Metal and Metallic Oxide Nanofluid over a Shrinking Surface with ‎Thermal Radiation and Heat Generation/Absorption

Document Type : Research Paper


1 Department of Mechanical engineering, National Institute of Technology Arunachal Pradesh, Yupia, Papum Pare District, Arunachal Pradesh, India‎

2 Department of Mathematics, Siksha O Anusandhan Deemed to be University, Khandagiri Square, Bhubaneswar, 751030, Odisha, India


In transport as well as manufacturing industries, the two basic aspects are heating and cooling. The use of metal or metallic oxide nanofluids has an effective cooling technique than that of conventional fluids. Therefore, the work is aimed at describing the three-dimensional MHD flow of metal and metallic oxide nanofluids past a stretching/shrinking sheet embedding with a permeable media. Further, thermal properties are enhanced by incorporating heat generation/absorption and radiative heat energy in the heat equation, enhancing the efficiency of temperature profiles. The convective boundary condition for temperature is used, which affects the temperature profile. Suitable similarity transformation is used to transform the governing equations to ordinary differential equations. The approximate analytical solution is obtained for these transformed differential equations employing the Adomian Decomposition Method (ADM). The influences of characterizing parameters are obtained and displayed via graphs, and the computation results of the heat transfer rate for various values of constraints are shown in a table. It is observed that both the momentum and energy profiles decrease with an enhance in the porosity parameter. Also, the fluid temperature decreases with an increasing thermal radiation parameter, but the opposite effect is encountered for the energy generation/absorption parameter.


Main Subjects

[1] Choi, S.U.S., Enhancing thermal conductivity of fluids with nanoparticles, in proc. ASME Int.mechanical engineering Congress and exposition ASME, FED 231/MD66, 1995, 99-105.
[2] Mishra, S.R., Nayak,B., Sharma, R.P., MHD stagnation-point flow over a stretching sheet in the presence of non-Darcy porous medium and heat source/sink, Defect and Diffusion Forum, 374, 2017, 92-105.
[3] Mishra, S.R., Rout, B.C., Analytical solution of electrical conducting water-based (KKL model) nanofluid flow over a linearly stretching sheet, Iranian Journal of Science and Technology, Transactions A: Science, 43, 2019, 1239–1247.
[4] Parida, S.K., Mishra, S.R., Heat and mass transfer of MHD stretched nanofluids in the presence of chemical reaction, Journal of Nanofluids, 8(1), 2019, 143-149.
[5] Bhatti, M. M., Mishra, S. R., Abbas, T., Rashidi, M. M., A mathematical model of MHD nanofluid flow having gyrotactic microorganisms with thermal radiation and chemical reaction effects, Neural Computing and Applications, 30, 2018, 1237–1249.
[6] Makinde, O. D., Mishra, S. R., On stagnation point flow of variable viscosity nanofluids past a stretching surface with radiative heat, International Journal of Applied and Computational Mathematics, 3(2), 2017, 561-578.
[7] Takhar, H. S., Chamkha, A. J., Nath,G., Unsteady three-dimensional MHD-boundary-layer flow due to the impulsive motion of a stretching surface, Acta Mechanica, 146, 2001, 59–71.
[8] Gorla, R.S.R., Chamkha, A.J., Natural convective boundary layer flow over a nonisothermal vertical plate embedded in a porous medium saturated with a nanofluid, Nanoscale and Microscale Thermophysical Engineering, 15(2), 2009, 81-94.
[9] Damseh, R. A., Al-Odat, M.Q., Chamkha, A.J., Shannak,B.A., Combined effect of heat generation or absorption and first-order chemical reaction on micropolar fluid flows over a uniformly stretched permeable surface, International Journal of Thermal Sciences, 48(8), 2009, 1658-1663.
[10] Zaraki, A., Ghalambaz, M., Chamkha, A.J., Ghalambaz, M., Rossi, D.D., Theoretical analysis of natural convection boundary layer heat and mass transfer of nanofluids: effects of size, shape, and type of nanoparticles, type of base fluid and working temperature, Advanced Powder Technology, 26(3), 2015, 935-946.
[11] Sandeep, N., Malvandi, A., Enhanced heat transfer in liquid thin film flow of non- Newtonian nanofluids embedded with graphene nanoparticles, Advanced Powder Technology, 27(6), 2016, 2448-2456.
[12] Sandeep, N., Sharma, R.P., Ferdows, M., Enhanced heat transfer in unsteady magnetohydrodynamic nanofluid flow embedded with aluminum alloy nanoparticles, Journal of Molecular Liquids, 234, 2017, 437–443.
[13] Das, S., Sharma, A.S., Jana, R.N., Sharma, R.P., Slip flow of nanofluid past a vertical plate with ramped wall temperature considering thermal radiation, Journal of Nanofluids, 6(6), 2017, 1054-1064.
[14] Das, S., Sen,A., Jana, R. N., Sharma, R. P., Stability of Nanofluid Flow Through a Vertical Channel with Wall Thermal Conductance and Radiation, Journal of Nanofluids, 6(4), 2017, 680–690.
[15] Das, S., Jana, R. N., Sharma, R. P., Makinde, O. D., MHD nanofluid flow and heat transfer in the Ekman layer on an oscillating porous plate, Journal of Nanofluids, 5(6), 2016, 968–981.
[16] Chamkha, A.J., Solar radiation assisted natural convection in uniform porous medium supported by a vertical flat plate, Journal of Heat Transfer, 119(1), 1997, 89-96.
[17] Chamkha, A.J., Hydromagnetic Natural Convection from an Isothermal Inclined Surface Adjacent to a Thermally Stratified Porous Medium, International Journal of Engineering Science, 35(10–11), 1997, 975-986.
[18] Ghalambaz, M., Behseresh, A., Behseresh, J., Chamkha, A.J., Effects of nanoparticles diameter and concentration on natural convection of the Al2O3-water nanofluids considering variable thermal conductivity around a vertical cone in porous media, Advanced Powder Technology, 26(1), 2015, 224-235.
[19] Chamkh, A.J., Abbasbandy, S., Rashad, A. M., Vajravelu, K., Radiation Effects on Mixed Convection over a Wedge Embedded in a Porous Medium Filled with a Nanofluid, Transport in Porous Media, 91(1), 2013, 261-279.
[20] Gorla, R.S.R., Chamkha, A.J., Rashad, A.M., Mixed convective boundary layer flow over a vertical wedge embedded in a porous medium saturated with a nanofluid: Natural convection dominated regime, Nanoscale Research Letters, 6, 2011, 207.
[21] Sheikholeslami, M., Ellahi, R., Ashorynejad, H.R., Donairry, G., Hayat, T., Effects of heat transfer in the flow of nanofluids over a permeable stretching wall in a porous medium, Journal of Computational and Theoretical Nanoscience, 11, 2014, 486–496.
[22] Sheikholeslami, M., Bandpy, M.G., Ganji, D.D., Soleimani, S., Natural convection heat transfer in a cavity with a sinusoidal wall filled with CuO–water nanofluid in presence of the magnetic field, Journal of the Taiwan Institute of Chemical Engineers, 45, 2014, 40–49.
[23] Salem, A.M., Ismail, G., Fathy, R., Hydromagnetic flow of Cu water nanofluid over a moving wedge with viscous dissipation, Chinese Physics B, 23, 2014, 044402.
[24] Sudarsana Reddy, P., Chamkha, A.J., Soret and Dufour Effects on MHD Convective Flow of Al2O3-Water and TiO2-Water nanofluids past a stretching sheet in porous media with heat generation/absorption, Advanced Powder Technology, 27(4), 2016, 1207-1218.
[25] Chamkha, A.J., Rashad, A. M., Natural convection from a vertical permeable cone in a nanofluid saturated porous media for uniform heat and nanoparticles volume fraction fluxes, International Journal of Numerical Methods for Heat and Fluid Flow, 22(8), 2012, 1073-1085.
[26] Chamkha, A.J., Al-Mudhaf, A.F., Pop, I., Effect of heat generation or absorption on thermophoretic free convection boundary layer from a vertical flat plate embedded in a porous medium, International Communications in Heat and Mass Transfer, 33(9), 2006, 1096-1102.
[27] Turkyilmazoglu, M., Multiple solutions of heat and mass transfer of MHD slip flow for the viscoelastic fluid over a stretching sheet, International Journal of Thermal Sciences, 50, 2011, 2264–2276.
[28] Hamad, M.A.A., Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of the magnetic field, International Communications in Heat and Mass Transfer, 38, 2011, 487–492.
[29] Sheikholeslami, M., Bandpy, M.G., Ellahi, R., Zeeshan, A., Simulation of MHD CuO–water nanofluid flow and convective heat transfer considering Lorentz forces, Journal of Magnetism and Magnetic Materials, 369,2014, 69–80.
[30] Ibrahim, W., Makinde, O.D., Double-diffusive in mixed convection and MHD stagnation point flow of nanofluid over a stretching sheet, Journal of Nanofluids, 4(1), 2015, 28–37.
[31] Magyari, E., Chamkha, A.J., Exact analytical results for the thermosolutal MHD Marangoni boundary layers, International Journal of Thermal Sciences, 47(7), 2008, 848-857.
[32] Nadeem, S., Hag, R.U., Effect of Thermal Radiation for magnetohydrodynamic Boundary Layer Flow of a Nanofluid Past a Stretching Sheet with Convective Boundary Conditions, Journal of Computational and Theoretical Nanoscience, 11, 2013, 32-40.
[33] Nadeem, S., Hag, R.U., MHD boundary layer flow of a nanofluid past a porous shrinking with thermal radiation, Journal of Aerospace Engineering, 28(2), 2015, 04014061.
[34] Turkyilmazoglu, M., Pop, I., Heat and mass transfer of unsteady natural convection flow of some nanofluids past a vertical infinite flat plate with radiation effect, International Journal of Heat and Mass Transfer, 59, 2013, 167–171.
[35] Chamkha, A.J., Khaled, A.-R.A., Similarity solutions for hydromagnetic mixed convection heat and mass transfer for Hiemenz flow through porous media, International Journal of Numerical Methods for Heat and Fluid Flow, 10(1), 2000, 94-115.
[36] Ramzan, M., Bilal, M., Time-dependent MHD nano-second grade fluid flow induced by the permeable vertical sheet with mixed convection and thermal radiation, PLoS One, 10(5), 2015, e0124929.
[37] Hayat, T., Muhammad, T., Alsaedi, A., Alhuthali, M.S., Magnetohydrodynamic three-dimensional flow of a viscoelastic nanofluid in the presence of nonlinear thermal radiation, Journal of Magnetism and Magnetic Materials, 385, 2015, 222–229.
[38] Hag, R.U., Nadeem, S., Khan, Z.H., Akbar, N.S., Thermal radiation and slip effects on MHD stagnation point flow of nanofluid over a stretching sheet, Physica E: Low- dimensional Systems and Nanostructures, 65, 2015, 17-23.
[39] Lakshmi, S., Reddy, S., Effect of Radiation on Mixed Convection Flow of a Non-Newtonian Nanofluid over a Non-Linearly Stretching Sheet with Heat Source/Sink, International Journal of Modern Eng. Research, 3, 2013, 2675-2696.
[40] Hayat, T., Muhammad, T., Shehzad, S. A., Alsaedi, A., Similarity solution to three-dimensional boundary layer flow of second grade nanofluid past a stretching surface with thermal radiation and heat source/sink, AIP Advances, 5, 2015,017107.
[41] Malvandi, A., Hedayati, F., Nobari, M. R. H., An HAM analysis of the stagnation-point flow of a nanofluid over a porous stretching sheet with heat generation, Journal of Applied Fluid Mechanics, 7(1), 2014, 135–145.
[42] Kahar, A., Kandasamy, R.R., Muhaimin, I., Scaling group transformation for the boundary-layer flow of a nanofluid past a porous vertical stretching surface in the presence of chemical reaction with heat radiation, Computers & Fluids, 52, 2011, 15–21.
[43] Rashidi, M.M., Chamkha, A.J., Keimanesh, M., Application of multi-step differential transform method on the flow of a second-grade fluid over a stretching or shrinking sheet, American Journal of Computational Mathematics, 1(2), 2011, 119-128.
[44] Sheikholeslami, M., Ganji, D. D., Heated permeable stretching surface in a porous medium using nanofluids, Journal of Applied Fluid Mechanics, 7(3), 2014, 535–542.
[45] Takhar, H.S., Chamkha, A.J., Nath, G., MHD flow over a moving plate in a rotating fluid with the magnetic field, Hall currents and free stream velocity, International Journal of Engineering Science, 40(13), 2002, 1511-1527.
[46] Chamkha, A.J., Coupled heat and mass transfer by natural convection about a truncated cone in the presence of magnetic field and radiation effects, Numerical Heat Transfer, Part A: Applications, 39(5), 200, 511-530.
[47] Sharma, R.P., Seshadri,R., Mishra, S.R., Manjum,S.R., Effect of thermal radiation on the magnetohydrodynamic three‐dimensional motion of a nanofluid past a shrinking surface under the influence of a heat source, Heat Transfer, 48(6), 2019, 2105-2121.
[48] Hayat, T., Imtiaz, M., and Alsaedi, A., MHD 3D flow of a nanofluid in the presence of convective conditions, Journal of Molecular Liquids, 212, 2015, 203-208.
[49] Zheng, L., Niu, J., Zhang, X., Gao, Y., MHD flow and heat transfer over a porous shrinking surface with velocity slip and temperature jump, Mathematical and Computer Modelling, 56, 2012, 133–144.
[50] Gherasim, I., Roy, G., Nguyen, C.T., Vo-Ngoc D. Experimental investigation of nanofluids in confined laminar radial flows, International Journal of Thermal Sciences, 48, 2009, 1486–1493.
[51] Angue Mintsa, H., Roy, G., Nguyen, C.T., Doucet, D., New temperature-dependent thermal conductivity data for water-based nanofluids, International Journal of Thermal Sciences, 48, 2009, 363–371.