Vol.:(0123456789) 1 3 Applied Nanoscience https://doi.org/10.1007/s13204-020-01546-0 ORIGINAL ARTICLE Numerical simulation for MHD fow of Casson nanofuid by heated surface Sudheer Khan 1  · Wang Shu 1  · Mehboob Ali 2  · Faisal Sultan 2  · Muhammad Shahzad 3 Received: 16 February 2020 / Accepted: 20 August 2020 © King Abdulaziz City for Science and Technology 2020 Abstract This research intends elaborate the nanoscience and nanotechnology to rheological and thermal aspect of the nanofuids. The conventional heat transfer fuids are mostly described the reduced performing of heat transport tools and increasing the energy charges. For this reason,nanofuids have been familiar such as likely proxies to established practices of fuids due to their intensify aptitude of heat transport coefcient. Here, magnetohydrodynamic of Casson nanofuid toward a stretching sheet is addressed. Furthermore, efect of nonlinear radiated and Arrhenius activation energy with new mass fux theory are explored. The solution of the problems are obtained by using numerical procedure bvp4c technique. The graphical behavior of velocity feld is decresed function of Magnetohydrodynamic. The radiation and thermophoresis parameters enhancing the temperature feld. Also, the concentration performance for increasing Brownian motion and activation energy parameters. Keywords Cassonnanofuid · New mass fux theory · Magnetohydrodynamic · Nanoparticles · Activation energy List of symbols x, y, z Space coordinates ( C fx , C fy ) Skin friction coefcients (  xz ,  yz ) Surface shear stresses  Electrical conductivity Nu x Local Nusselt N ∗ Buoyancy ratio parameter N b Brownian motion parameter N t Thermophoresis parameter T w Wall temperature U w (x), V w (x) Stretching velocities t Time (f , g) Dimensionless velocities  ∗ Stefan–Boltzmann constant  ∗ Mean absorption coefcient  Mixed convection parameter Pr Prandtl number T Temperature q r Radiative heat fux  Dimensionless temperature  T Thermal expansion coefcient  C Solutal expansion coefcient B(t) Strength of magnetic feld D T Thermophoresis difusion coefcient a, b,  Positive constants  Ratio of stretching rates parameter  Thermal conductivity  Dimensionless variable m(- < m < 1) Fitted rate constant Le Lewis number M Magnetic parameter R d Thermal radiation Re x Local Reynolds number u, v, w Velocity components  Temperature diference parameter (c) f Heat capacity of fuid E Activation energy  ∗∗ Reaction rate parameter g Gravity C Concentration of fuid  Efective heat capacity ratio  f Fluid density  1 Thermal difusivity  Dimensionless concentration * Sudheer Khan soudkayani@hotmail.com * Wang Shu wangshu@bjut.edu.pk 1 Beijing University of Technology, Beijing 100081, China 2 Department of Mathematics, Hazara University, Mansehra 21300, Pakistan 3 Department of Mathematics and Statistics, University of Haripur, Haripur 22620, Pakistan