy, G.V., Radiative Magnetohydro-dynamic Sakiadis and Blasius Flow in a Suspension of Cu-Nanofluid with Non-Uniform Heat Source/Sink, Journal of Nanofluids 6(6) (2017) 1159-1165.

[26] Harish Babu, D., Venkateswarlu, B., Satya Narayana, P.V., Soret and Dufour effects on MHD radiative heat and mass transfer flow of a Jeffrey fluid over a stretching sheet, Frontiers in Heat and Mass Transfer 8 (2017) 1-5.

[27] Khan, W.A., Irfan, M., Khan, M., Alshomrani, A.S., Alzahrani, A.K., Alghamdi, M.S., Impact of chemical processes on magneto nanoparticle for the generalized Burgers fluid, Journal of Molecular Liquids 234 (2017) 201–208.

[28] Turkyilmazoglu, M. Algebraic solutions of flow and heat for some nanofluids over deformable and permeable surfaces, International Journal of Numerical Methods for Heat & Fluid Flow 27(10) (2017) 2259–2267

[29] Khan, W.A., Haq, I., Ali, M., Shahzad, M., Khan, M., Irfan, M. Significance of static–moving wedge for unsteady Falkner–Skan forced convective flow of MHD cross fluid, Journal of the Brazilian Society of Mechanical Sciences and Engineering 40(17) (2018) 1-12.

[30] Roberts, L., On the Melting of a Semi-Infinite Body of Ice Placed in a Hot Stream of Air, J. Fluid Mech. 4 (1958) 505–528.

[31] Epstein, M., Cho, D.H., Melting heat transfer in steady laminar flow over a flat plate, J. Heat Transfer 98 (1976) 531–533.

[32] Ishak, R. Nazar, N. Bachok, and I. Pop, Melting heat transfer in steady laminar flow over a moving surface, Heat Mass Transf. und Stoffuebertragung 46(4) (2010) 463–468.

[33] Das, K., Radiation and melting effects on MHD boundary layer flow over a moving surface, Ain Shams Eng. J. 5(4) (2014) 1207–1214.

[34] Azizah, N., Ishak, A., Pop, I., Melting heat transfer in boundary layer stagnation-point flow towards a stretching/shrinking sheet in a micropolar fluid, Comput. Fluids 47(1) (2011) 16–21.

[35] Mabood, F., Abdel-Rahman, R.G., Lorenzini, G., Effect of melting heat transfer and thermal radiation on Casson fluid flow in porous medium over moving surface with magnetohydrodynamics, J. Eng. Thermophys. 25(4) (2016) 536–547.

[36] Khan, W.A., Khan, M., Irfan, M., Alshomrani, A.S., Impact of melting heat transfer and nonlinear radiative heat flux mechanisms for the generalized Burgers fluids, Results in Physics 7 (2017) 4025–4032.

[37] Hashim, K.M., Saleh, A.A., Characteristics of melting heat transfer during flow of Carreau fluid induced by a stretching cylinder, Eur. Phys. J. Soft. Matter. 40(1) (2017) 1-8.

[38] Sheikholeslami, M., Rokni, H.B., Effect of melting heat transfer on nanofluid flow in existence of magnetic field considering Buongiorno Model, Chinese J. of Phy. 55(4) (2017) 1115-1126.

[39] Arifuzzaman, M., Khan, M.S., Mehedi, M.F.U., Rana,  B.M.J., Ahmmed, S.F., Chemically reactive and naturally convective high speed MHD fluid flow through an oscillatory vertical porous plate with heat and radiation absorption effect, Eng. Sci. and Tech.,Int. J. 21(2) (2018) 215-228.

[40] Cortell, R., Radiation Effects for the Blasius and Sakiadis flows with convective surface boundary conditions, Appl. Math. Comput. 206 (2010) 832–840.

[41] Hayat, T., Abbas, Z., Pop, I., Momentum and heat transfer over a continuously moving surface with a parallel free stream in a viscoelastic fluid, Numer. Methods Partial Differ. Equ. 26 (2010) 305–319.

[42] Bianchi, M.V.A., Viskanta, R., Momentum and heat transfer on a continuous flat surface moving in parallel counter flow free stream, Wärme- und Stoffübertr 29 (1993) 89–94.

[43] Turkyilmazoglu, M., Determination of the correct range of physical parameters in the approximate analytical solutions of nonlinear equations using the Adomian Decomposition method, Mediterranean Journal of Mathematics 13(6) (2016) 4019-4037.