The noncommutative values of quantum observables

We discuss the notion of representing the values of physical quantities by the real numbers, and its limits to describe the nature to be understood in the relation to our appreciation that the quantum theory is a better theory of natural phenomena than its classical analog. Getting from the algebra of physical observables to their values for a fixed state is, at least for classical physics, really a homomorphic map from the algebra into the real number algebra. The limitation of the latter to represent the values of quantum observables with noncommutative algebraic relation is obvious. We introduce and discuss the idea of the noncommutative values of quantum observables and its feasibility, arguing that at least in terms of the representation of such a value as an infinite set of complex numbers, the idea makes reasonable sense theoretically as well as practically.     

Weak dissipation of electrostatic solitary structures in warm collisional pair-ion plasmas with non-Maxwellian electron population

The localized electrostatic structures with dissipation due to ion-neutral collisions in a symmetric warm pair-ion plasma in the presence of non-Maxwellian population of electrons are studied. The analytical model for ion dynamics is based on fluid equations and the evolution equation is derived by using the reductive perturbation scheme in the form of a damped Korteweg-de Vries equation. The parameter regime relevant to space-based observations and laboratory plasmas is considered and time evolution of the propagating ion-acoustic soliton is discussed. The energetic-particles-driven properties of soliton for various spectral indices, dissipation, ion temperature, and density are illustrated with comparison to the thermal mode for Boltzmann distribution of electrons.     

MHD flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge

The steady flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge with magnetic field and radiation effects are studied. The governing equations of the hybrid nanofluid are converted to the similarity equations by techniques of the similarity transformation. The bvp4c function that is available in MATLAB software is utilized for solving the similarity equations numerically. The numerical results are obtained for selected different values of parameters. The results discover that two solutions exist, up to a certain value of the stretching/shrinking and suction strengths. The critical value in which the solution is in existence decreases as nanoparticle volume fractions for copper and wedge angle parameter increase. It is also found that the hybrid nanofluid enhances the heat transfer rate compared with the regular nanofluid. The reduction of the heat transfer rate is observed with the increase in radiation parameter. The temporal stability analysis is performed to analyze the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.     

Magnetohydrodynamics (MHD) axisymmetric flow and heat transfer of a hybrid nanofluid past a radially permeable stretching/shrinking sheet with Joule heating

The main interest of the present work is to fundamentally investigate the flow characteristics and heat transfer of a hybrid Cu-Al₂O₃/water nanofluid due to a radially stretching/shrinking surface with the mutual effects of MHD, suction and Joule heating. The surface is permeable to physically allow the wall mass fluid suction. Tiwari and Das model of nanofluid is used with the new thermophysical properties of hybrid nanofluid to represent the problem. A similarity transformation is adopted to convert the governing model (PDEs) into a nonlinear set of ordinary differential equations (ODEs). A bvp4c solver in MATLAB software is employed to numerically compute the transformed system. The numerical results are discussed and graphically manifested in velocity and temperature profiles, as well as the skin friction coefficient and heat transfer rate with the pertinent values of the dimensionless parameters namely magnetic, Cu volume fraction, suction and Eckert number. The Eckert number has no impact on the boundary layer separation while the higher value of the suction parameter may affect the heat transfer performance. The presence of dual solutions (first and second) is seen on all the profiles within a limited range of the physical parameters. The stability analysis is executed, and it is validated that the first solution is the real solution.     

Influence of metallic nanoparticles in water driven along a wavy circular cylinder

In the present study, simultaneous effects of metallic nanoparticles and magnetohydrodynamic due to stagnation point flow of nanofluid along a wave circular cylinder is presented. The effect of induced magnetic field is incorporated to deal the boundary and thermal boundary layer domain. Mathematical modelling for momentum and energy equation is constructed that is based upon three different kinds of nanoparticles namely: copper (Cu), Titanium di oxide (TiO₂), and alumina (Al₂O₃) within the working fluid water. Each mixture is analysed at the individual level and made comparison amongst all the mixture to examine the resistance and thermal conductivity of nanofluid within the boundary layer region. The solutions are exposed via boundary value problem using shooting method along with the Runge-Kutta-Fehlberg method. The characteristics of emerging parameters for the fluid flow and heat transfer are discussed through graphs and tables. The effects of ϕ (nanoparticle volume fraction) on heat transfer and shear stress at the wall are analysed in detail. It is finally concluded that by increasing the ratio of nanoparticles there is a significant increase in the temperature but slight decrease in the velocity profile.     

Mathematical modeling and simulation for the flow of magneto-Powell-Eyring fluid in an annulus with concentric rotating cylinders

The rheological fluid flows through concentric rotating cylinders have wide range of applications in many machinary parts such as axles and shafts to spinning projectiles. Whenever, the rotating motion connected with the discs, the proximity of a surface may be remarkably change the structure of the flow. The main purpose of this study is to discuss the motion of Powell-Eyring fluid between two concentric rotating cylinders. We formulated the problem in cylindrical coordinate system with suitable boundary conditions. The existence and uniqueness of the solution for the equation governing the flow is provided with the help of Schauder’s fixed point theorem. The velocity distribution is obtained by Mathematica software. The numerical results are presented for the sundry parameters through graphical representations. It is depicted from our analysis that, the velocity is an increasing function of rotation parameter and Powell-Eyring fluid parameter. The present analysis has wide range of applications in engineering sciences.     

Magnetohydrodynamic tangent hyperbolic fluid flow past a stretching sheet

In this article, we investigate the MHD tangent hyperbolic fluid flow along a stretching sheet with suction/injection effect at the boundary. The governing nonlinear partial differential equations are transformed into a set of nonlinear ordinary differential equations using the similarity transformation developed by the Lie group analysis. The transformed non-dimensional ordinary differential equations are solved numerically by a shooting technique. The impacts of the governing parameters on the fluid flow and heat transfer characteristics are investigated and discussed, with the help of graphical representations.     

Hybrid nanofluid flow induced by an exponentially shrinking sheet

The flow and heat transfer induced by an exponentially shrinking sheet with hybrid nanoparticles is investigated in this paper. The alumina (Al₂O₃) and copper (Cu) nanoparticles are suspended in water to form Al₂O₃–Cu/water hybrid nanofluid. In addition, the effects of magnetohydrodynamic (MHD) and radiation are also taken into account. The similarity equations are gained from the governing equations using similarity transformation, and their solutions are obtained by the aid of the bvp4c solver available in Matlab software. Results elucidate that dual solutions exist for suction strength S > S_c and shrinking strength λ > λ_c. The critical values S_c and λ_c for the existence of the dual solutions decrease with the rising of the solid volume fractions of Cu, φ₂ and the magnetic parameter, M. Besides, the skin friction and the heat transfer rate increase with the increasing of φ₂ and M for the upper branch solutions. The increasing of radiation, R leads to reduce the surface temperature gradient which implies to the reduction of the heat transfer rate for both branches when λ < 0 (shrinking sheet). The stability of the dual solutions is determined by the temporal stability analysis, and it is discovered that only one of them is stable and physically applicable.     

Bioremediation strategies of palm oil mill effluent and landfill leachate using microalgae cultivation: An approach contributing towards environmental sustainability

Palm oil mill effluent (POME) is defined as the wastewater that contains high concentrations of organics, nutrients and oil and grease generated from the production process of palm oil. Therefore, proper discharge and management of POME is important to avoid deleterious impact on the environment. In fact, solid waste generation is a precursor for its disposal issues as most of the solid waste generated in developing nations is dumped into landfills. This has led to the threat posed by the generation of landfill leachate (LL). LL is a complex dark coloured liquid consisting of organic matter, inorganic substances, trace elements and xenobiotics. Hence, it is essential to effectively treat the landfill leachate before discharging it to avoid contamination of soil, surface & groundwater bodies. Conventional treatment methods comprises of physical, biological and chemical treatment, however, microalgal-based treatment could also be incorporated. Furthermore, with the benefits offered by microalgae in valorisation, the application of microalgae in POME and leachate treatment as well as biofuel production, is considerably viable. This paper provides an acumen of the microalgae-based treatment of POME and LL, integrated with biofuel production in a systematic and critical manner. The pollutants assimilation from wastewater and CO₂ biosequestration are discussed for environmental protection. Cultivation systems for wastewater treatment with simultaneous biomass production and its valorisation, are summarised. The study aims to provide insight to industrial stakeholders on economically viable and environmentally sustainable treatment of wastewaters using microalgae, and eventually contributing to the circular bioeconomy and environmental sustainability.