Thermal stratification effects on MHD radiative flow of nanofluid over nonlinear stretching sheet with variable thickness Yahaya Shagaiya Daniel a,b , Zainal Abdul Aziz a,b,⇑ , Zuhaila Ismail a,b , Faisal Salah c a Department of Mathematical Science, Faculty of Sciences, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia b UTM Centre for Industrial and Applied Mathematics, Institute Ibnu Sina for Scientific and Industrial Research, 81310 UTM Johor Bahru, Johor, Malaysia c Department of Mathematics, Faculty of Science, University of Kordofan, Elobied 51111, Sudan article info Article history: Received 3 July 2017 Received in revised form 8 September 2017 Accepted 8 September 2017 Available online 19 September 2017 Keywords: MHD nanofluid Variable thickness Thermal radiation Similarity solution Thermal stratification abstract The combined effects of thermal stratification, applied electric and magnetic fields, thermal radiation, vis- cous dissipation and Joules heating are numerically studied on a boundary layer flow of electrical con- ducting nanofluid over a nonlinearly stretching sheet with variable thickness. The governing equations which are partial differential equations are converted to a couple of ordinary differential equations with suitable similarity transformation techniques and are solved using implicit finite difference scheme. The electrical conducting nanofluid particle fraction on the boundary is passively rather than actively con- trolled. The effects of the emerging parameters on the electrical conducting nanofluid velocity, temper- ature, and nanoparticles concentration volume fraction with skin friction, heat transfer characteristics are examined with the aids of graphs and tabular form. It is observed that the variable thickness enhances the fluid velocity, temperature, and nanoparticle concentration volume fraction. The heat and mass transfer rate at the surface increases with thermal stratification resulting to a reduction in the fluid temperature. Electric field enhances the nanofluid velocity which resolved the sticking effects caused by a magnetic field which suppressed the profiles. Radiative heat transfer and viscous dissipation are sensitive to an increase in the fluid temperature and thicker thermal boundary layer thickness. Comparison with pub- lished results is examined and presented. Ó 2017 Society for Computational Design and Engineering. Publishing Services by Elsevier. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 1. Introduction More recently, a new class of fluids known as nanofluids has drawn attentions of researchers in diverse areas of science and engineering technology as result of wide coverage of industrial applications of these fluids. This new innovation aims at enhancing the thermal conductivities and the convective heat transfer of flu- ids through suspensions of ultrafine nanoparticles in the base flu- ids (Choi, 1995). Nanofluid is a mixture of an ultrafine nanoparticle of diameter less than 100 nm dispersed in the conventional basic fluid namely water, toluene, ethylene, and oil. Some common metallic nanoparticles are copper, silver, silicon, aluminum, and titanium which tends to enhances the thermal conductivities and hence convective heat transfer rate of such fluids, which increases the energy transport strength and enactment (Bhatti, Abbas, & Rashidi, 2017; Daniel, 2015; Hayat, Waqas, Shehzad, & Alsaedi, 2016; Kandasamy, Mohammad, Zailani, & Jaafar, 2017; Kumar, Sood, Sheikholeslami, & Shehzad, 2017; M’hamed et al., 2016). Considering variable thickness due to flow, it has gained consider- ation due to widely advances recently in the area of engineering enhancement in the fields of mechanical, civil, architectural, etc. (Hayat, Khan, Alsaedi, & Khan, 2017; Hayat, Shah, Alsaedi, & Khan, 2017; Khan, Hayat, Khan, & Alsaedi, 2017). This is rooted in the innovative work of Fang, Zhang, and Zhong (2012) against variable thickness using pure fluid. The surface medium of variable thickness have influential values and significant noticed in indus- trial and engineering processes. It aims at reducing the heaviness of supplementary component and enhance the operation of devices. Consequently, this drew the attention of various research- ers (Hayat, Khan, Alsaedi, & Khan, 2016; Hayat et al., 2016; Khan, Hayat, Waqas, Khan, & Alsaedi, 2017; Khan, Khan, Waqas, Hayat, & Alsaedi, 2017; Khan, Waqas, Khan, Alsaedi, & Hayat, 2017; Waqas, Khan, Hayat, Alsaedi, & Khan, 2017) for flow behavior against stretching sheet involving variable thickness. The study of nanofluids with effects of magnetic fields has enor- mous applications in the fields of metallurgy and engineering advancement (Alsaedi, Khan, Farooq, Gull, & Hayat, 2017; Daniel, https://doi.org/10.1016/j.jcde.2017.09.001 2288-4300/Ó 2017 Society for Computational Design and Engineering. Publishing Services by Elsevier. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer review under responsibility of Society for Computational Design and Engineering. ⇑ Corresponding author at: UTM Centre for Industrial and Applied Mathematics, Institute Ibnu Sina for Scientific and Industrial Research, 81310 UTM Johor Bahru, Johor, Malaysia. E-mail addresses: shagaiya12@gmail.com (Y.S. Daniel), zainalaz@utm.my (Z.A. Aziz), zuhaila@utm.my (Z. Ismail), faisal19999@yahoo.com (F. Salah). 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