Effect of Joule heating on the flow over an exponentially stretching sheet with convective thermal condition

Sakiadis, B.C.: Boundary-layer equations for two-dimensional and axisymmetric flow. AIChE J. 7(1), 26–28 (1961)

Sakiadis, B.C.: The boundary layer on a continuous flat surface. AIChE J. 7(2), 221–225 (1961)

Abbas, Z., Javed, T., Ali, N., Sajid, M.: Flow and heat transfer of Maxwell fluid over an exponentially stretching sheet: a non-similar solution. Heat Transf. Asian Res. 43, 233–242 (2014)

Krishnamurthy, M.R., Prasannakumara, B.C., Gireesha, B.J., Gorla, R.S.R.: Effect of viscous dissipation on hydromagnetic fluid flow and heat transfer of nanofluid over an exponentially stretching sheet with fluid-particle suspension. Cogent Math. 2, 1050973 (2015)

Aleng, N.L., Bachok, N., Arifin, N.M.: Flow and heat transfer of a nanofluid over an exponentially shrinking sheet. Indian J. Sci. Technol. 8, 1–6 (2015)

Sreedevi, P., Reddy, P.S., Chamkha, A.J.: Heat and mass transfer analysis of nanofluid over linear and non-linear stretching surfaces with thermal radiation and chemical reaction. Powder Technol. 315, 194–204 (2017)

Nayak, M.K., Akbar, N.S., Pandey, V.S., Khan, Z.H., Tripathi, D.: 3D free convective MHD flow of nanofluid over permeable linear stretching sheet with thermal radiation. Powder Technol. 315, 205–215 (2017)

Shateyi, S., Gerald, T.M.: Numerical solution of mixed convection flow of an MHD Jeffery fluid over an exponentially stretching sheet in the presence of thermal radiation and chemical reaction. Open Phys. 16, 249–259 (2018)

Kumar, M.S., Sandeep, N., Kumar, B.R., Dinesh, P.A.: A comparative analysis of magnetohydrodynamic non-Newtonian fluids flow over an exponential stretched sheet. Alex. Eng. J. 57(3), 2093–2100 (2018)

Jusoh, R., Nazar, R., Pop, I.: Magnetohydrodynamic rotating flow and heat transfer of ferrofluid due to an exponentially permeable stretching/shrinking sheet. J. Magn. Magn. Mater. 465, 365–374 (2018)

Hayat, T., Khan, M.W.A., Khan, M.I., Alsaedi, A.: Nonlinear radiative heat flux and heat source/sink on entropy generation minimization rate. Phys. B 538, 95–103 (2018)

Srinivasacharya, D., Jagadeeshwar, P.: Effect of variable properties on the flow over an exponentially stretching sheet with convective thermal conditions. Model. Meas. Control B 87(1), 7–14 (2018)

Khan, M.I., Hayat, T., Alsaedi, A.: Numerical investigation for entropy generation in hydromagnetic flow of fluid with variable properties and slip. Phys. Fluids 30, 023601 (2018)

Jat, R.N., Chand, G.: MHD flow and heat transfer over an exponentially stretching sheet with viscous dissipation and radiation effects. Appl. Math. Sci. 7, 167–180 (2013)

Yadav, R.S., Sharma, P.R.: Effects ff radiation and viscous dissipation on MHD boundary layer flow due to an exponentially moving stretching sheet in porous medium. Asian J. Multidiscip. Stud. 2(8), 119–124 (2014)

Rao, J.A., Vasumathi, G., Mounica, J.: Joule heating and thermal radiation effects on MHD boundary layer flow of a Nanofluid over an exponentially stretching sheet in a porous medium. World J. Mech. 5, 151–164 (2015)

Adeniyan, A., Adigun, J.A.: Similarity solution of hydromagnetic flow and heat transfer past an exponentially stretching permeable vertical sheet with viscous dissipation, Joulean and viscous heating effects. Ann. Fac. Eng. Hunedoara Int. J. Eng. 14, 113–120 (2016)

Srinivasacharya, D., Jagadeeshwar, P.: MHD flow with Hall current and Joule heating effects over an exponentially stretching sheet. Nonlinear Eng. Model. Appl. 6(2), 101–114 (2017)

Khan, M.I., Waqas, M., Hayat, T., Khan, M.I., Aslaedi, A.: Numerical solution of nonlinear thermal radiation and homogeneous-heterogeneous reactions in convective flow by a variable thicked surface. J. Mol. Liquids 246, 259–267 (2017)

Hayat, T., Khan, M.I., Qayyum, S., Aslaedi, A.: Modern developments about statistical declaration and probable for skin friction and Nusselt number with copper and silver nanoparticles. Chin. J. Phys. 55, 2501–2513 (2017)

Hayat, T., Qayyum, S., Khan, M.I., Aslaedi, A.: Entropy generation in magnetohydrodynamic radiative flow due to rotating disk in presence of viscous dissipation and Joule heating. Phys. Fluids 30, 017101 (1-12) (2018)

Hayat, T., Khan, M.I., Qayyum, S., Aslaedi, A.: Entropy generation in flow with silver copper particles. Colloids Surf. A 529, 335–346 (2018)

Hayat, T., Khan, M.I., Qayyum, S., Aslaedi, A., Khan, M.I.: New thermodynamics of entropy generation minimization with nonlinear thermal radiation and nanomaterials. Phys. Lett. A 382, 749–760 (2018)

Ijaz Khan, M., Qayyuma, S., Hayat, T., Imran Khan, M., Alsaedi, A., Ahmad Khan, T.: Entropy generation in radiative motion of tangent hyperbolic nanofluid in presence of activation energy and nonlinear mixed convection. Phys. Lett. A 382(31), 2017–2026 (2018)

Khan, M., Ullah, S., Hayat, T., Khan, M.I., Aslaedi, A.: Entropy generation minimization (EGM) for convection nanomaterial flow with nonlinear radiative heat flux. J. Mol Liq. 260, 279–291 (2018)

Khan, M.I., Hayat, S., Khan, M.I., Aslaedi, A.: Activation energy impact in nonlinear radiative stagnation point flow Cross nanofluid. Int. Commun. Heat Mass Transf. 91, 216–224 (2018)

Naiver, C.L.M.: Sur les lois du mouvement des uides. Memoires del Academie Royale des Sciences 6, 389–440 (1827)

Su, X., Zheng, L.: Hall effect on MHD flow and heat transfer of nanofluids over a stretching wedge in the presence of velocity slip and Joule heating. Cent. Eur. J. Phys. 11(12), 1694–1703 (2013)

Merkin, J.H.: Natural-convection boundary-layer flow on a vertical surface with Newtonian heating. Int. J. Heat Fluid Flow 15, 392–398 (1994)

Gideon, O.T., Abah, S.O.: Plane stagnation double-diffusive MHD convective flow with convective boundary condition in a porous media. Am. J. Comput. Math. 2, 223–227 (2012)

Mustafaa, M., Hayat, T., Obaidat, S.: Boundary layer flow of a nanofluid over an exponentially stretching sheet with convective boundary conditions. Int. J. Numer. Meth. Heat Fluid Flow 23, 945–959 (2013)

Hayat, T., Imtiaz, M., Alsaedi, A., Mansoora, R.: MHD flow of nanofluids over an exponentially stretching sheet in a porous medium with convective boundary conditions. Chin. Phys. B 23(5), 054701 (2014)

Rahman, M., Rosca, A.V., Pop, I., Al-Solamy, F., Ramzan, M.: Boundary layer flow of a nanofluid past a permeable exponentially shrinking surface with convective boundary condition using Buongiorno’s model. Int. J. Numer. Meth. Heat Fluid Flow 25, 299–319 (2015)

Mabood, F., Khan, W.A., Ismail, AIMd: Approximate analytical solution of stagnation point flow and heat transfer over an exponential stretching sheet with convective boundary condition. Heat Transf. Asian Res. 44, 293–304 (2015)

Khan, J.A., Mustafa, M., Hayat, T., Alsaedi, A.: Numerical study on three-dimensional flow of nanofluid past a convectively heated exponentially stretching sheet. Can. J. Phys. 93, 1131–1137 (2015)

Srinivasachary, D., Jagadeeshwar, P.: Slip viscous flow over an exponentially stretching porous sheet with thermal convective boundary conditions. Int. J. Appl. Comput. Math. 3(4), 3525–3537 (2017)

Magyari, E., Keller, B.: Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface. J. Phys. D Appl. Phys. 32(5), 577–585 (1999)

Gupta, A.S.: Steady and transient free convection of an electrically conducting fluid from a vertical plate in the presence of a magnetic field. Appl. Sci. Res. Sect. A 9(1), 319 (1960)

Sparrow, E.M., Yu, H.S.: Local nonsimilarity thermal boundary-layer solutions. J. Heat Transf. 93, 328–334 (1971)

Minkowycz, W.J., Sparrow, E.M.: Local non-similar solution for natural convection on a vertical cylinder. J. Heat Transf. 96, 178–183 (1974)

Awad, F.G., Sibanda, P., Motsa, S.S., Makinde, O.D.: Convection from an inverted cone in a porous medium with cross-diffusion effects. Comput. Math Appl. 61, 1431–1441 (2011)

Motsa, S.S., Shateyi, S.: Successive linearisation solution of free convection non-Darcy flow with heat and mass transfer. Adv. Top. Mass Transf. 19, 425–438 (2006)

Makukula, Z.G., Sibanda, P., Motsa, S.S.: A novel numerical technique for two dimensional laminar flow between two moving porous walls. Math. Probl. Eng. 2010, 1–15 (2010)

Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral methods-fundamentals in single domains. J. Appl. Math. Mech. 87(1), 149–169 (2007)