Numerical study of Casson nanofluid over an elongated surface in presence of Joule heating and viscous dissipation: Buongiorno model analysis

[1]          L. J. Crane, Flow past a stretching plate, Zeitschrift für angewandte Mathematik und Physik ZAMP, Vol. 21, No. 4, pp. 645-647, 1970.

[2]          T. Mahapatra, A. Gupta, Heat transfer in stagnation-point flow towards a stretching sheet, Heat and Mass transfer, Vol. 38, No. 6, pp. 517-521, 2002.

[3]          J. Misra, A. Sinha, Effect of thermal radiation on MHD flow of blood and heat transfer in a permeable capillary in stretching motion, Heat and Mass Transfer, Vol. 49, No. 5, pp. 617-628, 2013.

[4]          S. Mukhopadhyay, P. R. De, K. Bhattacharyya, G. Layek, Casson fluid flow over an unsteady stretching surface, Ain Shams Engineering Journal, Vol. 4, No. 4, pp. 933-938, 2013.

[5]          G. Seth, R. Tripathi, M. Mishra, Hydromagnetic thin film flow of Casson fluid in non-Darcy porous medium with Joule dissipation and Navier’s partial slip, Applied Mathematics and Mechanics, Vol. 38, No. 11, pp. 1613-1626, 2017.

[6]          D. Gopal, N. Kishan, C. Raju, Viscous and Joule's dissipation on Casson fluid over a chemically reacting stretching sheet with inclined magnetic field and multiple slips, Informatics in medicine Unlocked, Vol. 9, pp. 154-160, 2017.

[7]          P. Sreenivasulu, T. Poornima, N. B. Reddy, Influence of joule heating and non-linear radiation on MHD 3D dissipating flow of casson nanofluid past a non-linear stretching sheet, Nonlinear Engineering, Vol. 8, No. 1, pp. 661-672, 2019.

[8]          M. Abd El-Aziz, A. A. Afify, MHD Casson fluid flow over a stretching sheet with entropy generation analysis and Hall influence, Entropy, Vol. 21, No. 6, pp. 592, 2019.

[9]          M. Das, G. Mahanta, S. Shaw, S. Parida, Unsteady MHD chemically reactive double‐diffusive Casson fluid past a flat plate in porous medium with heat and mass transfer, Heat Transfer—Asian Research, Vol. 48, No. 5, pp. 1761-1777, 2019.

[10]        C. K. Kumar, S. Srinivas, A. S. Reddy, MHD pulsating flow of Casson nanofluid in a vertical porous space with thermal radiation and Joule heating, Journal of Mechanics, Vol. 36, No. 4, pp. 535-549, 2020.

[11]        B. Gireesha, C. Srinivasa, N. Shashikumar, M. Macha, J. Singh, B. Mahanthesh, Entropy generation and heat transport analysis of Casson fluid flow with viscous and Joule heating in an inclined porous microchannel, Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, Vol. 233, No. 5, pp. 1173-1184, 2019.

[12]        B. Kumar, S. Srinivas, Unsteady hydromagnetic flow of Eyring-Powell Nanofluid over an inclined permeable stretching sheet with joule heating and thermal radiation, Journal of applied and computational mechanics, Vol. 6, No. 2, pp. 259-270, 2020.

[13]        M. A. El-Aziz, A. Afify, Effect of Hall current on MHD slip flow of Casson nanofluid over a stretching sheet with zero nanoparticle mass flux, Thermophysics and Aeromechanics, Vol. 26, No. 3, pp. 429-443, 2019.

[14]        S. Ibrahim, P. Kumar, G. Lorenzini, E. Lorenzini, Influence of Joule heating and heat source on radiative MHD flow over a stretching porous sheet with power-law heat flux, Journal of Engineering Thermophysics, Vol. 28, No. 3, pp. 332-344, 2019.

[15]        K. Das, P. R. Duari, P. K. Kundu, Nanofluid flow over an unsteady stretching surface in presence of thermal radiation, Alexandria engineering journal, Vol. 53, No. 3, pp. 737-745, 2014.

[16]        B. Nagaraja, B. Gireesha, Exponential space-dependent heat generation impact on MHD convective flow of Casson fluid over a curved stretching sheet with chemical reaction, Journal of Thermal Analysis and Calorimetry, Vol. 143, No. 6, pp. 4071-4079, 2021.

[17]        B. Rout, S. Mishra, Thermal energy transport on MHD nanofluid flow over a stretching surface: a comparative study, Engineering science and technology, an international journal, Vol. 21, No. 1, pp. 60-69, 2018.

[18]        B. Mahanthesh, G. Lorenzini, F. M. Oudina, I. L. Animasaun, Significance of exponential space-and thermal-dependent heat source effects on nanofluid flow due to radially elongated disk with Coriolis and Lorentz forces, Journal of Thermal Analysis and Calorimetry, Vol. 141, No. 1, pp. 37-44, 2020.

[19]        S. R. Asemi, A. Farajpour, H. R. Asemi, M. Mohammadi, Influence of initial stress on the vibration of double-piezoelectric-nanoplate systems with various boundary conditions using DQM, Physica E: Low-dimensional Systems and Nanostructures, Vol. 63, pp. 169-179, 2014.

[20]        S. R. Asemi, A. Farajpour, M. Mohammadi, Nonlinear vibration analysis of piezoelectric nanoelectromechanical resonators based on nonlocal elasticity theory, Composite Structures, Vol. 116, pp. 703-712, 2014.

[21]        S. R. Asemi, M. Mohammadi, A. Farajpour, A study on the nonlinear stability of orthotropic single-layered graphene sheet based on nonlocal elasticity theory, Latin American Journal of Solids and Structures, Vol. 11, No. 9, pp. 1515-1540, 2014.

[22]        M. Baghani, M. Mohammadi, A. Farajpour, Dynamic and Stability Analysis of the Rotating Nanobeam in a Nonuniform Magnetic Field Considering the Surface Energy, International Journal of Applied Mechanics, Vol. 08, No. 04, pp. 1650048, 2016.

[23]        M. Danesh, A. Farajpour, M. Mohammadi, Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method, Mechanics Research Communications, Vol. 39, No. 1, pp. 23-27, 2012.

[24]        A. Farajpour, M. Danesh, M. Mohammadi, Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics, Physica E: Low-dimensional Systems and Nanostructures, Vol. 44, No. 3, pp. 719-727, 2011.

[25]        A. Farajpour, M. H. Yazdi, A. Rastgoo, M. Loghmani, M. Mohammadi, Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates, Composite Structures, Vol. 140, pp. 323-336, 2016.

[26]        A. Farajpour, M. Mohammadi, A. Shahidi, M. Mahzoon, Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model, Physica E: Low-dimensional Systems and Nanostructures, Vol. 43, No. 10, pp. 1820-1825, 2011.

[27]        A. Farajpour, A. Rastgoo, M. Mohammadi, Surface effects on the mechanical characteristics of microtubule networks in living cells, Mechanics Research Communications, Vol. 57, pp. 18-26, 2014/04/01/, 2014.

[28]        A. Farajpour, A. Rastgoo, M. Mohammadi, Vibration, buckling and smart control of microtubules using piezoelectric nanoshells under electric voltage in thermal environment, Physica B: Condensed Matter, Vol. 509, pp. 100-114, 2017.

[29]        A. Farajpour, A. Shahidi, M. Mohammadi, M. Mahzoon, Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics, Composite Structures, Vol. 94, No. 5, pp. 1605-1615, 2012.

[30]        A. Farajpour, M. Yazdi, A. Rastgoo, M. Mohammadi, A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment, Acta Mechanica, Vol. 227, No. 7, pp. 1849-1867, 2016.

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[32]        N. GHAYOUR, A. SEDAGHAT, M. MOHAMMADI, WAVE PROPAGATION APPROACH TO FLUID FILLED SUBMERGED VISCO-ELASTIC FINITE CYLINDRICAL SHELLS, JOURNAL OF AEROSPACE SCIENCE AND TECHNOLOGY (JAST), Vol. 8, No. 1, pp. -, 2011.

[33]        M. Goodarzi, M. Mohammadi, A. Farajpour, M. Khooran, Investigation of the effect of pre-stressed on vibration frequency of rectangular nanoplate based on a visco-Pasternak foundation, 2014.

[34]        H. Mohammadi, M. Ghayour, A. Farajpour, Analysis of free vibration sector plate based on elastic medium by using new version of differential quadrature method, Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, Vol. 3, No. 2, pp. 47-56, 2010.

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[36]        A. G. Arani, S. Maghamikia, M. Mohammadimehr, A. Arefmanesh, Buckling analysis of laminated composite rectangular plates reinforced by SWCNTs using analytical and finite element methods, Journal of mechanical science and technology, Vol. 25, No. 3, pp. 809-820, 2011.

[37]        M. Mohammadi, M. Goodarzi, M. Ghayour, S. Alivand, Small scale effect on the vibration of orthotropic plates embedded in an elastic medium and under biaxial in-plane pre-load via nonlocal elasticity theory, 2012.

[38]        M. Mohammadi, A. Farajpour, M. Goodarzi, R. Heydarshenas, Levy Type Solution for Nonlocal Thermo-Mechanical Vibration of Orthotropic Mono-Layer Graphene Sheet Embedded in an Elastic Medium, Journal of Solid Mechanics, Vol. 5, No. 2, pp. 116-132, 2013.

[39]        M. Mohammadi, M. Goodarzi, M. Ghayour, A. Farajpour, Influence of in-plane pre-load on the vibration frequency of circular graphene sheet via nonlocal continuum theory, Composites Part B: Engineering, Vol. 51, pp. 121-129, 2013.

[40]        M. Mohammadi, M. Ghayour, A. Farajpour, Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model, Composites Part B: Engineering, Vol. 45, No. 1, pp. 32-42, 2013.

[41]        M. Mohammadi, A. Farajpour, M. Goodarzi, H. Mohammadi, Temperature Effect on Vibration Analysis of Annular Graphene Sheet Embedded on Visco-Pasternak Foundation Journal of Solid Mechanics, Vol. 5, No. 3, pp. 305-323, 2013.

[42]        M. Mohammadi, A. Farajpour, M. Goodarzi, H. Shehni nezhad pour, Numerical study of the effect of shear in-plane load on the vibration analysis of graphene sheet embedded in an elastic medium, Computational Materials Science, Vol. 82, pp. 510-520, 2014/02/01/, 2014.

[43]        M. Mohammadi, A. Farajpour, A. Moradi, M. Ghayour, Shear buckling of orthotropic rectangular graphene sheet embedded in an elastic medium in thermal environment, Composites Part B: Engineering, Vol. 56, pp. 629-637, 2014.

[44]        M. Mohammadi, A. Farajpour, M. Goodarzi, F. Dinari, Thermo-mechanical vibration analysis of annular and circular graphene sheet embedded in an elastic medium, Latin American Journal of Solids and Structures, Vol. 11, pp. 659-682, 2014.

[45]        M. Mohammadi, A. Moradi, M. Ghayour, A. Farajpour, Exact solution for thermo-mechanical vibration of orthotropic mono-layer graphene sheet embedded in an elastic medium, Latin American Journal of Solids and Structures, Vol. 11, No. 3, pp. 437-458, 2014.

[46]        M. Safarabadi, M. Mohammadi, A. Farajpour, M. Goodarzi, Effect of surface energy on the vibration analysis of rotating nanobeam, 2015.

[47]        H. Asemi, S. Asemi, A. Farajpour, M. Mohammadi, Nanoscale mass detection based on vibrating piezoelectric ultrathin films under thermo-electro-mechanical loads, Physica E: Low-dimensional Systems and Nanostructures, Vol. 68, pp. 112-122, 2015.

[48]        M. Goodarzi, M. Mohammadi, M. Khooran, F. Saadi, Thermo-Mechanical Vibration Analysis of FG Circular and Annular Nanoplate Based on the Visco-Pasternak Foundation, Journal of Solid Mechanics, Vol. 8, No. 4, pp. 788-805, 2016.

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[69]        A. Abdalla, I. Abbas, H. Sapoor, The effects of fractional derivatives of bio-heat model in living tissues using analytical-numerical method, Information Sciences Letters, Vol. 11, No. 1, pp. 6, 2022.

[70]        T. Hayat, T. Muhammad, S. Shehzad, G. Chen, I. A. Abbas, Interaction of magnetic field in flow of Maxwell nanofluid with convective effect, Journal of Magnetism and Magnetic Materials, Vol. 389, pp. 48-55, 2015.

[71]        M. S. Ram, N. Ashok, S. Salawu, M. Shamshuddin, Significance of cross diffusion and uneven heat source/sink on the variable reactive 2D Casson flowing fluid through an infinite plate with heat and Ohmic dissipation, International Journal of Modelling and Simulation, pp. 1-15, 2022.

[72]        M. Shamshuddin, M. R. Eid, nth order reactive nanoliquid through convective elongated sheet under mixed convection flow with joule heating effects, Journal of Thermal Analysis and Calorimetry, Vol. 147, No. 5, pp. 3853-3867, 2022.

[73]        M. Shamshuddin, W. Ibrahim, Finite element numerical technique for magneto-micropolar nanofluid flow filled with chemically reactive Casson fluid between parallel plates subjected to rotatory system with electrical and Hall currents, International Journal of Modelling and Simulation, pp. 1-20, 2022.

[74]        M. Shamshuddin, F. Mebarek-Oudina, S. Salawu, A. Shafiq, Thermophoretic Movement Transport of Reactive Casson Nanofluid on Riga Plate Surface with Nonlinear Thermal Radiation and Uneven Heat Sink/Source, Journal of Nanofluids, Vol. 11, No. 6, pp. 833-844, 2022.

[75]        F. Mabood, M. Shamshuddin, S. Mishra, Characteristics of thermophoresis and Brownian motion on radiative reactive micropolar fluid flow towards continuously moving flat plate: HAM solution, Mathematics and Computers in Simulation, Vol. 191, pp. 187-202, 2022.

[76]        G. R. Rajput, M. Shamshuddin, S. O. Salawu, Thermosolutal convective non‐Newtonian radiative Casson fluid transport over a vertical plate propagated by Arrhenius kinetics with heat source/sink, Heat Transfer, Vol. 50, No. 3, pp. 2829-2848, 2021.

[77]        M. Senapati, K. Swain, S. K. Parida, Numerical analysis of three-dimensional MHD flow of Casson nanofluid past an exponentially stretching sheet, Karbala Int. J. Mod. Sci, Vol. 6, No. 1, pp. 93-102, 2020.

[78]        K. Swain, S. Parida, G. Dash, MHD heat and mass transfer on stretching sheet with variable fluid properties in porous medium, AMSE J Model B, Vol. 86, pp. 706-726, 2017.

[79]        S. K. Das, S. U. Choi, W. Yu, T. Pradeep, 2007, Nanofluids: science and technology, John Wiley & Sons,

[1]          L. J. Crane, Flow past a stretching plate, Zeit Angew Math Phys., Vol. 21, pp. 645-647, 1970.

[2]          T. R. Mahapatra, A. S. Gupta, Heat transfer in stagnation-point flow towards a stretching sheet, Heat and Mass Transfer, Vol. 38, pp. 517-521, 2002.

[3]          J. C. Misra, A. Sinha, Effect of thermal radiation on MHD flow of blood and heat transfer in a permeable capillary in stretching motion, Heat Mass Transfer, Vol. 49, pp. 617-628, 2013.

[4]          S. Mukhopadhyay, P. R. De, K. Bhattacharyya, G. C. Layek, Casson fluid flow over an unsteady stretching surface, Ain Shams Engineering Journal, Vol. 4, pp. 933-938, 2013.

[5]          G. S. Seth, R. Tripathi, M. K.Mishra, Hydromagnetic thin film flow of Casson fluid in non-Darcy porous medium with Joule dissipation and Navier’s partial slip, Appl. Math. Mech.-Engl. Ed., Vol. 38, pp. 1613-1626, 2017.

[6]          D. Gopal, N. Kishan, C. S. K. Raju, Viscous and Joule's dissipation on Casson fluid over a chemically reacting stretching sheet with inclined magnetic field and multiple slips,  Informatics in Medicine Unlocked, Vol. 9, pp. 154-160, 2017.

[7]          P. Sreenivasulu, T. Poornima, N. B. Reddy, Influence of Joule Heating and Non-Linear Radiation on MHD 3D Dissipating Flow of Casson Nanofluid past a Non-Linear Stretching Sheet, Nonlinear Engineering, Vol. 8, pp. 661-672, 2019.

[8]          M. A. El-Aziz, A. A. Afify, MHD Casson Fluid Flow over a Stretching Sheet with Entropy Generation Analysis and Hall Influence, Entropy, Vol. 21, pp. 592, 2019.

[9]          M. Das, G. Mahanta, S. Shaw, S. B. Parida, Unsteady MHD chemically reactive double‐diffusive Casson fluid past a flat plate in porous medium with heat and mass transfer, Heat Transfer-Asian Res., Vol. 48, pp. 1761-1777, 2019.

[10]        C. K. Kumar, S. Srinivas, A. S. Reddy, MHD pulsating flow of Casson nanofluid in a vertical porous space with thermal radiation and Joule heating, Journal of Mechanics, Vol. 36, pp. 535-549, 2020.

[11]        B. J. Gireesha, C. T. Srinivasa, N. S. Shashikumar, M. Macha, J. K. Singh JK, B. Mahanthesh, Entropy generation and heat transport analysis of Casson fluid flow with viscous and Joule heating in an inclined porous microchannel, Proc I Mech E Part E: J Process Mechanical Engineering, Vol. 233, pp.1173-1184, 2019.

[12]        B. Kumar, S. Srinivas, Unsteady Hydromagnetic Flow of Eyring-Powell Nanofluid over an Inclined Permeable Stretching Sheet with Joule Heating and Thermal Radiation, J. Appl. Comput. Mech., Vol. 6, pp. 259-270, 2020.

[13]        M. A. El-Aziz, A. A. Afify, Effect of Hall current on MHD slip flow of Casson nanofluid over a stretching sheet with zero nanoparticle mass flux, Thermophysics and Aeromechanics, Vol. 26, pp. 429-443, 2019.

[14]        S. M. Ibrahim, P. V. Kumar, G. Lorenzini, E. Lorenzini, Influence of Joule Heating and Heat Source on Radiative MHD Flow over a Stretching Porous Sheet with Power-Law Heat Flux, Journal of Engineering Thermophysics, Vol. 28, pp. 332-344, 2019.

[15]        K. Das, P. R. Duari P, P. K. Kundu, Nanofluid flow over an unsteady stretching surface in presence of thermal radiation, Alexandria Engineering Journal, Vol. 53, pp. 737-745, 2014.

[16]        B. Nagaraja, B. J. Gireesha, Exponential space‑dependent heat generation impact on MHD convective flow of Casson fluid over a curved stretching sheet with chemical reaction, J Therm Anal Calorim., Vol. 143, pp. 4071-4079, 2021.

[17]        B. C. Rout, S. R. Mishra, Thermal energy transport on MHD nanofluid flow over a stretching surface: A comparative study, Engineering Science and Technology, an International Journal, Vol. 21, pp. 60-69, 2018.

[18]       B. Mahanthesh, G. Lorenzini, F. M. Oudina, I. L. Animasaun, Significance of exponential space-and thermal-dependent heat source effects on nanofluid flow due to radially elongated disk with Coriolis and Lorentz forces, J Therm Anal Calorim., Vol. 141, pp. 37-44, 2020.

[19]        M. Senapati, K. Swain, S. K. Parida, Numerical analysis of three-dimensional MHD flow of Casson nanofluid past an exponentially stretching sheet, Karbala International Journal of Modern Science, Vol. 6, pp. 93-102, 2020.

[20]        K. Swain, S. K. Parida, G. C.  Dash, Effects of non-uniform heat source/sink and viscous dissipation on MHD boundary layer flow of Williamson nanofluid through porous medium, Defect and Diffusion Forum, Vol. 389, pp. 110-127, 2018.

[21]        H. R. Asemi, S. R. Asemi, A. Farajpour, M. Mohammadi, Nanoscale mass detection based on vibrating piezoelectric ultrathin films under thermo-electro-mechanical loads, Physica E: Low-dimensional Systems and Nanostructures, Vol. 68, pp. 112-122, 2015.

[22]        S. R. Asemi, A. Farajpour, H. R. Asemi, M. Mohammadi, Influence of initial stress on the vibration of double-piezoelectric-nanoplate systems with various boundary conditions using DQM, Physica E: Low-dimensional Systems and Nanostructures, Vol. 63, pp. 169-179, 2014.

[23]        S. R. Asemi, A. Farajpour, M. Mohammadi, Nonlinear vibration analysis of piezoelectric nanoelectromechanical resonators based on nonlocal elasticity theory, Composite Structures, Vol. 116, pp. 703-712, 2014.

[24]        S. R. Asemi, M. Mohammadi, A. Farajpour, A study on the nonlinear stability of orthotropic single-layered graphene sheet based on nonlocal elasticity theory, Latin American Journal of Solids and Structures, Vol. 11, No. 9, pp. 1515-1540, 2014.

[25]        M. Baghani, M. Mohammadi, A. Farajpour, Dynamic and stability analysis of the rotating nanobeam in a nonuniform magnetic field considering the surface energy, International Journal of Applied Mechanics, Vol. 8, No. 04, pp. 1650048, 2016.

[26]        M. Danesh, A. Farajpour, M. Mohammadi, Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method, Mechanics Research Communications, Vol. 39, No. 1, pp. 23-27, 2012.

[27]        A. Farajpour, M. Danesh, M. Mohammadi, Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics, Physica E: Low-dimensional Systems and Nanostructures, Vol. 44, No. 3, pp. 719-727, 2011.

[28]        A. Farajpour, M. R. Hairi Yazdi, A. Rastgoo, M. Loghmani, M. Mohammadi, Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates, Composite Structures, Vol. 140, pp. 323-336, 2016.

[29]        A. Farajpour, M. R. Hairi Yazdi, A. Rastgoo, M. Loghmani, M. Mohammadi, Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates, Composite Structures, Vol. 140, pp. 323-336, 2016.

[30]        A. Farajpour, M. Mohammadi, A. R. Shahidi, M. Mahzoon, Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model, Physica E: Low-dimensional Systems and Nanostructures, Vol. 43, No. 10, pp. 1820-1825, 2011.

[31]        A. Farajpour, A. Rastgoo, M. Mohammadi, Surface effects on the mechanical characteristics of microtubule networks in living cells, Mechanics Research Communications, Vol. 57, pp. 18-26, 2014.

[32]        A. Farajpour, A. Rastgoo, M. Mohammadi, Vibration, buckling and smart control of microtubules using piezoelectric nanoshells under electric voltage in thermal environment, Physica B: Condensed Matter, Vol. 509, pp. 100-114, 2017.

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[34]        A. Farajpour, M. R. H. Yazdi, A. Rastgoo, M. Mohammadi, A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment, Acta Mechanica, Vol. 227, No. 7, pp. 1849-1867, 2016.

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[37]        M. Goodarzi, M. Mohammadi, A. Farajpour, M. Khooran, Investigation of the effect of pre-stressed on vibration frequency of rectangular nanoplate based on a visco-Pasternak foundation, Journal of Solid Mechanics, Vol. 6, pp. 98-121, 2014.

[38]        M. Mohammadi, A. Farajpour, M. Goodarzi, F. Dinari, Thermo-mechanical vibration analysis of annular and circular graphene sheet embedded in an elastic medium, Latin American Journal of Solids and Structures, Vol. 11, No. 4, pp. 659-682, 2014.

[39]        M. Mohammadi, A. Farajpour, M. Goodarzi, R. Heydarshenas, Levy type solution for nonlocal thermo-mechanical vibration of orthotropic mono-layer graphene sheet embedded in an elastic medium, Journal of Solid Mechanics, Vol. 5, No. 2, pp. 116-132, 2013.

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[41]        M. Mohammadi, A. Farajpour, M. Goodarzi, H. Shehni nezhad pour, Numerical study of the effect of shear in-plane load on the vibration analysis of graphene sheet embedded in an elastic medium, Computational Materials Science, Vol. 82, pp. 510-520, 2014.

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[44]        M. Mohammadi, M. Ghayour, A. Farajpour, Analysis of free vibration sector plate based on elastic medium by using new version of differential quadrature method, Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, Vol. 3, No. 2, pp. 47-56, 2010.

[45]        M. Mohammadi, M. Goodarzi, M. Ghayour, S. Alivand, Small scale effect on the vibration of orthotropic plates embedded in an elastic medium and under biaxial in-plane pre-load via nonlocal elasticity theory, Journal of Solid Mechanics, Vol. 4, No. 2, pp. 128-143, 2012.

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[47]        M. Mohammadi, M. Hosseini, M. Shishesaz, A. Hadi, A. Rastgoo, Primary and secondary resonance analysis of porous functionally graded nanobeam resting on a nonlinear foundation subjected to mechanical and electrical loads, European Journal of Mechanics - A/Solids, Vol. 77, pp. 103793, 2019.

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