Significance of homogeneous–heterogeneous reactions in Darcy– Forchheimer three-dimensional rotating flow of carbon nanotubes Tasawar Hayat 1,2 • Arsalan Aziz 1 • Taseer Muhammad 3 • Ahmed Alsaedi 2 Received: 17 October 2018 / Accepted: 27 April 2019 Ó Akade ´miai Kiado ´, Budapest, Hungary 2019 Abstract Three-dimensional rotating flow of water-based carbon nanotubes is investigated in the presence of Darcy–Forchheimer porous space and homogeneous–heterogeneous reactions. Variable surface temperature condition is employed. Expo- nentially stretchable sheet induces the flow. Xue model has been implemented for nanoliquid transport mechanism. Suitable transformations lead to strong nonlinear ordinary differential system. An optimal homotopic algorithm is used to tackle the governing nonlinear system. Results for single-wall carbon nanotubes and multi-wall carbon nanotubes have been studied. Plots are displayed just to explore the role of flow parameters on solutions. Skin friction coefficients and heat transfer rate have been plotted and discussed. Our findings indicate that the skin friction coefficients and local Nusselt number are enhanced for larger values of nanoparticles volume fraction. Keywords 3D flow Á Carbon nanotubes (SWCNTs and MWCNTs) Á Rotating frame Á Darcy–Forchheimer porous space Á Homogeneous–heterogeneous reactions Á Exponential stretching surface List of symbols u, v, w Velocity components l f Fluid dynamic viscosity m f Kinematic fluid viscosity k f Basefluid thermal conductivity a f Thermal diffusivity of base fluid T w Surface temperature u w ðxÞ Surface stretching velocity u 0 Reference velocity F Non-uniform inertia coefficient C b Drag coefficient k Local porosity parameter Sc Schmidt number / Nanoparticles volume fraction h Dimensionless temperature Pr Prandtl number k c , k s Rate constants k 1 Homogeneous reaction parameter Re x Local Reynolds number C fx , C fy Skin friction coefficients x, y, z Space coordinates q f Fluid density m nf Kinematic nanofluid viscosity k nf Nanofluid thermal conductivity a nf Thermal diffusivity of nanofluid T ! Ambient fluid temperature k CNT CNTs thermal conductivity k* Permeability of porous medium D A , D B Diffusion coefficients X Local rotation parameter Fr Forchheimer number f Dimensionless variable f 0 , g Dimensionless velocities r Dimensionless concentration a Ratio number A, B Chemical species k 2 Heterogeneous reaction parameter H ÃÃ j Arbitrary constants Nu x Local Nusselt number & Arsalan Aziz arsalan_qau@yahoo.com 1 Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan 2 Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia 3 Department of Mathematics, Government College Women University, Sialkot 51310, Pakistan 123 Journal of Thermal Analysis and Calorimetry https://doi.org/10.1007/s10973-019-08316-3