Melting heat transfer in hydromagnetic convective flow of nanofluid

Abstract

Nanofluid is a mixture of base fluid (water, oil and ethylene glycol) and nano-sized (1-100nm) solid particles (metals, metals oxide non-metals). Heat transfer characteristics of a nanoliquid dependent on thermophysical behaviors of nanoparticles, the volume fraction of solid particles and base liquid thermophysical characteristics. Heat transfer phenomena are immense significance for biotechnology, manufacturing and physiographical developments. Nanofluids have unique features that made them particularly in heat transfer phenomena like engine temperature control, hybrid powered vehicles, compressors, thermal management, nuclear reactor cooling etc. It is widely accepted that the presence of nanoparticles modifies the transportation properties and improves heat transfer performance of nanofluids. An exceptional technique for the improvement of heat transfer phenomena is the utilization of nano-size solid particles dispersed in conservatively utilizable materials (oil, ethylene glycol, water etc.) [1]. Nanomaterial flows possess tremendous real-world applications in industrial, pharmaceuticals, surgical processes and engineering fields including metal extrusion, nuclear reactor, oil survey, radiators, hot rolling, stretching of plastic foil, fiber glass, polymer processing, generic drug processing and geothermic energy extraction. Initially Choi [2] has done pioneering approach for heat transfer enhancement through insertion of nanoparticles in conservatively utilizable materials. Heat transfer enhancement of a nanoliquids is explained by Buongiorno [3]. He determined that Brownian and thermophoresis diffusion impacts are main factors for heat transfer enhancement. Brownian and thermophoresis diffusion impacts in nanomaterial flow subject to stretching surface is studied Khan and Pop [4]. Irreversibility analysis in dissipative flow of Ree-Eyring nanoliquids over a rotating disk with heat source/sink is scrutinized by Hayat et al. [5]. Kandasamy et. al. [6] explored the hydromagnetic flow of nanomaterials over a vertical stretching sheet with Brownian and thermophoresis diffusion effects. Das [7] reported the slip effect in convective flow of hybrid nanofluid with thermal buoyancy over a permeable stretching sheet. Few relevant studies about this topic are presented in Refs. [8-15]. Hydrodynamic is the study of electrically conducting liquid and magnetic characteristics. These liquids include salt water, plasmas, electrolytes and liquid metals etc. The fundamental idea of hydromagnetic (MHD) is that magnetic force produce induce current in a conductive liquid which polarize the liquids. Magnetic field effect has been extensively utilizable in heat convection direction and fluid motion direction. Study of magnetohydromagnetic is important in nuclear reactor cooling, extraction of geothermal energy, heat exchange and many other processes. Heat transfer analysis for unsteady hydromagnetic flow with Hall effect is highlighted by Chi and Zhang [16]. Sulochana et al. [17] reported the thermal and solutal transfer rate in hydromagnetic flow of viscous liquid over a rotating cone. Chu et al. [18] discussed the hydromagnetic flow of non-Newtonian nanofluid with activation energy subject to stretched surface. Some studies about this topic are mentioned in Refs. [19-25]. The measure of energy which is lost during any irreversible process is of great importance in many physical and engineering problems. In last few decades the study of entropy generation become more popular among many researchers. The rate of total entropy generation is calculated using the second law of thermodynamics. The second law of thermodynamics is more important than the first law because the first law's ability to transfer heat is limited. The theoretical idea of considering entropy optimization was first given by Bejan [26]. Entropy optimization of nanomaterials flow with heat transfer rates was noted by Sheikholeslami et al. [27]. Bhatti et al. [28] reported the irreversibility analysis in radiative flow of viscous fluid over a stretched surface. Qayyum et al. [29] explored the irreversibility effect for Von-Karman's flow with thermo-diffusion and diffusion thermo effects. Melting and entropy analysis in hydromagnetic flow of nanofluid over a stretchable surface with Brownian and thermophoresis diffusion is illuminated by Khan et al. [30]. Some investigations about this topic are presented in Refs. [31-40]. Prime objective of this study is to investigate the irreversibility in convective flow of nanoliquid with Lorentz force over a stretching sheet. Energy expression is deliberated with radiation, dissipation and joule heating. Furthermore Brownian and thermophoresis diffusion effects are addressed. Melting heat transfer and slip conditions are scrutinized. First order reaction rate is discussed. Physical feature of entropy analysis is discussed through thermodynamics second law. Partial differential system is reduced to ordinary one by suitable variables. The given system are solved through Newton build in-shooting technique. Influence of different flow variables on velocity, concentration, temperature and entropy generation are scrutinized. Performance of drag force, heat transfer rate and Sherwood number with variation of sundry variables are examined.