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Int. J. Automot. Technol. 23(6), 1651–1661 (2022). https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs12239-022-0143-6\nSurcel, M.D., Michaelsen, J.: Evaluation of tractor-trailer rolling resistance reducing measures. SAE Tech. Pap. 2010-01–19 (2010). https:\u002F\u002Fdoi.org\u002F10.4271\u002F2010-01-1917\nEjsmont, J., Taryma, S., Ronowski, G., Swieczko-Zurek, B.: Influence of temperature on the tyre rolling resistance. Int. J. Automot. Technol. 19(1), 45–54 (2018). https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs12239$-$018$-$0005$-$4\nOswald, A.L., Browne, L.J.: The airflow field around an operating tire and its effect on tire power loss. SAE Tech. Pap. (1981). https:\u002F\u002Fdoi.org\u002F10.4271\u002F810166\nGreiner, M.: Verfahren zur Prädiktion des Rollwiderstands bei variablen Betriebsparametern auf Basis standardisierter Rollwiderstandsmessungen. https:\u002F\u002Fpublikationen.bibliothek.kit.edu\u002F1000091012 (2019). [Online]\nBode, O.: Der Einfluss von Wärmeverlusten auf den Rollwiderstand von Reifen, FAT-Schriftenreihe 325. Verband der Automobilindustrie (VDA), Hannover. vda.de\u002Fvda\u002Fde\u002Faktuelles\u002Fpublikationen\u002Fpublication\u002Ffat-schriftenreihe-325 (2020). [Online]\nEjsmont, J., Ronowski, G., Owczarzak, W., Sommer, S.: Temperature influence on tire rolling resistance measurements quality. Int. J. Automot. Technol. 23(1), 109–123 (2022). https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs12239-022-0009-y\nISO 28580:2009 (2009)\nFarroni, F., Mancinelli, N., Timpone, F.: A real-time thermal model for the analysis of tire\u002Froad interaction in motorcycle applications. Appl. Sci. 10(5), Article ID 1604 (2020). https:\u002F\u002Fdoi.org\u002F10.3390\u002Fapp10051604\nFévrier, P., Fandard, G.: Thermal and mechanical tyre modelling for handling simulation. ATZ Worldw. 110(5), 26–31 (2008). https:\u002F\u002Fdoi.org\u002F10.1007\u002Fbf03225006\nHyttinen, J., Ussner, M., Österlöf, R., Jerrelind, J., Drugge, L.: Truck tyre transient rolling resistance and temperature at varying vehicle velocities - measurements and simulations. Polym. Test. (2023). https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.polymertesting.2023.108004\nGreiner, M., Unrau, H.J., Gauterin, F.: A model for prediction of the transient rolling resistance of tyres based on inner-liner temperatures. Veh. Syst. Dyn. 56(1), 78–94 (2018). https:\u002F\u002Fdoi.org\u002F10.1080\u002F00423114.2017.1343955\nNielsen, L., Sandberg, T.: A New Model for Rolling Resistance of Pneumatic Tires. SAE Technical Paper Series (2002)\nMars, W.V., Luchini, J.R.: Analytical model for the transient rolling resistance behavior of tires. Tire Sci. Technol. 27(3), 161–175 (1999). https:\u002F\u002Fdoi.org\u002F10.2346\u002F1.2135982\nHentschke, R.: The Payne effect revisited. eXPRESS Polym. Lett. 11(4), 278–292 (2017). https:\u002F\u002Fdoi.org\u002F10.3144\u002Fexpresspolymlett.2017.28\nDiani, J., Fayolle, B., Gilormini, P.: A review on the Mullins effect. Eur. Polym. J. 45, 601–612 (2009). https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.eurpolymj.2008.11.017\nFröhlich, J., Niedermeier, W., Luginsland, H.-D.: The effect of filler–filler and filler–elastomer interaction on rubber reinforcement. Composites, Part A, Appl. Sci. Manuf. 36(4), 449–460 (2005)\nBergström, J.: Mechanics of Solid Polymers. Elsevier, Amsterdam (2015)\nÖsterlöf, R., Wentzel, H., Kari, L.: A finite strain viscoplastic constitutive model for rubber with reinforcing fillers. Int. J. Plast. 87, 1–14 (2016)\nHyttinen, J., Österlöf, R., Drugge, L., Jerrelind, J.: Constitutive rubber model suitable for rolling resistance simulations of truck tyres. Proc. Inst. Mech. Eng., Part D, J. Automob. Eng. (2022). https:\u002F\u002Fdoi.org\u002F10.1177\u002F09544070221074108\nDiani, J., Fayolle, B., Gilormini, P., Diani, J., Fayolle, B., Gilormini, P.: A review on the Mullins effect. Eur. Polym. J. 45, 601–612 (2009). https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.eurpolymj.2008.11.017\nYdrefors, L.: The relationship between rolling resistance and tyre operating conditions, with a focus on tyre temperature. KTH Royal Institute of Technology (2022)\nDavari, M.M., Jerrelind, J., Trigell, A.S., Drugge, L.: Extended brush tyre model to study rolling loss in vehicle dynamics simulations. Int. J. Veh. Des. 73(4), 255–280 (2017). https:\u002F\u002Fdoi.org\u002F10.1504\u002FIJVD.2017.083418\nDal, H., Kaliske, M.: Bergström-Boyce model for nonlinear finite rubber viscoelasticity: Theoretical aspects and algorithmic treatment for the FE method. Comput. Mech. 44(6), 809–823 (2009). https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs00466-009-0407-2\nBergström, J.S., Boyce, M.C.: Constitutive modeling of the large strain time-dependent behavior of elastomers. J. Mech. Phys. Solids 46(5), 931–954 (1998). https:\u002F\u002Fdoi.org\u002F10.1016\u002FS0022-5096(97)00075-6\nTaryma, S., et al.: Road texture influence on tire rolling resistance. Key Eng. Mater. 597, 193–198 (2014). https:\u002F\u002Fdoi.org\u002F10.4028\u002Fwww.scientific.net\u002FKEM.597.193\nWong, J.Y.: Theory of Ground Vehicles, 3 rd. Wiley, New York (2001)\nEjsmont, J., Sjögren, L., Świeczko-Żurek, B., Ronowski, G.: Influence of road wetness on tire-pavement rolling resistance. J. Civ. Eng. Archit. 9, 1302–1310 (2015). https:\u002F\u002Fdoi.org\u002F10.17265\u002F1934-7359\u002F2015.11.004\nSurcel, M.D., Bonsi, A.K.: The impact of lift axles on fuel economy and GHG emissions reduction. SAE Int. J. Commer. Veh. 8(2), 673–681 (2015). https:\u002F\u002Fdoi.org\u002F10.4271\u002F2015-01-2874\nNakajima, Y.: Advanced Tire Mechanics. Springer, Singapore (2019). https:\u002F\u002Fdoi.org\u002F10.1007\u002F978-981-13-5799-2\nAldhufairi, H.S., Olatunbosun, O.A.: Developments in tyre design for lower rolling resistance: a state of the art review. Proc. Inst. Mech. Eng., Part D, J. Automob. Eng. 232(14), 1865–1882 (2018). https:\u002F\u002Fdoi.org\u002F10.1177\u002F0954407017727195\nMandal, A., Pan, S., Mukherjee, S., Saha, A.K., Thomas, S., Sengupta, A.: Variations in specific heat and microstructure in natural rubber filled with different fillers as studied by differential scanning calorimetry. Polym. Biopolym. Phys. Chem. 2(1), 25–28 (2014). https:\u002F\u002Fdoi.org\u002F10.12691\u002Fjpbpc-2-1-4\nNamjoo, M., Golbakhshi, H.: Finite element analysis for estimating the effect of various working conditions on the temperature gradients created inside a rolling tire. Int. J. Eng. 27(12C), 1920–1927 (2014). https:\u002F\u002Fdoi.org\u002F10.5829\u002Fidosi.ije.2014.27.12c.16\nQin, Y., Hiller, J.E.: Ways of formulating wind speed in heat convection significantly influencing pavement temperature prediction (2013). https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs00231-013-1116-0\nHolzapfel, G.: Nonlinear Solid Mechanics: A Continuum Approach for Engineering. Wiley, New York (2000)\nReoroji, N., Vol, G.: Filler effects on temperature shift factors in viscoelastic properties of carbon black filled rubbers. Nihon Reoroji Gakkaishi 41(3), 137–144 (2013)\nÖsterlöf, R., Wentzel, H., Kari, L.: An efficient method for obtaining the hyperelastic properties of filled elastomers in finite strain applications. Polym. Test. 41, 44–54 (2015)\nMelly, S.K., Liu, L., Liu, Y., Leng, J.: A review on material models for isotropic hyperelasticity. Int. J. Mech. Syst. Dyn. 1(1), 71–88 (2021). https:\u002F\u002Fdoi.org\u002F10.1002\u002Fmsd2.12013\nDaesa, C., Rodkwan, S.: Prediction of rolling resistance coefficient of retreaded truck tyres through numerical simulation. Maejo Int. J. Sci. Technol. 12(2), 152–166 (2018)\nMashadi, B., Ebrahimi-Nejad, S., Abbaspour, M.: A rolling resistance estimate using nonlinear finite element numerical analysis of a full three-dimensional tyre model. Proc. Inst. Mech. Eng., Part D, J. Automob. Eng. 233(1), 147–160 (2019). https:\u002F\u002Fdoi.org\u002F10.1177\u002F0954407018802733\nAustrell, P.-E., Olsson, A.K.: Considering amplitude dependence during cyclic loading of elastomers using an equivalent viscoelastic approach. Polym. Test. 31(7), 909–915 (2012)\nBergström, J.S., Boyce, M.C.: Constitutive modeling of the time-dependent and cyclic loading of elastomers and application to soft biological tissues. Mech. Mater. 33, 523–530 (2001). https:\u002F\u002Fdoi.org\u002F10.1016\u002FS0167-6636(01)00070-9\nRafei, M., Ghoreishy, M.H.R., Naderi, G.: Computer simulation of tire rolling resistance using finite element method: effect of linear and nonlinear viscoelastic models. Proc. Inst. Mech. Eng., Part D, J. Automob. Eng. 233(11), 2746–2760 (2019). https:\u002F\u002Fdoi.org\u002F10.1177\u002F0954407018804117\nBergström, J.S., Boyce, M.C.: Deformation of elastomeric networks: relation between molecular level deformation and classical statistical mechanics models of rubber elasticity. Macromolecules 34(3), 614–626 (2001). https:\u002F\u002Fdoi.org\u002F10.1021\u002Fma0007942\nBergström, J.S., Boyce, M.C.: Large strain time-dependent behavior of filled elastomers. Mech. Mater. 32(11), 627–644 (2000). https:\u002F\u002Fdoi.org\u002F10.1016\u002FS0167-6636(00)00028-4\nBrowne, A.L., Wickliffe, L.E.: Parametric study of convective heat transfer coefficients at the tire surface. Tire Sci. Technol. 8(3–4), 37–67 (1980). https:\u002F\u002Fdoi.org\u002F10.2346\u002F1.2151020\nAssaad, M.C., et al.: Thin-film heat flux sensor for measuring the film coefficient of rubber components of a rolling tire. Tire Sci. Technol. 36(4), 275–289 (2008). https:\u002F\u002Fdoi.org\u002F10.2346\u002F1.2999702",{"EN":190},"Rolling resistance dictates a large part of the energy consumption of trucks. Therefore, it is necessary to have a sound understanding of the parameters affecting rolling resistance. This article proposes a semi-physical thermodynamic tyre rolling resistance model, which captures the essential properties of rolling resistance, such as transient changes due to temperature effects and the strain-amplitude dependency of the viscous properties. In addition, the model includes cooling effects from the surroundings. Both tyre temperature and rolling resistance are obtained simultaneously in the simulation model for each time step. The nonlinear viscoelasticity in rubber is modelled using the Bergström–Boyce model, where the viscous creep function is scaled with temperature changes. The cooling of the tyre is considered with both convective and radiative cooling. Moreover, the article explains different material parameters and their physical meaning. 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Smart Mater. Struct. 21, 125013 (2012)\nAkbarzadeh, A.H., Chen, Z.T.: Hygrothermal stresses in one-dimensional functionally graded piezoelectric media in constant magnetic field. Compos. Struct. 97, 317–331 (2013)\nAllam, M.N.M., Zenkour, A.M., Tantawy, R.: Analysis of functionally graded piezoelectric cylinders in a hygrothermal environment. Adv. Appl. Math. Mech. 6, 233–246 (2014)\nAvellaneda, M., Harshe, G.: Magnetoelectric effect in piezoelectric\u002Fmagnetostrictive multilayer composites. J. Intell. Mater. Syst. Struct. 5, 501–513 (1994)\nBabaei, M.H., Chen, Z.T.: Exact solutions for radially polarized and magnetized magneto electro elastic rotating cylinders. Smart Mater. Struct. 17, 025035 (2008)\nBakhshizadeh, A., Nejad, M.Z., Kashkoli, M.D.: Time-dependent hygro-thermal creep analysis of pressurized FGM rotating thick cylindrical shells subjected to uniform magnetic field. J. Mech. Phys. 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Smart Mater. Struct. 13, 762 (2004)\nJabbari, M., Sohrabpour, S., Eslami, M.R.: Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads. Int. J. Press. Vessels Piping 79, 493–497 (2002)\nJafari Fesharaki, J., Loghman, A., Yazdipoor, M., Golabi, S.: Semi-analytical solution of time-dependent thermomechanical creep behavior of FGM hollow spheres. Mech. Time-Depend. Mater. 18, 41–53 (2014)\nJamian, S., Sato, H., Tsukamoto, H., Watanabe, Y.: Creep analysis of functionally graded material thick-walled cylinder. Appl. Mech. Mater. 315, 867–871 (2013)\nKashkoli, M.D., Tahan, K.N., Nejad, M.Z.: Time-dependent creep analysis for life assessment of cylindrical vessels using first order shear deformation theory. J. Mech. 33, 461–474 (2017a)\nKashkoli, M.D., Tahan, K.N., Nejad, M.Z.: Time-dependent thermomechanical creep behavior of FGM thick hollow cylindrical shells under non-uniform internal pressure. Int. J. Appl. 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Smart Struct. Syst. 15, 1411–1437 (2015a)\nSaadatfar, M., Aghaie-Khafri, M.: Hygrothermal analysis of a rotating smart exponentially graded cylindrical shell with imperfect bonding supported by an elastic foundation. Aerosp. Sci. Technol. 43, 37–50 (2015b)\nSaadatfar, M., Aghaie-Khafri, M.: On the magneto-thermo-elastic behavior of a FGM cylindrical shell with pyroelectric layers featuring interlaminar bonding imperfections rested in an elastic foundation. J. Solid Mech. 7, 344–363 (2015c)\nSaadatfar, M., Aghaie-Khafri, M.: On the behavior of a rotating functionally graded hybrid cylindrical shell with imperfect bonding subjected to hygrothermal condition. J. Therm. Stresses 38, 854–881 (2015d)\nSharma, S., Sahay, I., Kumar, R.: Creep transition in non-homogeneous thick-walled circular cylinder under internal and external pressure. Appl. Math. Sci. 122, 6075–6080 (2012)\nSharma, S., Yadav, S., Sharma, R.: Thermal creep analysis of functionally graded thick-walled cylinder subjected to torsion and internal and external pressure. J. Mech. Phys. Solids 9, 302–318 (2017)\nSingh, T., Gupta, V.K.: Effect of anisotropy on steady state creep in functionally graded cylinder. Compos. Struct. 93, 747–758 (2011)\nSingh, T., Gupta, V.K.: Analysis of steady state creep in whisker reinforced functionally graded thick cylinder subjected to internal pressure by considering residual stress. Mech. Adv. Mat. Struct. 21, 384–392 (2014)\nSmittakorn, W., Heyliger, P.R.: A discrete-layer model of laminated hygrothermopiezoelectric plates. Mech. Compos. Mater. Struct. 7, 79–104 (2000)\nSmittakorn, W., Heyliger, P.R.: An adaptive wood composite: theory. Wood Fiber Sci. 33, 595–608 (2001)\nWang, H.M., Ding, H.J.: Transient responses of a special non-homogeneous magneto-electro-elastic hollow cylinder for a fully coupled axisymmetric plane strain problem. Acta Mech. 184, 137–157 (2006)\nZenkour, A.M.: Bending analysis of piezoelectric exponentially graded fiber-reinforced composite cylinders in hygrothermal environments. Int. J. Mech. Mater. Des. 13, 515–529 (2017)",{"EN":491},"In this paper, we investigate the history of radial displacement, stresses, electric potential, and magnetic potential of a functionally graded magneto-electro-elastic (FGMEE) hollow cylinder subjected to an axisymmetric hygro-thermo-magneto-electro-mechanical loading for the plane strain condition. The material properties are taken as a power-law function of radius. Using stress-displacement relations, equations of equilibrium, electrostatic and magnetostatic equations, we find a differential equation including creep strains. Initially, eliminating creep strains, we obtain an analytical solution for the primitive stresses and electric and magnetic potential. In the next step, considering creep strains, we find the creep stress rates by applying the Norton law and Prandtl–Reuss equations for steady-state hygrothermal boundary condition. Finally, using an iterative method, we find the time-dependent creep stresses, radial displacement, and magnetic and potential field redistributions at any time. 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Chem. Phys. 43, 1965, 139-144.\nArcan, M., Hashin, Z. and Voloshin, A., 'A method to produce uniform plane-stress states with applications to fiber-reinforced materials', Exp. Mech. 18, 1978, 141-146.\nArcan, M., 'Discussion of the Iosipescu shear test as applied to composite materials', Exp. Mech. 24(1), 1984, 66-67.\nBland, D.R., The Theory of Linear Viscoelasticity, Pergamon Press, New York, 1960.\nChristensen, R.M., Theory of Viscoelasticity: An Introduction, Academic Press, New York, 1971.\nDuran, R.S. and McKenna, G.B., 'A torsional dilatometer for volume change measurements on deformed glasses: Instrument description and measurements on equilibrated glasses', J. Rheol. 34, 1990, 813-839.\nFlügge, W., Viscoelasticity, Springer-Verlag, New York, 1975.\nGoldenberg, N., Arcan, M. and Nicolau, E., 'On the most suitable specimen shape for testing shear strength of plastics', ASTM STP 247, 1958, 115-121.\nGoldstein, M., 'Some thermodynamic aspects of the glass transition: Free volume, entropy and enthalpy theories', J. Chem. Phys. 39, 1963, 3369-3374.\nGonzalez, J. and Knauss, W.G., 'Strain inhomogeneity and discontinuous crack growth in a particulate composite', J. Mech. Phys. Solids 46, 1998, 1981-1995.\nGross, B., Mathematical Structure of the Theories of Viscoelasticity, Hermann, Paris, 1968.\nHung, S.C. and Liechti, K.M., 'An evaluation of the Arcan specimen for determining the shear moduli of fiber reinforced composites', Exp. Mech. 37, 1997, 460-468.\nHung, S.C. and Liechti, K.M., 'Finite element analysis of the Arcan specimen for fiber Reinforced composites under pure shear and biaxial loading', J. Comp. Mater. 33, 1999, 1288-1317.\nKnauss, W.G. and Emri, I., 'Non-linear viscoelasticity based on free volume consideration', Comput. & Structures, 13, 1981, 123-128.\nKnauss, W.G. and Emri, I., 'Volume change and the nonlinearly thermo-viscoelastic constitution of polymers', Polym. Engrg. Sci. 27, 1987, 86-100.\nKnauss, W.G and Zhu, W., 'Nonlinearly viscoelastic behavior of polycarbonate I. Response under pure shear', Mech. Time-Dependent. Mater. 6, 2002, 231-269.\nLiang, Y.M. and Liechti, K., 'On the large deformation and localization behavior of an epoxy resin under multiaxial stress states', Internat. J. Solids Struct. 33, 1996, 1479-1500.\nLu, H. and Knauss, W.G., 'The role of dilatation in the nonlinearly viscoelastic behavior of PMMA under multiaxial stress states', Mech. Time-Dependent. Mater. 2(4), 1999, 307-334.\nLustig, S.R., Shay, R.M. and Caruthers, J.M., 'Thermodynamic constitutive equations for materials with memory on a material time scale', J. Rheol. 40, 1996, 69-106.\nPoynting, J.H., 'On the change in the dimensions of a steel wire when twisted, and on the pressure of distorsional waves in steel', Proc. Roy. Soc. London Ser. A. Phys. Sci. 86, 1912, 534-561.\nRobertson, R.E. and Patel, A.M., 'Tthe elastic, anelastic and plastic components of strain in the loadextension curve for bisphenol-A polycarbonate', Polym. Engrg. Sci. 12, 1972, 346-352.\nSane, S. and Knauss, W.G., 'The time-dependent bulk response of poly (methyl methacrylate)', Mech. Time-Dependent Mater. 5, 2001, 293-324.\nSchapery, R.A., 'Nonlinear viscoelastic and viscoplastic constitutive equations based on thermodynamics', Mech. Time-Dependent Mater. 1, 1997, 209-240.\nSchapery, R.A., 'An engineering theory of nonlinear viscoelasticity with applications', Internat. J. Solids Struct. 2, 1969, 407-425\nSchapery, R.A., 'A theory of nonlinear thermoviscoelasticity based on irreversible thermodynamics', in Proceedings 5th U.S. National Congress of Applied Mechanics, ASME, New York, 1966, 511-530.\nSchapery, R.A., 'Approximate methods of transform inversion for viscoelastic stress analysis', in Proceedings 4th U.S. National Congress of Applied Mechanics, ASME, New York, 1962, 1075-1085.\nSutton, M.A., Wolters, W.J., Peters, W.H., Ranson, W.F. and McNeil, S.R., 'Determination of displacements using an improved digital image correlation method', Image Vis. Comput. 1, 1983, 133-139.\nVendroux G. and KnaussW.G., 'Submicron deformation fieldmeasurements: Part 2. Improved digital image correlation', Exp. Mech. 38, 1998, 86-92.\nWineman, A.S. and Waldron, W.K., Jr., 'Yieldlike response of a compressible nonlinear viscoelastic solid', J. Rheol. 39, 1995, 401-423.",{"EN":855},"The creep responses of (bisphenol A) polycarbonate at 80°C undercombined two-dimensional shear with superposed tensile and compressivestress states were measured on Arcan specimens in the nonlinearlyviscoelastic regime. Of particular interest is the influence of thedilatational deformation component on the nonlinearly viscoelastic creepbehavior. Because the nonlinear material response determines the stressdistribution under fixed deformation or load, but is not known a priori,a re-estimation of the latter is essential to verify or adjust thestress state(s). This is accomplished by approximating isochronalstress-strain relations derived from shear creep behavior, encompassingthe nonlinear domain, by a classical incremental elasto-plastic materialdescription at appropriate times. To the extent that the two-dimensionalcharacter of the test configuration permits accessing three-dimensionalinformation, a coherent representation of the results is examined interms of maximum shear and\u002For octahedral representation. It is found that the creep behavior under shear and normal stressor deformation imposition differ significantly: When viewed as aresponse to the imposition of a maximum shear stress, the creepresponses differ depending on whether one or the other dominates. On theother hand, if the response is formulated in terms of an octahedraldescription the representation becomes less sensitive to normal vs.shear behavior. It is clear in either case, however, that normal strainhas a disproportionately large effect on creep response in shear. Withinthe precision underlying the measurements it is found that the shear andnormal strain components accumulate under creep in nearly constantratios. Under this scenario it is demonstrated clearly that theinfluence of negative dilatational stress (or deformation) on pure sheardeformation leads to distinctly lower creep rates. The converse is true,if positive dilatational stresses are added, though not monotonically so.",{"EN":857},"Nonlinearly Viscoelastic Behavior of Polycarbonate. II. 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Arch. 28(1), 433–457 (2020)\nLiu, Q., Peng, Q., Ming, P.: A control volume finite element method for the thermoelastic problem in functional graded material with one relaxation time. Proc. Inst. Mech. Eng., Part C, J. Mech. Eng. Sci. 235(14), 2554–2569 (2021)\nLord, H.W., Shulman, Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15(5), 299–309 (1967)\nMalikan, M., Eremeyev, V.A.: On time-dependent nonlinear dynamic response of micro-elastic solids. Int. J. Eng. Sci. 182, 103793 (2023)\nMoaaz, O., Abouelregal, A.E., Awrejcewicz, J.: Theoretical investigation of a rotating thermomagnetic isotropic transverse-constrained annular cylinder with generalized Ohm’s law using the Moore–Gibson–Thompson model of heat transfer. Symmetry 15, 572 (2023)\nNadeem, M., He, J.H., He, C.H., Sedighi, H.M., Shirazi, A.: A numerical solution of nonlinear fractional Newell–Whitehead–Segel equation using natural transform. TWMS J. Pure Appl. Math. 13(2), 168–182 (2022)\nNasrollah Barati, A.H., Etemadi Haghighi, A.A., Haghighi, S.: Free and forced vibration analysis of shape memory alloy annular circular plate in contact with bounded fluid. Iran. J. Sci. Technol. Trans. Mech. Eng. 46(4), 1015–1030 (2022a)\nNowacki, W.: Dynamical problems of thermodiffusion in solids, I. Bull. Acad. Pol. Sci., Sér. Sci. Tech. 22, 55–64 (1974a)\nNowacki, W.: Dynamical problems of thermodiffusion in solids, II. Bull. Acad. Pol. Sci., Sér. Sci. Tech. 22, 129–135 (1974b)\nOlesiak, Z.S.: Problems of thermodiffusion of deformable solids. Matter Sci. 34, 297–303 (1998)\nPeng, W., Chen, L., He, T.: A modified fractional order thermo-viscoelastic theory with fractional order strain and its application in a thermo-viscoelastic problem containing a spherical cavity. Mech. Time-Depend. Mater. 26, 891–907 (2022). https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs11043-021-09518-9\nPodstrigac, J.C., Pavlina, V.S.: Fundamental equations of thermo-diffusion in isotropic deformable solids. Prikl. Mech. L 3 (1965). (In Russian)\nQuintanilla, R.: Moore–Gibson–Thompson thermoelasticity. Math. Mech. Solids 24, 4020–4031 (2019)\nQuintanilla, R.: Moore–Gibson–Thompson thermoelasticity with two temperatures. Appl. Eng. Sci. 1, 100006 (2020)\nRaddadi, M.H., Lotfy, K., Elidy, E.S., El-Bary, A., Tantawi, R.S.: A novel photo elasto-thermodiffusion waves with electron-holes in semiconductor materials with hyperbolic two temperature. Crystals 12, 1458 (2022)\nRoy Choudhuri, S.K.: On a thermoelastic three-phase-lag model. J. Therm. Stresses 30(3), 231–238 (2007)\nSae-Long, W., Limkatanyu, S., Sukontasukkul, P., Damrongwiriyanupap, N., Rungamornrat, J., Prachasaree, W.: Fourth-order strain gradient bar-substrate model with nonlocal and surface effects for the analysis of nanowires embedded in substrate media. Facta Univ., Mech. Eng. 19(4), 657–680 (2021)\nSafaei, B., Onyibo, E.C., Hurdoganoglu, D.: Thermal buckling and bending analyses of carbon foam beams sandwiched by composite faces under axial compression. Facta Univ., Mech. Eng. 20(3), 589–615 (2022)\nSherief, H.H., Hamza, F.A., Saleh, H.A.: The theory of generalized thermoelastic diffusion. Int. J. Eng. Sci. 42(5–6), 591–608 (2004)\nSingh, S.S., Debnath, S., Othman, M.I.: Thermoelastic theories on the refracted waves in microstretch thermoelastic diffusion media. Int. J. Appl. Mech. 14(2), 2250008 (2022)\nTiwari, R., Kumar, R., Abouelregal, A.E.: Analysis of a magneto-thermoelastic problem in a piezoelastic medium using the non-local memory-dependent heat conduction theory involving three phase lags. Mech. Time-Depend. Mater. 26, 271–287 (2022). https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs11043-021-09487-z\nVernotte, P.: Some possible complications in the phenomena of thermal conduction. C. R. Acad. Sci. Paris, Ser. II 252, 2190–2191 (1961)\nYadav, A.K.: Effect of impedance on the reflection of plane waves in a rotating magneto-thermoelastic solid half-space with diffusion. AIP Adv. 10(7), 075217 (2020)\nZenkour, A.M., Mashat, D.S., Abouelregal, A.E.: Generalized thermodiffusion for an unbounded body with a spherical cavity subjected to periodic loading. J. Mech. Sci. Technol. 26, 749–757 (2012)",{"EN":1588},"The main objective of the present paper is to investigate the relationship between the thermal processes and diffusion in thermoelastic solids. For this reason, a new model of thermo-diffusion interactions has been derived, which, unlike the traditional models, allows the thermo-diffusion waves to propagate at finite speeds. The Moore–Gibson–Thompson (MGT) equation is an essential part of the proposed model, as it is included in the mass diffusion and thermal conductivity equations by adding two relaxation times. The introduced model is then used to investigate a one-dimensional thermodiffusion problem for a homogeneous spherical shell. In the field of the Laplace transform, the analytical expressions for different transformed thermophysical fields are found. Moreover, a numerical inversion algorithm is used to obtain the physical domain solutions. The differences between the presented model and previous theories are graphically presented and discussed in detail. It is exhibited that depending on the relaxation time taken into account, the magnitude of the mass flow rate and heat waves can meaningfully change.",{"EN":1590},"Thermodiffusion interactions in a homogeneous spherical shell based on the modified Moore–Gibson–Thompson theory with two time delays",{"VOID":1592},"10.1007\u002Fs11043-023-09598-9","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs11043-023-09598-9",[1595,1621,1636,1663],{"id":1596,"sortIndex":130,"researcher":20,"roles":1597,"affiliations":1598,"properties":1618},"ede29fb5-321e-40e5-bd1e-78985186a3a5",[203],[1599,1610],{"id":1600,"sortIndex":130,"affiliation":1601,"properties":1609},"7b4c3836-29cd-4111-b471-871cbed9dcf5",{"id":1602,"createTime":1603,"updateTime":1603,"relativeEntities":1604,"slug":1605,"properties":1606,"entityType":64,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"91495a4e-aa38-4d42-b862-658ff0f9d526","2024-04-16T09:55:54.545+00:00",[],"Department-of-Mathematics-College-of-Science-and-Arts-Jouf-University-Al-Qurayat-Saudi-Arabia",{"title":1607},{"EN":1608},"Department of Mathematics, College of Science and Arts, Jouf University, Al-Qurayat, Saudi Arabia",{},{"id":20,"sortIndex":21,"affiliation":1611,"properties":20},{"id":1612,"createTime":1613,"updateTime":1613,"relativeEntities":1614,"slug":20,"properties":1615,"entityType":64,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"cae36480-cb91-4d75-a8c7-fab73c8a5c62","2024-01-12T09:41:34.848+00:00",[],{"title":1616},{"VI":1617},"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt",{"title":1619},{"VI":1620},"Ahmed E. Abouelregal",{"id":1622,"sortIndex":132,"researcher":20,"roles":1623,"affiliations":1624,"properties":1633},"f7626f4c-2dce-43ed-b948-7d53f32c6ab6",[203],[1625],{"id":20,"sortIndex":21,"affiliation":1626,"properties":20},{"id":1627,"createTime":1628,"updateTime":1628,"relativeEntities":1629,"slug":20,"properties":1630,"entityType":64,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"23b425e1-3834-47dd-9cd8-8ffe8869af93","2023-12-05T22:29:55.583+00:00",[],{"title":1631},{"VI":1632},"Department of Mathematics, College of Science, Qassim University, Buraydah, Saudi Arabia",{"title":1634},{"VI":1635},"Rasmiyah A. Alharb",{"id":1637,"sortIndex":136,"researcher":20,"roles":1638,"affiliations":1639,"properties":1660},"601084b6-94a9-40cf-b548-6bdfc30e97f5",[203],[1640,1650],{"id":1641,"sortIndex":130,"affiliation":1642,"properties":1649},"6ae73622-bf23-4365-93be-33306f230f16",{"id":1643,"createTime":1644,"updateTime":1644,"relativeEntities":1645,"slug":20,"properties":1646,"entityType":64,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"e45ea3d3-0181-4835-a83b-51b1a79180f3","2024-01-25T06:53:29.023+00:00",[],{"title":1647},{"VI":1648},"Drilling Center of Excellence and Research Center, Shahid Chamran University of Ahvaz, Ahvaz, Iran",{},{"id":20,"sortIndex":21,"affiliation":1651,"properties":20},{"id":1652,"createTime":1653,"updateTime":1654,"relativeEntities":1655,"slug":1656,"properties":1657,"entityType":64,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"2cc6bf39-48cf-41a3-88b9-a25cae49cd2a","2024-04-11T23:44:00.088+00:00","2024-07-19T00:10:51.236+00:00",[],"Mechanical-Engineering-Department-Faculty-of-Engineering-Shahid-Chamran-University-of-Ahvaz-Ahvaz-Iran",{"title":1658},{"EN":1659},"Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran",{"title":1661},{"VI":1662},"Hamid M. Sedighi",{"id":1664,"sortIndex":21,"researcher":20,"roles":1665,"affiliations":1666,"properties":1679},"f952f7f3-c362-4f3d-aad2-1b5cef66129f",[203],[1667,1674],{"id":1668,"sortIndex":130,"affiliation":1669,"properties":1673},"c8dd0515-c820-4383-aa83-3db688984192",{"id":1612,"createTime":1613,"updateTime":1613,"relativeEntities":1670,"slug":20,"properties":1671,"entityType":64,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},[],{"title":1672},{"VI":1617},{},{"id":20,"sortIndex":21,"affiliation":1675,"properties":20},{"id":1627,"createTime":1628,"updateTime":1628,"relativeEntities":1676,"slug":20,"properties":1677,"entityType":64,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},[],{"title":1678},{"VI":1632},{"title":1680},{"VI":1681},"Doaa Atta",{"url":1593,"publisher":1683,"properties":1711},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":1684,"slug":10,"properties":1685,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":1689,"manageAffiliations":1690,"indexDatabases":1691,"url":20,"thumbnailPath":20,"statistic":1706,"gsStatistic":20,"type":20,"analyzePriority":20},[],{"issn":1686,"eissn":1687,"title":1688},{"VOID":13},{"VOID":15},{"EN":17},[],[],[1692,1699],{"id":102,"indexDatabase":1693,"url":117,"indexYears":20,"academicFieldIds":1698,"indexDatabaseRanking":20},{"id":104,"createTime":105,"updateTime":106,"relativeEntities":1694,"label":1695,"description":1696,"key":113,"publicationTags":1697,"standard":20},[],{"EN":109,"VI":109},{"VI":111,"EN":112},[115,116],[119,120,121],{"id":80,"indexDatabase":1700,"url":93,"indexYears":94,"academicFieldIds":1705,"indexDatabaseRanking":100},{"id":82,"createTime":83,"updateTime":84,"relativeEntities":1701,"label":1702,"description":1703,"key":90,"publicationTags":1704,"standard":20},[],{"EN":87,"VI":87},{"EN":87,"VI":89},[92],[96,97,98,99],{"impactFactor":21,"impactFactorByYear":1707,"i10Index":135,"i10IndexLast5Year":136,"totalPublication":137,"totalPublicationByYear":1708,"totalCitation":142,"totalCitationByYear":1709,"totalCitationPerPublication":159,"totalCitationPerPublicationByYear":1710,"hindexLast5Year":157,"hindex":157},{"2012":124,"2013":125,"2014":126,"2015":127,"2016":128,"2017":129,"2018":129,"2019":130,"2020":131,"2021":132,"2022":133,"2023":134},{"2005":132,"2006":132,"2007":132,"2008":130,"2009":139,"2010":130,"2011":133,"2012":136,"2013":139,"2014":140,"2015":132,"2016":140,"2017":132,"2018":130,"2019":130,"2020":132,"2021":136,"2022":140,"2023":141,"2024":139},{"2005":144,"2006":145,"2007":146,"2008":147,"2009":148,"2010":141,"2011":149,"2012":150,"2013":151,"2014":152,"2015":153,"2016":154,"2017":155,"2018":75,"2019":140,"2020":156,"2021":141,"2022":157,"2023":158,"2024":136},{"2005":161,"2006":162,"2007":163,"2008":147,"2009":164,"2010":141,"2011":165,"2012":166,"2013":167,"2014":157,"2015":168,"2016":169,"2017":170,"2018":75,"2019":140,"2020":171,"2021":172,"2022":173,"2023":174,"2024":175},{"pages":1712},{"VOID":297},"2023-04-11",{"id":1715,"createTime":1716,"updateTime":1717,"relativeEntities":1718,"slug":1719,"properties":1720,"entityType":195,"verifyStatus":196,"verifyTime":1717,"verifyNote":197,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":1729,"fullTextUrl":20,"authors":1730,"publicationType":265,"publisherRelationship":1799,"citationCount":20,"citationInfo":20,"publishDate":1833,"publishYear":1834,"citationAnalyzeStatus":19,"lastCitationAnalyze":20,"indexDatabases":20,"openAccess":20,"references":20,"isForceReanalyzing":300},"f2b1ac4a-9ac3-4e33-a637-7a70f11efa77","2024-01-17T01:34:27.236+00:00","2025-02-01T23:41:00.577+00:00",[],"A-fractional-derivative-approach-to-full-creep-regions-in-salt-rock",{"references":1721,"abstract":1723,"title":1725,"doi":1727},{"VOID":1722},"Adolfsson, K., Enelund, M., Olsson, P.: On the fractional order model of viscoelasticity. Mech. Time-Depend. Mater. 9, 15–34 (2005)\nBagley, R.L., Torvik, P.J.: Fractional calculus—a different approach to the analysis of viscoelastically damped structures. AIAA J. 21, 741–748 (1983)\nBagley, R.L., Torvik, P.J.: Fractional calculus in the transient analysis of viscoelastically damped structures. AIAA J. 23, 918–925 (1985)\nBarpi, F., Valente, S.: A fractional order rate approach for modeling concrete structures subjected to creep and fracture. Int. J. Solids Struct. 41, 2607–2621 (2004)\nBazant, Z.P., Xi, Y.: Drying creep of concrete: constitutive model and new experiments separating its mechanism. Mater. Struct. 27, 3–14 (1994)\nCarter, N.L., Hansen, F.D.: Creep of rock salt. Tectonophysics 92, 275–333 (1983)\nCarter, N.L., Horseman, S.T., Russell, J.E., Handin, J.: Rheology of salt rock. J. Struct. Geol. 15, 1257–1272 (1993)\nChan, K.S., Bodner, S.R., Fossum, A.F., Munson, D.E.: A damage mechanics treatment of creep failure in rock salt. Int. J. Damage Mech. 6, 121–152 (1997)\nCristescu, N.D.: A general constitutive equation for transient and stationary creep of rock salt. Int. J. Rock Mech. Min. Sci. 30, 125–140 (1993)\nHerrmann, R.: Fractional Calculus: An Introduction for Physicists. World Scientific, Singapore (2011)\nHomand-Etienne, F., Houpert, R.: Thermally induced microcracking in granites: characterization and analysis. Int. J. Rock Mech. Min. Sci. 26, 125–134 (1989)\nHou, Z.: Mechanical and hydraulic behaviour of salt in the excavation disturbed zone around underground facilities. Int. J. Rock Mech. Min. Sci. 40, 725–738 (2003)\nJin, J., Cristescu, N.D.: An elastic\u002Fviscoplastic model for transient creep of rock salt. Int. J. Plast. 14, 85–107 (1998)\nKilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)\nKing, M.S.: Creep in model pillars of Saskatchewan potash. Int. J. Rock Mech. Min. Sci. 10, 363–371 (1973)\nKoeller, R.C.: Application of fractional calculus to the theory of viscoelasticity. J. Appl. Mech. 51, 299–307 (1984)\nKoeller, R.C.: Toward an equation of state for solid materials with memory by use of the half-order derivative. Acta Mech. 191, 125–133 (2007)\nKoeller, R.C.: A theory relating creep and relaxation for linear materials with memory. J. Appl. Mech. 77, 1–9 (2010)\nKrishnan, B., Jitendra, S.V., Raghu, V.P.: Creep damage characterization using a low amplitude nonlinear ultrasonic technique. Mater. Charact. 62, 275–286 (2011)\nMainardi, F.: Fractional Calculus and Waves in Linear Viscoelasticity. World Scientific, Singapore (2010)\nMetzler, R., Nonnenmacher, T.F.: Fractional relaxation processes and fractional rheological models for the description of a class of viscoelastic materials. Int. J. Plast. 19, 941–959 (2003)\nOrtigueira, M.D.: Fractional Calculus for Scientists and Engineers. Springer, Berlin (2011)\nPodlubny, I.: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Academic Press, San Diego (1999)\nRogers, L.: Operators and fractional derivatives for viscoelastic constitutive equations. J. Rheol. 27, 351–372 (1983)\nSenseny, P.E., Hansen, F.D., Russell, J.E., Carter, N.L., Handin, J.: Mechanical behavior of rock salt: phenomenology and micromechanisms. Int. J. Rock Mech. Min. Sci. 29, 363–378 (1992)\nScott Blair, G.W.: The role of psychophysics in rheology. J. Colloid Sci. 2, 21–32 (1947)\nTan, T.K., Kang, W.F.: Locked in stresses, creep and dilatancy of rocks constitutive equation. Rock Mech. Rock Eng. 13, 5–22 (1980)\nTang, S., Green, M.S., Liu, W.K.: Two-scale mechanism-based theory of nonlinear viscoelasticity. J. Mech. Phys. Solids 60, 199–226 (2012)\nUrai, J.L., Spiers, C.J., Hendrik, H.J., Zwart, H.J., Lister, G.S.: Weakening of rock-salt by water during long-term creep. Nature 324, 554–557 (1986)\nWelch, S.W.J., Rorrer, R.A.L., Duren, J.R.G.: Application of time-based fractional calculus methods to viscoelastic creep and stress relaxation of materials. Mech. Time-Depend. Mater. 3, 279–303 (1999)\nYang, C.H., Daemen, J.J.K., Yin, J.H.: Experimental investigation of creep behavior of salt rock. Int. J. Rock Mech. Min. Sci. 36, 233–242 (1999)\nZhou, H.W., Wang, C.P., Duan, Z.Q., Han, B.B.: Time-dependent constitutive model of rock salt based on Caputo fractional derivative. In: Hou, Z.M., Xie, H., Yoon, J.S. (eds.) Underground Storage of CO2 and Energy, pp. 161–165. CRC Press, Leiden (2010)\nZhou, H.W., Wang, C.P., Han, B.B., Duan, Z.Q.: A creep constitutive model for salt rock based on fractional derivatives. Int. J. Rock Mech. Min. Sci. 48, 116–121 (2011)\nZhou, H.W., Wang, C.P., Duan, Z.Q., Zhang, M., Liu, J.F.: Time-based fractional derivative approach to creep constitutive model of salt rock. Sci. China Ser. G, Phys. Mech. Astron. 42, 310–318 (2012) (in Chinese)",{"EN":1724},"Based on the definition of the constant-viscosity Abel dashpot, a new creep element, referred to as the variable-viscosity Abel dashpot, is proposed to characterize damage growth in salt rock samples during creep tests. Ultrasonic testing is employed to determine a formula of the variable viscosity coefficient, indicating that the change of the variable viscosity coefficient with the time meets a negative exponent law. In addition, by replacing the Newtonian dashpot in the classical Nishihara model with the variable-viscosity Abel dashpot, a damage-mechanism-based creep constitutive model is proposed on the basis of time-based fractional derivative. The analytic solution for the fractional-derivative creep constitutive model is presented. The parameters of the fractional derivative creep model are determined by the Levenberg–Marquardt method on the basis of the experimental results of creep tests on salt rock. Furthermore, a sensitivity study is carried out, showing the effects of stress level, fractional derivative order and viscosity coefficient exponent on creep strain of salt rock. It is indicated that the fractional derivative creep model proposed in the paper provides a precise description of full creep regions in salt rock, i.e., the transient creep region (the primary region), the steady-state creep region (the secondary region) and the accelerated creep region (the tertiary region).",{"EN":1726},"A fractional derivative approach to full creep regions in salt rock",{"VOID":1728},"10.1007\u002Fs11043-012-9193-x","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs11043-012-9193-x",[1731,1746,1758,1775,1787],{"id":1732,"sortIndex":130,"researcher":20,"roles":1733,"affiliations":1734,"properties":1743},"a8e3a634-e0a1-4109-a10d-5fbec8f673ac",[203],[1735],{"id":20,"sortIndex":21,"affiliation":1736,"properties":20},{"id":1737,"createTime":1738,"updateTime":1738,"relativeEntities":1739,"slug":20,"properties":1740,"entityType":64,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"576a24de-f8d5-4f6c-902d-e206c6b32096","2024-01-12T18:00:01.775+00:00",[],{"title":1741},{"VI":1742},"State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology, Beijing, China",{"title":1744},{"VI":1745},"C. P. Wang",{"id":1747,"sortIndex":133,"researcher":20,"roles":1748,"affiliations":1749,"properties":1755},"c2b75e11-66f6-4d80-8b88-452b7c05acbb",[203],[1750],{"id":20,"sortIndex":21,"affiliation":1751,"properties":20},{"id":1737,"createTime":1738,"updateTime":1738,"relativeEntities":1752,"slug":20,"properties":1753,"entityType":64,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},[],{"title":1754},{"VI":1742},{"title":1756},{"VI":1757},"J. Y. 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PLoS ONE 9(2), e85099 (2014)\nArshad, K., Abro, K.A., Tassddiq, A., Khan, I.: Atangana–Baleanu and Caputo–Fabrizio analysis of fractional derivatives for heat and mass transfer of second grade fluids over a vertical plate: a comparative study. Entropy 19, 1–12 (2017)\nAsjad, M.I., Shah, N.A., Aleem, M., Khan, I.: Heat transfer analysis of fractional second-grade fluid subject to Newtonian heating with Caputo and Caputo–Fabrizio fractional derivatives: a comparison. Eur. Phys. J. Plus 132, 340–359 (2017)\nAtangana, A., Baleanu, D.: New fractional derivatives with nonlocal and nonsingular kernel: theory and application to heat transfer model. Therm. Sci. 20, 1–7 (2016)\nAzhar, W.A., Fetecau, C., Vieru, D.: MHD free convection flow of a viscous fluid in a rotating system with damped thermal transport, hall current and slip effects. Eur. Phys. J. Plus 133, 353 (2018)\nBagley, R.L., Torvik, P.J.: A theoretical basis for the application of fractional calculus to viscoelasticity. J. Rheol. 27(3), 201–210 (1983)\nBandelli, R.: Unsteady unidirectional flows of second grade fluids in domains with heated boundary. Int. J. Non-Linear Mech. 30, 263–269 (1995)\nCaputo, M., Fabrizio, M.: A new definition of fractional derivative without singular kernel. Prog. Fract. Differ. Appl. 1, 1–13 (2015)\nCaputo, M., Mainardi, F.: A new dissipation model based on memory mechanism. Pure Appl. Geophys. 91(1), 134–147 (1971)\nFetecau, C.: The Rayleigh–Stokes problem for heated second grade fluids. Int. J. Non-Linear Mech. 37, 1011–1015 (2002)\nGhoshdastidar, P.S.: Heat Transfer. Oxford University Press, Oxford (2004)\nHayat, T., Abbas, Z.: Heat transfer analysis on the MHD flow of a second grade fluid in a channel with porous medium. Chaos Solitons Fractals 38(2), 556–567 (2008)\nHonig, G., Hirdes, U.: A method for the numerical inversion of Laplace transforms. J. Comput. Appl. Math. 10(1), 113–132 (1984)\nHristove, J.: Frontiers in Fractional Calculus, 1st edn. pp. 235–295. Bentham Science Publishers, Sharjah (2017). Edited by Sanchin Bhalekar, Chap. 10\nHussanan, A.: Natural convection flow past an oscillating plate with Newtonian heating. Heat Transf. Res. 45, 119–135 (2014)\nImran, M.A., Sarwar, S., Abdullah, M., Khan, I.: An analysis of the semi-analytic solutions of a viscous fluid with old and new definitions of fractional derivatives. Chin. J. Phys. 56, 1853–1871 (2018)\nImran, M.A., Aleem, M., Riaz, M.B., Ali, R., Khan, I.: A comprehensive report on convective flow of fractional (ABC) and (CF) MHD viscous fluid subject to generalized boundary conditions. Chaos Solitons Fractals 118, 274–289 (2019)\nKhan, M., Iqbal, K., Azram, M.: Closed form solutions for MHD flow of a second grade fluid through porous space. Spec. Top. Rev. Porous Media Int. J. 2(2), 125–132 (2011)\nKilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, vol. 204. Elsevier Science, New York (2006)\nKuhlman, K.L.: Review of inverse Laplace transform algorithms for Laplace-space numerical approaches. Numer. Algorithms 63(2), 339–355 (2013)\nMakris, N., Dargush, G.F., Constantinou, M.C.: Dynamic analysis of generalized viscoelastic fluids. J. Eng. Mech. 119, 1663–1679 (1963)\nMerkin, J.H.: Natural convection boundary-layer plow on a vertical surface with Newtonian heating. Int. J. Heat Fluid Flow 15, 392–398 (1994)\nMiller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York (1993)\nMustafa, N., Asghar, S., Hossain, M.A.: Natural convection flow of second grade fluid along a vertical heated surface with power-law temperature. Chem. Eng. Commun. 195, 209–228 (2007)\nNarahari, M.: Newtonian heating and mass transfer on free convection flow past an accelerated plate in the presence of thermal radiation. AIP Conf. Proc. 1482, 340–346 (2012)\nNarahari, M., Dutta, B.K.: Effect of thermal radiation and mass diffusion on free convection flow near a vertical plate with Newtonian heating. Chem. Eng. Commun. 199, 628–643 (2012)\nPovstenko, Y.: Fractional thermoelasticity. In: Hetnarski, R.B. (ed.) Encyclopedia of Thermal Stresses, vol. 4, pp. 1778–1787. Springer, New York (2014)\nQasim, M., Khan, I., Shafie, S.: Heat transfer in a micropolar fluid over a stretching sheet with Newtonian heating. PLoS ONE 8, e59393 (2013)\nRamzan, M.: MHD three-dimensional flow of couple stress fluid with Newtonian heating. Eur. Phys. J. Plus 128, 49 (2013)\nSaad, K.M.: Comparing the Caputo, Caputo–Fabrizio and Atangana–Baleanu derivative with fractional order: fractional cubic isothermal auto-catalytic chemical system. Eur. Phys. J. Plus 133, 94 (2018)\nSheikh, N.A., Ali, F., Saqib, M., Khan, I., Jan, S.A.A., Alshomrani, A.S., Alghamdi, M.S.: Comparison and analysis of the Atangana–Baleanu and Caputo–Fabrizio fractional derivatives for generalized Casson fluid model with heat generation and chemical reaction. Results Phys. 7, 789–800 (2017)\nSheoran, S.S., Kundu, P.: Fractional order generalized thermoelasticity theories: a review. Int. J. Adv. Math. Mech. 3(4), 76–81 (2016)\nTan, W., Masuoka, T.: Stokes first problem for a second grade fluid in a porous half-space with heated boundary. Int. J. Non-Linear Mech. 40, 515–522 (2005)\nToki, C.K., Tokis, J.N.: Exact solutions of the unsteady free convection flows on porous plate with time-dependent heating. Z. Angew. Math. Mech. 87(1), 4–14 (2007)\nVieru, D., Fetecau, C., Fetecau, C., Nigar, N.: Magnetohydrodynamic natural convection flow with Newtonian heating and mass diffusion over an infinite plate that applies shear stress to a viscous fluid. Z. Naturforsch. 69a, 714–724 (2014)\nVieru, D., Imran, M.A., Rauf, A.: Slip effect on free convection flow of second grade fluids with ramped wall temperature. Int. J. Heat Transf. Res. 46, 713–724 (2015)",{"EN":1845},"Unsteady free convection flows of an incompressible differential type fluid over an infinite vertical plate with fractional thermal transport are studied. Modern definitions of the fractional derivatives in the sense of Atangana–Baleanu (ABC) and Caputo Fabrizio (CF) are used in the constitutive equations for the thermal flux. Exact solutions in both cases of the (ABC) and (CF) derivatives for the dimensionless temperature and velocity fields are established by using the Laplace transform technique. Solutions for the ordinary case and some well-known results from the literature are recovered as a limiting case. Expressions for Nusselt number and Skin friction coefficient are also determined. The influence of the pertinent parameters on temperature and velocity fields are discussed graphically. A comparison of ordinary model, and (ABC) and (CF) models are also depicted. It is found that memory of the physical aspects of the problem is well explained by fractional order (ABC) and (CF) models as compared to ordinary one. 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