{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T23:06:50Z","timestamp":1782169610718,"version":"3.54.5"},"reference-count":57,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,5,5]],"date-time":"2020-05-05T00:00:00Z","timestamp":1588636800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This article is concerned with the nanofluid flow in a rotating frame under the simultaneous effects of thermal slip and convective boundary conditions. Arrhenius activation energy is another important aspect of the present study. Flow phenomena solely rely on the Darcy\u2013Forchheimer-type porous medium in three-dimensional space to tackle the symmetric behavior of viscous terms. The stretching sheet is assumed to drive the fluid. Buongiorno\u2019s model is adopted to see the features of Brownian diffusion and thermophoresis on the basis of symmetry fundamentals. Governing equations are modeled and transformed into ordinary differential equations by suitable transformations. Solutions are obtained through the numerical RK45-scheme, reporting the important findings graphically. The outputs indicate that larger values of stretching reduce the fluid velocity. Both the axial and transverse velocity fields undergo much decline due to strong retardation produced by the Forchheimer number. The thermal radiation parameter greatly raises the thermal state of the field. The temperature field rises for a stronger reaction within the fluid flow, however reducing for an intensive quantity of activation energy. A declination in the concentration profile is noticed for stronger thermophoresis. The Forchheimer number and porosity factors result in the enhancement of the skin friction, while both slip parameters result in a decline of skin friction. The thermal slip factor results in decreasing both the heat and mass flux rates. The study is important in various industrial applications of nanofluids including the electro-chemical industry, the polymer industry, geophysical setups, geothermal setups, catalytic reactors, and many others.<\/jats:p>","DOI":"10.3390\/sym12050741","type":"journal-article","created":{"date-parts":[[2020,5,7]],"date-time":"2020-05-07T04:46:07Z","timestamp":1588826767000},"page":"741","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":97,"title":["Significance of Thermal Slip and Convective Boundary Conditions in Three Dimensional Rotating Darcy-Forchheimer Nanofluid Flow"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7186-7216","authenticated-orcid":false,"given":"Anum","family":"Shafiq","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China"},{"name":"Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modeling, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5880-9553","authenticated-orcid":false,"given":"Ghulam","family":"Rasool","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1986-4859","authenticated-orcid":false,"given":"Chaudry Masood","family":"Khalique","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modeling, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa"},{"name":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China"},{"name":"Department of Mathematics and Informatics, Azerbaijan University, Jeyhun Hajibeyli str., 71, Baku AZ1007, Azerbaijan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.molliq.2014.03.006","article-title":"Copper nanoparticle analysis for peristaltic flow in a curved channel with heat transfer characteristics","volume":"196","author":"Akbar","year":"2014","journal-title":"J. Mol. Liq."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2264","DOI":"10.1016\/j.ijthermalsci.2011.05.014","article-title":"Multiple solutions of heat and mass transfer of MHD slip flow for the viscoelastic fluid over a stretching sheet","volume":"50","author":"Turkyilmazoglu","year":"2011","journal-title":"Int. J. Therm. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.compfluid.2012.01.009","article-title":"Dual and triple solutions for MHD slip flow of non-Newtonian fluid over a shrinking surface","volume":"70","author":"Turkyilmazoglu","year":"2012","journal-title":"Comput. Fluids"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/j.molliq.2017.03.087","article-title":"Numerical study of partial slip effects on MHD flow of nanofluids near a convectively heated stretchable rotating disk","volume":"234","author":"Mustafa","year":"2017","journal-title":"J. Mol. Liq."},{"key":"ref_5","unstructured":"Choi, S.U.S., and Eastman, J.A. (1995, January 12\u201317). Enhancing thermal conductivity of fluids with nanoparti-cles. Proceedings of the ASME International Mechanical Engineering Congress & Exposisition, American Society of Mechanical Engineers, San Francisco, CA, USA."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2599","DOI":"10.1007\/s10973-018-7339-z","article-title":"A numerical investigation of magneto-hydrodynamic natural convection of Cu-water nanofluid in a wavy cavity using CVFEM","volume":"135","author":"Dogonchi","year":"2019","journal-title":"J. Therm. Anal. Calorim."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"50","DOI":"10.14302\/issn.2689-2855.jan-19-2716","article-title":"Marangoni effect in second grade forced convective flow of water based nanofluid","volume":"1","author":"Rasool","year":"2019","journal-title":"J. Adv. Nanotechnol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1016\/j.renene.2019.04.091","article-title":"Diurnal thermal evaluation of an evacuated tube solar collector (ETSC) charged with graphene nanoplatelets-methanol nano-suspension","volume":"142","author":"Sarafraz","year":"2019","journal-title":"Renew. Energy"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Sarafraz, M.M., Safaei, M.R., Tian, Z., Goodarzi, M., Filho, E.P.B., and Arjom, M. (2019). Thermal Assessment of Nano-Particulate Graphene-Water\/Ethylene Glycol (WEG 60:40) Nano-Suspension in a Compact Heat Exchanger. Energies, 12.","DOI":"10.3390\/en12101929"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"061020","DOI":"10.1115\/1.4043809","article-title":"Numerical Simulation of Natural Convection Heat Transfer of Nanofluid With Cu, MWCNT, and Al2O3 Nanoparticles in a Cavity With Different Aspect Ratios","volume":"11","author":"Goodarzi","year":"2019","journal-title":"J. Thermal Sci. Eng. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Sarafraz, M.M., Tlili, I., Baseer, M.A., and Safaei, M.R. (2019). Potential of Solar Collectors for Clean Thermal Energy Production in Smart Cities using Nanofluids: Experimental Assessment and efficiency improvement. Appl. Sci., 9.","DOI":"10.3390\/app9091877"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"122146","DOI":"10.1016\/j.physa.2019.122146","article-title":"Smart optimization of a thermosyphon heat pipe for an evacuated tube solar collector using response surface methodology (RSM)","volume":"534","author":"Sarafraz","year":"2019","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1166\/jon.2019.1574","article-title":"MHD flow of nanofluid flow across horizontal circular cylinder: Steady forced convection","volume":"8","author":"Tlili","year":"2019","journal-title":"J. Nanofluids"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1166\/jon.2018.1513","article-title":"Entropy generation due to MHD stagnation point flow of a nanofluid on a stretching surface in the presence of radiation","volume":"7","author":"Tlili","year":"2018","journal-title":"J. Nanofluids"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"125212","DOI":"10.1088\/1402-4896\/ab3990","article-title":"Second grade nanofluidic flow past a convectively heated vertical Riga plate","volume":"94","author":"Rasool","year":"2019","journal-title":"Phys. Scr."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1523","DOI":"10.1016\/j.cjph.2017.05.009","article-title":"Radiative flow of Powell-Eyring nanofluid with convective boundary conditions","volume":"55","author":"Hayat","year":"2017","journal-title":"Chin. J. Phys."},{"key":"ref_17","unstructured":"Rasool, G., Shafiq, A., and Khalique, C.M. (2019). Marangoni forced convective Casson type nanofluid flow in the presence of Lorentz force generated by Riga plate. Discret. Contin. Dyn. Syst. Ser. S, in press."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Sohail, M., Naz, R., and Abdelsalam, S.I. (2019). On the onset of entropy generation for a nanofluid with thermal radiation and gyrotactic microorganisms through 3D flows. Phys. Scr., 95.","DOI":"10.1088\/1402-4896\/ab3c3f"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Sohail, M., and Naz, R. (2020). Modified heat and mass transmission models in the magnetohydrodynamic flow of Sutterby nanofluid in stretching cylinder. Phys. A Stat. Mech. Appl., in press.","DOI":"10.1016\/j.physa.2019.124088"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Rasool, G., Shafiq, A., and Tlili, I. (2019). Marangoni convective nano-fluid flow over an electromagnetic actuator in the presence of first order chemical reaction. Heat Transf. Asian Res.","DOI":"10.1002\/htj.21612"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"e01345","DOI":"10.1016\/j.heliyon.2019.e01345","article-title":"Analysis of dual solution for MHD flow of Williamson fluid with slippage","volume":"5","author":"Lund","year":"2019","journal-title":"Heliyon"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Lund, L.A., Omar, Z., Khan, I., Raza, J., Bakouri, M., and Tlili, I. (2019). Stability analysis of Darcy\u2013Forchheimer flow of Casson type nanofluid over an exponential sheet: Investigation of critical points. Symmetry, 11.","DOI":"10.3390\/sym11030412"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1283","DOI":"10.1007\/s11771-019-4087-6","article-title":"Multiple solutions of Cu-C6H9NaO7 and Ag-C6H9NaO7 nanofluids flow over nonlinear shrinking surface","volume":"26","author":"Lund","year":"2019","journal-title":"J. Cent. South Univ."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Goodarzi, M., Tlili, I., Tian, Z., and Safaei, M. (2019). Efficiency assessment of using graphene nanoplatelets-silver\/water nanofluids in microchannel heat sinks with different cross-sections for electronics cooling. Int. J. Numer. Methods Heat Fluid Flow.","DOI":"10.1108\/HFF-12-2018-0730"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Tlili, I. (2019). Effects MHD and Heat Generation on Mixed Convection Flow of Jeffrey Fluid in Microgravity Environment over an Inclined Stretching Sheet. Symmetry, 11.","DOI":"10.3390\/sym11030438"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Tlili, I., and Alkanhal, T.A. (2019). Nanotechnology for water purification: Electrospun nanofibrous membrane in water and wastewater treatment. J. Water Reuse Desalin., 24.","DOI":"10.2166\/wrd.2019.057"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Shafiq, A., Khan, I., Rasool, G., Seikh, A.H., and Sherif, E.M. (2019). Significance of double stratification in stagnation point flow of third-grade fluid towards a radiative stretching cylinder. Mathematics, 7.","DOI":"10.3390\/math7111103"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Shafiq, A., Zari, I., Rasool, G., Tlili, I., and Khan, T.S. (2019). On the MHD Casson axisymmetric Marangoni forced convective flow of nanofluids. Mathematics, 7.","DOI":"10.3390\/math7111087"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Rasool, G., Shafiq, A., Khan, I., Baleanu, D., Nisar, K.S., and Shahzadi, G. (2020). Entropy generation and consequences of MHD in Darcy\u2013Forchheimer nanofluid flow bounded by non-linearly stretching surface. Symmetry, 29.","DOI":"10.3390\/sym12040652"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/BF00945764","article-title":"Stretching a surface in a rotating fluid","volume":"39","author":"Wang","year":"1988","journal-title":"Zeitschrift f\u00fcr Angewandte Mathematik und Physik"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Rashid, S., Hayat, T., Qayyum, S., Ayub, M., and Alsaedi, A. (2019). Three dimensional rotating Darcy\u2013Forchheimer flow with activation energy. Int. J. Numer. Methods Heat Fluid Flow.","DOI":"10.1108\/HFF-06-2018-0292"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1016\/j.molliq.2016.12.095","article-title":"Three dimensional rotating flow of Maxwell nanofluid","volume":"229","author":"Hayat","year":"2017","journal-title":"J. Mol. Liq."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3390","DOI":"10.1016\/j.rinp.2017.08.052","article-title":"Framing the performance of heat absorption\/generation and thermal radiation in chemically reactive Darcy\u2013Forchheimer flow","volume":"7","author":"Hayat","year":"2017","journal-title":"Results Phys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"025012","DOI":"10.1063\/1.4942091","article-title":"Three-dimensional rotating flow of Jeffrey fluid for Cattaneo-Christov heat flux model","volume":"6","author":"Hayat","year":"2016","journal-title":"AIP Adv."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1108\/09615530110399503","article-title":"Darcy\u2013Forchheimer mixed convection heat and mass transfer in fluid saturated porous media","volume":"11","author":"Jumah","year":"2001","journal-title":"Int. J. Numer. Methods Heat Fluid Flow"},{"key":"ref_36","unstructured":"Rasool, G., Shafiq, A., and Durur, H. (2019). Darcy\u2013Forchheimer relation in Magnetohydrodynamic Jeffrey nanofluid flow over stretching surface. Discret. Contin. Dyn. Syst. Ser. S, accepted."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"105221","DOI":"10.1088\/1402-4896\/ab18c8","article-title":"Magnetohydrodynamic Darcy Forchheimer nanofluid flow over nonlinear stretching sheet","volume":"94","author":"Rasool","year":"2019","journal-title":"Phys. Scr."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Rasool, G., and Zhang, T. (2019). Darcy\u2013Forchheimer nanofluidic flow manifested with Cattaneo-Christov theory of heat and mass flux over non-linearly stretching surface. PLoS ONE, 14.","DOI":"10.1371\/journal.pone.0221302"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Rasool, G., Zhang, T., Chamkha, A.J., Shafiq, A., Tlili, I., and Shahzadi, G. (2020). Entropy Generation and Consequences of Binary Chemical Reaction on MHD Darcy\u2013Forchheimer Williamson Nanofluid Flow Over Non-Linearly Stretching Surface. Entropy, 22.","DOI":"10.3390\/e22010018"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1002\/er.4440140403","article-title":"Natural convection boundary layer with suction and mass transfer in a porous medium","volume":"14","author":"Bestman","year":"1990","journal-title":"Int. J. Energy Res."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s13370-011-0008-z","article-title":"Unsteady convection with chemical reaction and radiative heat transfer past a flat porous plate moving through a binary mixture","volume":"22","author":"Makinde","year":"2011","journal-title":"Afr. Mat."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1340","DOI":"10.1016\/j.ijheatmasstransfer.2017.01.029","article-title":"Buoyancy effects on the MHD nanofluid flow past a vertical surface with chemical reaction and activation energy","volume":"108","author":"Mustafa","year":"2017","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"e01479","DOI":"10.1016\/j.heliyon.2019.e01479","article-title":"Characteristics of chemical reaction and convective boundary conditions in Powell-Eyring nanofluid flow along a radiative Riga plate","volume":"5","author":"Rasool","year":"2019","journal-title":"Heliyon"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"32","DOI":"10.14302\/issn.2689-2855.jan-19-2598","article-title":"Influence of chemical reaction on Marangoni convective flow of nanoliquid in the presence of Lorentz forces and thermal radiation: A numerical investigation","volume":"1","author":"Rasool","year":"2019","journal-title":"J. Adv. Nanotechnol."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.tsep.2017.11.005","article-title":"Impact of radiation in a stagnation point flow of Walters\u2019 B fluid towards a Riga plate","volume":"6","author":"Shafiq","year":"2018","journal-title":"Therm. Eng. Prog."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1166\/jon.2018.1501","article-title":"Effects of homogenous-Heterogeneous reactions on radiative NaCl-CNP nanofluid flow past a convectively heated vertical Riga plate","volume":"7","author":"Nayak","year":"2018","journal-title":"J. Nanofluids"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"961","DOI":"10.1016\/j.rinp.2018.01.013","article-title":"Analytical investigation of third grade nanofluidic flow over a riga plate using Cattaneo-Christov model","volume":"9","author":"Naseem","year":"2018","journal-title":"Results Phys."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1016\/j.ijmecsci.2017.07.048","article-title":"Bioconvective MHD flow of tangent hyperbolic nanofluid with newtonian heating","volume":"133","author":"Shafiq","year":"2017","journal-title":"Int. J. Mech. Sci."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Liao, S.J. (2012). Homotopy Analysis Method in Nonlinear Differential Equations, Springer & Higher Education Press.","DOI":"10.1007\/978-3-642-25132-0"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Shafiq, A., Jabeen, S., Hayat, T., and Alsaedi, A. (2017). Cattaneo-Christov heat flux model for squeezed flow of third grade fluid. Surf. Rev. Lett., 1750098.","DOI":"10.1142\/S0218625X17500986"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"065013","DOI":"10.1063\/1.4983014","article-title":"MHD biconvective \u2021ow of Powell Eyring nanofluid over stretched surface","volume":"7","author":"Naseem","year":"2017","journal-title":"AIP Adv."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"3059","DOI":"10.1016\/j.rinp.2017.07.077","article-title":"Statistical study of hydromagnetic boundary layer flow of Williamson fluid regarding a radiative surface","volume":"7","author":"Shafiq","year":"2017","journal-title":"Results Phys."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.rinp.2016.11.051","article-title":"Radiation effects on stagnation point flow with melting heat transfer and second order slip","volume":"7","author":"Mabood","year":"2017","journal-title":"Results Phys."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Hayat, T., Jabeen, S., Shafiq, A., and Alsaedi, A. (2016). Radiative squeezing flow of second grade fluid with convective boundary conditions. PLoS ONE, 11.","DOI":"10.1371\/journal.pone.0152555"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1699","DOI":"10.1007\/s11012-015-0329-3","article-title":"Chemical reaction effect on MHD viscoelastic fluid over a stretching sheet through porous medium","volume":"51","author":"Nayak","year":"2016","journal-title":"Meccanica"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"3029","DOI":"10.1007\/s13369-015-1805-8","article-title":"Unsteady Radiative MHD Free Convective Flow and Mass Transfer of a Viscoelastic Fluid Past an Inclined Porous Plate","volume":"40","author":"Nayak","year":"2015","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1007\/s12043-017-1444-6","article-title":"Heat transfer with thermal radiation on MHD particle\u2013fluid suspension induced by metachronal wave","volume":"89","author":"Bhatti","year":"2017","journal-title":"Pramana J. Phys."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/5\/741\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:52:32Z","timestamp":1760363552000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/5\/741"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,5]]},"references-count":57,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2020,5]]}},"alternative-id":["sym12050741"],"URL":"https:\/\/doi.org\/10.3390\/sym12050741","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5,5]]}}}