Vol.:(0123456789) 1 3 Applied Nanoscience https://doi.org/10.1007/s13204-019-01038-w ORIGINAL ARTICLE Computational analysis of entropy generation for cross‑nanofluid flow M. Ali 1  · W. A. Khan 2,3  · M. Irfan 4  · F. Sultan 1  · M. Shahzed 1  · M. Khan 4 Received: 19 January 2019 / Accepted: 9 April 2019 © King Abdulaziz City for Science and Technology 2019 Abstract This research work is made to demonstrate diverse characteristics of entropy generation minimization for cross nanomaterial towards a stretched surface in the presence of Lorentz’s forces. Transportation of heat is analyzed through Joule heating and radiation. Nanoliquid model consists of activation energy and Brownian movement aspects. Concentration of cross material is scrutinized by implementing zero mass flux condition. Bejan number and entropy generation (EG) rate are formulated. The employment of transformation variables reduces the PDEs into nonlinear ODEs. Bvp4c scheme is implemented to compute the computational results of nonlinear system. Velocity, temperature, and concentration are conducted for cross nanomaterial. Consequences of current physical model are presented through graphical data and in tabular form. The outcomes for Bejan number and EG rates are presented through graphical data. It is noted that EG rates and Bejan number significantly affect rate of heat-mass transport mechanisms. In addition, graphical analysis reveals that E.G. rate has diminishing trend for diffusive variable. Moreover, achieved data reveal that profiles of Bejan number boost for augmented values of radiation parameter. Keywords Cross nanoliquid · Thermal radiation · Entropy generation · Activation energy Introduction The advancement in nanotechnology and nanoscience extended the application areas for researchers and scien- tists. Applications of nanofluids are encouraging in dif- ferent phenomena such as the heat transfer phenomena. Advancements in technology need the proficient methods for heat transfer, and nanofluids provide the more efficient medium for heat transfer from one source to another source. In addition, numerous procedures are available in the lit- erature which can intensifies heat transport properties in flow to improve the effectiveness of concentrating collec- tor. Nanoliquids have higher thermo-physical properties compared with those of base liquids. Moreover, nanoliquids were employed inside absorber to serve as heat transfer liq- uid and, therefore, boost the performance of solar system. Sheikholeslami et al. (2014) deliberated the flow for CuO water nanofluid by considering the aspects of Lorentz forces. Khan et al. (2014) described heat sink–source characteris- tics for 3D non-Newtonian nanofluid. Ellahi et al. (2015) inspected the colloidal analysis for CO–H 2 O over inverted vertical cone. Khan and Khan (2015), (2016a) and Khan et al. (2016a) described various properties of nanoliquid by considering different non-Newtonian fluid models. Waqas et al. (2016) examined the flow of micropoler liquid due to nonlinear stretched sheet with convective condition. Khan and Khan (2016b) reported features of Burgers fluid by considering nanoparticles. Sulochana et al. (2017) stud- ied the consequences of thin din needle with Joule heating. Hayat et al. (2017) analyzed radiative heat transfer in the presence of Lorentz’s force for nanofluid. Sheikholeslami and Shehzad (2017) reported the properties of nanofluid by considering characteristics of Lorentz force. Moreover, some recent development on nanofluid has been discussed in Sheikholeslami and Shamlooei (2017), Sheikholeslami and Rokni (2017), Irfan et al. (2018a, b, 2019a), Hayat et al. (2018), Sheikholeslami et al. (2018), Gireesha et al. (2018), Mahanthesh et al. (2018), Sheikholeslami (2018a, b), Akbar * W. A. Khan Waqar_qau85@yahoo.com 1 Department of Mathematics and Statistics, Hazara University, Mansehra 21300, Pakistan 2 School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China 3 Department of Mathematics, Mohi-ud-Din Islamic University, Nerian Sharif 12010, Azad Jammu & Kashmir, Pakistan 4 Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan