Computer Methods and Programs in Biomedicine 182 (2019) 105057 Contents lists available at ScienceDirect Computer Methods and Programs in Biomedicine journal homepage: www.elsevier.com/locate/cmpb Theoretical and mathematical analysis of entropy generation in fluid flow subject to aluminum and ethylene glycol nanoparticles Faisal Shah a , M. Ijaz Khan a,∗ , T. Hayat a,b , M. Imran Khan c , A. Alsaedi b , W.A. Khan d a Department of Mathematics, Quaid-I-Azam University, 45320, Islamabad 44000, Pakistan b Department of Mathematics, Faculty of Science, Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, King Abdulaziz University, Jeddah 21589, Saudi Arabia c Heriot Watt University, Edinburgh Campus, Edinburgh EH14 4AS, United Kingdom d School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China a r t i c l e i n f o Article history: Received 20 August 2019 Revised 28 August 2019 Accepted 30 August 2019 Keywords: Entropy generation Porous medium MHD Effective Prandtl number model Velocity slip Viscous dissipation Joule heating Thermal radiation a b s t r a c t Background: Here we have conducted a magnetohydrodynamic (MHD) flow of viscous material with alu- mina water and ethylene glycol over a stretched surface. The flow is discussed with and without effec- tive Prandtl number. MHD liquid is considered. Electric field is absent. Effect of uniform magnetic field is taken in the vertical direction to the surface. Influence of thermal radiation as well as Joule heating are taken into account for both aluminum oxide-water and aluminum oxide-Ethylene glycol nanofluids. Velocity slip and melting heat effects are considered. Methods: The nonlinear flow expressions are numerically solved via ND-solve technique (built-in- Shooting). Results: The physical impacts of flow variables like mixed convection parameter, magnetic parameter, Reynold number, Eckert number, melting parameter and heat source/sink parameter are graphically dis- cussed. Moreover, entropy generation (irreversibility) and Bejan number are discussed graphically through various flow variables. Physical quantities like skin friction coefficient and Sherwood and Nusselt numbers are numerically calculated and discussed through Tables. Conclusions: Impact of magnetic and slip parameters on the velocity field show decreasing behavior for both effective and without effective Prandtl number. Temperature field increases for both effective and without effective Prandtl number for higher values of magnetic and radiative parameters. Entropy num- ber is an increasing function of Reynolds number while Bejan number shows opposite impact against Reynolds number. Moreover, heat transfer rate upsurges versus larger melting and radiative parameter. © 2019 Published by Elsevier B.V. 1. Introduction Many industrial equipment need study of cooling effects in thermal processes for the quality of their end products. Bound- ary layer flows over stretched surfaces play a vital role in such processes. These processes are comprised of metallic sheets indus- tries, polymer extrusion, glass sheets, paper production and crystal growing etc. Crane [1] started the work on the flow of Newtonian fluids over stretching surfaces. Many researchers followed him in extending his theory of stretching surfaces for Newtonian as well as non-Newtonian fluids [2–20]. Increasing thermal properties of fluids is a topic of engineering interest. Classical methods were used earlier for cooling effects in ∗ Corresponding author. E-mail addresses: mikhan@math.qau.edu.pk (M.I. Khan), mk42@hw.ac.uk (M.I. Khan). many industrial and technological processes, for example use of air and water for cooling effects. Javed et al. [21] used the nanoparti- cles along with water as a base fluid to enhance thermal proper- ties of fluids and achieved better results. Turkyilmazoglu [22] stud- ied the flow of viscoselastic nanofluid over a stretchable surface. Many types of nanomaterials i.e., silver, copper, gold, aluminum, copper oxide, silver oxide, and aluminum oxides etc. with differ- ent base fluids were tested for enhancing thermal conductivities of fluids by different researchers [23–30]. Farooq et al. [31] studied the numerical solution for MHD Al 2 O 3 -water nanofluid in a porous medium. Patra et al. [32] analyzed CattaneoChristov heat flux in MHD nanofluid flow between parallel sheets having thermal radi- ation effect. Importance of porous medium in many technological appli- cations and transport phenomenon cannot be denied. Limestone, wood, sandstone and seepage of water in river beds are common examples of porous medium existing in nature. Darcy law has been https://doi.org/10.1016/j.cmpb.2019.105057 0169-2607/© 2019 Published by Elsevier B.V.