Impact of Activation Energy and Heat Source/Sink on 3D Flow of Williamson Nanofluid with GaN Nanoparticles over A Stretching Sheet


  •   Mamidala Jyotshna

  •   Vadlakonda Dhanalaxmi


Several novel techniques for the study of thermophysical characteristics have opened up new avenues for understanding the flow and heat transfer effects in nanofluids, leading to novel applications. There have been studies on nanofluids including different metal, ceramic and magnetic nanoparticles mixed with base fluids such as Water, Kerosene, and Ethylene glycol. However, research using semiconductor nanoparticles is restricted. For the investigation, Gallium nitrite, a binary semiconductor with excellent heat convection combined with base fluid Ethylene glycol in nanoparticle form, is employed.  Williamson MHD nanofluid (GaN nanoparticles + Ethylene glycol) is examined across a stretched sheet with porosity under the impact of convective boundary conditions, thermal radiation, thermal source/sink, and activation energy in three dimensions. The governing equations are turned into dimensionless ordinary differential equations via similarity transformations. Numerical analysis was carried out in MATLAB utilizing bvp5c and the shooting technique. The results are visually shown, and plausible scientific explanations for the velocity, temperature, and concentration profiles with respect to different parameters are provided. In addition, the Skin-friction coefficient, Nusselt number, and Sherwood number are presented in tabular form. The velocity and temperature profiles increased while the concentration profile decreased as the volume fraction of Gallium nitride nanoparticles in the Williamson nanofluid increased. Physical significances were also assigned to each observed outcome.

Keywords: Activation energy, Gallium nitride, heat source/sink, volume fraction, Williamson nanofluid


Bilal S, Khalil-ur-R, Malik MY, Hussain A, Khan M. Effects of temperature dependent conductivity and absorptive/generative heat transfer on MHD three dimensional flow of Williamson fluid due to bidirectional non-linear stretching surface. Results Phys. 2017; 7: 204–212.

Nandeppanavar MM, Vaishali S, Kemparaju MC, Raveendra N. Theoretical analysis of thermal characteristics of casson nano fluid flow past an exponential stretching sheet in Darcy porous media. Case Stud. Therm. Eng. 2020; 21: 100717.

Nandeppanavar MM, Vajravelu K, Subhas Abel M. Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with thermal radiation and non-uniform heat source/sink. Commun. Nonlinear Sci. Numer. Simul. 2011; 16(9): 3578–3590.

Das SK, Choi SUS Patel HE. Heat transfer in nanofluids - A review. Heat Transf. Eng. 2006; 27(10): 3–19.

Xuan Y, Li Q. Heat transfer enhancement of nanofluids. Int. J. Heat Fluid Flow. 2000; 21(1): 58–64.

Wong KV, De Leon O. Applications of nanofluids: Current and future. Adv. Mech. Eng. 2010; 2010.

Choi S. Nanofluid technology: current status and future research. Energy. 1998: 26.

Khan NA, Khan H. A Boundary layer flows of non-Newtonian Williamson fluid. Nonlinear Eng. 2014; 3(2): 107–115.

Nadeem S, Hussain ST. Analysis of MHD Williamson nano fluid flow over a heated surface. J. Appl. Fluid Mech. 2016; 9(2): 729–739.

Kurtcebe C, Erim MZ. Heat transfer of a non-newtonian viscoinelastic fluid in an axisymmetric channel with a porous wall for turbine cooling application. Int. Commun. Heat Mass Transf. 2002; 29(7): 971-982.

Ibrahim W, Shankar B. MHD boundary layer flow and heat transfer of a nanofluid past a permeable stretching sheet with velocity, thermal and solutal slip boundary conditions. Comput. Fluids. 2013; 75: 1-10.

Sheikholeslami M, Shehzad SA, Li Z, Shafee A. Numerical modeling for alumina nanofluid magnetohydrodynamic convective heat transfer in a permeable medium using Darcy law. Int. J. Heat Mass Transf. 2018; 127: 614–622.

Eid MR, Al-Hossainy AF. Synthesis, DFT calculations, and heat transfer performance large-surface TiO2: ethylene glycol nanofluid and coolant applications. Eur. Phys. J. Plus. 2020; 135(7).

Eid MR. Effects of NP Shapes on Non-Newtonian Bio-Nanofluid Flow in Suction/Blowing Process with Convective Condition: Sisko Model. J. Non-Equilibrium Thermodyn. 2020; 45(2): 97–108.

Kotresh MJ, Ramesh GK, Shashikala VKR, Prasannakumara BC. Assessment of Arrhenius activation energy in stretched flow of nanofluid over a rotating disc. Heat Transf. 2021; 50(3): 2807–2828.

Mallikarjuna HB, Nirmala T, Punith Gowda RJ, Manghat R, Varun KumarTw RS. Two-dimensional Darcy–Forchheimer flow of a dusty hybrid nanofluid over a stretching sheet with viscous dissipation. Heat Transf. 2021; 50(4): 3934–3947.

Jayadevamurthy PGR, Kumar Rangaswamy N, Prasannakumara BC, Nisar KC. Emphasis on unsteady dynamics of bioconvective hybrid nanofluid flow over an upward–downward moving rotating disk. Numer. Methods Partial Differ. Equ.. 2020: 1–22.

Al-Hossainy AF, Eid MR. Structure, DFT calculations and heat transfer enhancement in [ZnO/PG + H2O]C hybrid nanofluid flow as a potential solar cell coolant application in a double-tube. J. Mater. Sci. Mater. Electron. 2020; 31(18): 15243–15257.

Prasannakumara BC, Gireesha BJ, Krishnamurthy MR, Ganesh Kumar K. MHD flow and nonlinear radiative heat transfer of Sisko nanofluid over a nonlinear stretching sheet. Informatics Med. Unlocked. 2917; 9(August): 123–132.

Qayyum S, Khan MI, Chammam W, Khan WA, Ali Z, Ul-Haq W. Modeling and theoretical investigation of curved parabolized surface of second-order velocity slip flow: Combined analysis of entropy generation and activation energy. Mod. Phys. Lett. B. 2020; 34(33): 1–15.

Qayyum S, Hayat T, Alsaedi A. Thermal radiation and heat generation/absorption aspects in third grade magneto-nanofluid over a slendering stretching sheet with Newtonian conditions. Phys. B Condens. Matter. 2018; 537: 139–149.

Hayat T, Kiyani MZ, Alsaedi A, Ijaz Khan M, Ahmad I. Mixed convective three-dimensional flow of Williamson nanofluid subject to chemical reaction. Int. J. Heat Mass Transf. 2018; 127: 422–429.

Malik S, Bilal MY, Khalil-ur-R, Hussain A, Khan M. Effects of temperature dependent conductivity and absorptive/generative heat transfer on MHD three dimensional flow of Williamson fluid due to bidirectional non-linear stretching surface. Results Phys. 2017; 7: 204–212.

Malik MY, Bilal S, Salahuddin T, Rehman KU. Three-Dimensional Williamson Fluid Flow over a Linear Stretching Surface. Math. Sci. Lett. 2017; 6(1): 53–61.

Wang CY. The three-dimensional flow due to a stretching flat surface. Phys. Fluids. 1984; 27(8): 1915–1917.

Mahanthesh B, Gireesha BJ, Gorla RSR, Makinde OD. Magnetohydrodynamic three-dimensional flow of nanofluids with slip and thermal radiation over a nonlinear stretching sheet: a numerical study. Neural Comput. Appl. 2018; 30(5): 1557–1567.

Alaidrous AA, Eid MR. 3-D electromagnetic radiative non-Newtonian nanofluid flow with Joule heating and higher-order reactions in porous materials. Sci. Rep. 2020; 10(1): 1–19.

Geethan KS, Varma SVK, Kiran Kumar RVMSS, Raju CSK, Shehzad SA, Bashir MN. Three-dimensional hydromagnetic convective flow of chemically reactive williamson fluid with non-uniform heat absorption and generation. Int. J. Chem. React. Eng. 2019; 17(2): 1–17.

Nainaru T, Narayana PVS, Venkateswarlu B. Numerical simulation of variable thermal conductivity on 3D flow of nanofluid over a stretching sheet. Nonlinear Eng. 2020; 9(1): 233–243.

Thumma T, Mishra SR, Abbas MA, Bhatti MM, Abdelsalam SI. Three-dimensional nanofluid stirring with non-uniform heat source/sink through an elongated sheet. Appl. Math. Comput. 2022; 421: 126927.

Hemmat Esfe M, Motallebi SM, Bahiraei M. Employing response surface methodology and neural network to accurately model thermal conductivity of TiO2–water nanofluid using experimental data. Chinese J. Phys. 2021; 70(December): 14–25.

Hayat T, Waqas M, Khan MI, Alsaedi A. Analysis of thixotropic nanomaterial in a doubly stratified medium considering magnetic field effects. Int. J. Heat Mass Transf. 2016; 102: 1123–1129.

Farooq M, Khan MI, Waqas M, Hayat T, Alsaedi A, Khan MI. MHD stagnation point flow of viscoelastic nanofluid with non-linear radiation effects. J. Mol. Liq. 2016; 221: 1097–1103.

Hayat T, Khan MWA, Khan MI, Waqas M, Alsaedi A. Impact of chemical reaction in fully developed radiated mixed convective flow between two rotating disk. Phys. B Condens. Matter. 2018; 538(February): 138–149.

Hayat T, Khan MI, Waqas M, Alsaedi A, Yasmeen T. Diffusion of chemically reactive species in third grade fluid flow over an exponentially stretching sheet considering magnetic field effects. Chinese J. Chem. Eng. 2017; 25(3): 257–263.

Waqas M, Farooq M, Khan MI, Alsaedi A, Hayat T, Yasmeen T. Magnetohydrodynamic (MHD) mixed convection flow of micropolar liquid due to nonlinear stretched sheet with convective condition. Int. J. Heat Mass Transf. 2016; 102: 766–772.

Hayat T, Muhammad T, Alsaedi A, Alhuthali MS. Magnetohydrodynamic three-dimensional flow of viscoelastic nanofluid in the presence of nonlinear thermal radiation. J. Magn. Magn. Mater. 2015; 385: 222–229.

Gireesha BJ, Gorla RSR, Mahanthesh B. Effect of Suspended Nanoparticles on Three-Dimensional MHD Flow, Heat and Mass Transfer of Radiating Eyring-Powell Fluid Over a Stretching Sheet. J. Nanofluids. 2015; 4(4): 474–484.

Bachok N, Ishak A, Nazar R, Pop I. Flow and heat transfer at a general three-dimensional stagnation point in a nanofluid. Phys. B Condens. Matter. 2010; 405(24): 4914–4918.

Khan JA, Mustafa M, Hayat T, Alsaedi A. Three-dimensional flow of nanofluid over a non-linearly stretching sheet: An application to solar energy. Int. J. Heat Mass Transf. 2015; 86: 158–164.

Wang W, Zhang B, Cui L, Zheng H, Klemeš JJ, Wang J. Numerical study on heat transfer and flow characteristics of nanofluids in a circular tube with trapezoid ribs. Open Phys. 2021; 19(1): 224–233.

Muhammad N, Nadeem S. Ferrite nanoparticles Ni- ZnFe2O4 , Mn- ZnFe2O4 and Fe2O4 in the flow of ferromagnetic nanofluid. Eur. Phys. J. Plus. 2017; 132(9).

Ramzan M, Gul H, Zahri M. Darcy-Forchheimer 3D Williamson nanofluid flow with generalized Fourier and Fick’s laws in a stratified medium. Bull. Polish Acad. Sci. Tech. Sci. 2020; 68(2): 327–335.

Omiddezyani S, Gharehkhani S, Yousef-Asli V, Khazaee I, Ashjaee M, Nayebi R, et al. Experimental investigation on thermo-physical properties and heat transfer characteristics of green synthesized highly stable CoFe2O4/rGO nanofluid. Colloids Surfaces A Physicochem. Eng. Asp. 2021; 610(November): 125923.

Sheikh NA, Ching DL, Khan I, Sakidin HB, Jamil M, Khalid HU, Ahmed N. Fractional model for MHD flow of Casson fluid with cadmium telluride nanoparticles using the generalized Fourier’s law. Sci. Rep. 2021; 11(1): 1–21.

Kameswaran PK, Sibanda P, Murti ASN. Nanofluid flow over a permeable surface with convective boundary conditions and radiative heat transfer. Math. Probl. Eng. 2013; 2013.

Bachok N, Ishak A, Pop I. Boundary layer stagnation-point flow and heat transfer over an exponentially stretching/shrinking sheet in a nanofluid. Int. J. Heat Mass Transf. 2012; 55(25-26): 8122–8128.

Mandal G. Convective-Radiative Heat Transfer of Micropolar Nanofluid Over a Vertical Non-Linear Stretching Sheet. J. Nanofluids. 2016; 5(6): 852–860.

Mandal S, Shit GC. Entropy analysis of unsteady MHD three-dimensional flow of Williamson nanofluid over a convectively heated stretching sheet. Heat Transf. 2022; 51(2): 2034–2062.

Swain K, Mahanthesh B. Thermal Enhancement of Radiating Magneto-Nanoliquid with Nanoparticles Aggregation and Joule Heating: A Three-Dimensional Flow. Arab. J. Sci. Eng. 2021; 46(6): 5865–5873.

Siddiqui AA, Sheikholeslami M. TiO2-water nanofluid in a porous channel under the effects of an inclined magnetic field and variable thermal conductivity. Appl. Math. Mech. 2018; 39(8): 1201–1216.

Nayak MK, Prakash J, Tripathi D, Pandey VS. 3D radiative convective flow of ZnO-SAE50nano-lubricant in presence of varying magnetic field and heterogeneous reactions. Propuls. Power Res. 2019; 8(4): 339–350.

Yacob NA, Dasman A, Ahmad S. Regional Conference on Science, Technology and Social Sciences (RCSTSS 2016). Reg. Conf. Sci. Technol. Soc. Sci. (RCSTSS 2016). 2018.

Zhao Z, Buscaglia V, Vivani M, Buscaglia MT, Mitoseriu L, Testion A, et al. Grain-size effects on the ferroelectric behavior of dense nanocrystalline BaTiO3 ceramics. Phys. Rev. B. 2004; 70(2).

Hreniak D, Strek W, Amami J, Guyot Y, Boulon G, Goutaudier C, et al. The size-effect on luminescence properties of BaTiO3:Eu 3+ nanocrystallites prepared by the sol-gel method. J. Alloys Compd. 2004; 380(1-2): 348–351.

Hreniak D, Strȩk W. Synthesis and optical properties of Nd3+-doped Y 3Al5O12 nanoceramics. J. Alloys Compd. 2002; 341(1-2): 183–186.

Nadeem S, Hussain ST, Lee C. Flow of a williamson fluid over a stretching sheet. Brazilian J. Chem. Eng. 2013; 30(3): 619–625.

Shawky HM, Eldabe NTM, Kamel KA, Abd-Aziz EA. MHD flow with heat and mass transfer of Williamson nanofluid over stretching sheet through porous medium. Microsyst. Technol. 2019; 25(4): 1155–1169.

Sultan F, Khan WA, Ali M, Shahzad M, Irfan M, Khan M. Theoretical aspects of thermophoresis and Brownian motion for three-dimensional flow of the cross fluid with activation energy. Pramana - J. Phys. 2019; 92(2): 1–10.

Khashi’ie NS, Arifin NM, Pop I, Nazar R, Hafidzuddin EH, Wahi N. Three-Dimensional Hybrid Nanofluid Flow and Heat Transfer past a Permeable Stretching/Shrinking Sheet with Velocity Slip and Convective Condition. Chinese J. Phys. 2020; 66: 157–171.

Eid MR, Nafe MA. Thermal conductivity variation and heat generation effects on magneto-hybrid nanofluid flow in a porous medium with slip condition. Waves in Random and Complex Media. 2022; 32(3): 1103–1127.

Mion C, Muth JF, Preble EA, Hanser D. Thermal conductivity, dislocation density and GaN device design. Superlattices and Microstructures. 2006; 40(4-6): 338-342.

Krukowski S, Witek A, Adamczyk J, Jun J, Bockowski M, Grzegory I, Lucznik B, Nowak G, Wróblewski M, Presz A, Gierlotka S. Thermal properties of indium nitride. Journal of Physics and Chemistry of Solids. 1998; 59(3): 289-95.

Sreedevi P, Sudarsana Reddy P. Effect of magnetic field and thermal radiation on natural convection in a square cavity filled with TiO2 nanoparticles using Tiwari-Das nanofluid model. Alexandria Eng. J. 2022; 61(2): 1529–1541.

Nandi S, Kumbhakar B. Viscous Dissipation and Chemical Reaction Effects on Tangent Hyperbolic Nanofluid Flow Past a Stretching Wedge with Convective Heating and Navier’s Slip Conditions. Iran. J. Sci. Technol. - Trans. Mech. Eng. 2021; 46(2): 379–397.

Laxmi TV, Shankar B. Effect of Nonlinear Thermal Radiation on Boundary Layer Flow of Viscous Fluid over Nonlinear Stretching Sheet with Injection/Suction. J. Appl. Math. Phys. 2016; 4(2): 307–319.

Srinivasulu T, Goud BS. Effect of inclined magnetic field on flow, heat and mass transfer of Williamson nanofluid over a stretching sheet. Case Stud. Therm. Eng. 2021; 23(October): 100819.

Rushi B, Sivaraj KR, Prakash J. Editors. Lecture Notes in Mechanical Engineering Advances in Fluid Dynamics. [Internet]. 2018. Available:

Ariel PD. Generalized three-dimensional flow due to a stretching sheet. ZAMM Zeitschrift fur Angew. Math. und Mech. 2003; 83(12): 844–852.

Oyelakin IS, Lalramneihmawii P, Mondal S, Nandy SK, Sibanda P. Thermophysical analysis of three‐dimensional magnetohydrodynamic flow of a tangent hyperbolic nanofluid. Eng. Reports. 2020; 2(4): 1–13.

Ogunseye HA, Mondal H, Sibanda P, Mambili-Mamboundou H. Lie group analysis of a Powell–Eyring nanofluid flow over a stretching surface with variable properties. SN Appl. Sci. 2020; 2(1): 1–12.

Kandasamy R, Mohamad R, Ismoen M. Impact of chemical reaction on Cu, Al2O3 and SWCNTs–nanofluid flow under slip conditions. Eng. Sci. Technol. an Int. J. 2016; 19(2): 700–709.

Sajid T, Tanveer S, Sabir Z, Guirao JLG. Impact of Activation Energy and Temperature-Dependent Heat Source/Sink on Maxwell-Sutterby Fluid. Math. Probl. Eng. 2020; 2020.

Hamid A, Khan M. Impacts of binary chemical reaction with activation energy on unsteady flow of magneto-Williamson nanofluid. J. Mol. Liq. 2018; 262: 435–442.

Hayat T, Shah F, Khan MI, Khan MI, Alsaedi A. Entropy analysis for comparative study of effective Prandtl number and without effective Prandtl number via γAl2O3-H2O and γAl2O3-C2H6O2 nanoparticles. J. Mol. Liq. 2018; 266: 814–823.

Hussain ST, Nadeem S, Ul Haq R. Model-based analysis of micropolar nanofluid flow over a stretching surface,” Eur. Phys. J. Plus. 2014; 129(8).


How to Cite
Jyotshna, M. ., & Dhanalaxmi, V. (2022). Impact of Activation Energy and Heat Source/Sink on 3D Flow of Williamson Nanofluid with GaN Nanoparticles over A Stretching Sheet. European Journal of Mathematics and Statistics, 3(5), 16–29.