In this study, the influence of gravity-driven convection and Marangoni convection due to the temperature-dependent surface tension gradient on the rise of an axisymmetric bubble moving in another fluid in a self-rewetting system inside a rectangular tube is studied in the presence and absence of a magnetic field. The axisymmetric bubble (fluid 1) moving in another fluid (fluid 2) is considered immiscible. A two-dimensional cylindrical polar coordinate system has been chosen to present the sketch of the problem. Partial differential equations governing the mentioned flow situations are written and converted into non-dimensional forms and their analytical solutions have been obtained. The deformation in the bubble in the form of its radius and length is simulated. The motion of the droplet is also analysed in the microgravity region by graphing the position of the bubble. The graphical results show that there is a decrease in the contribution of the Marangoni effect and gravitational effect when the magnetic field is increased. In the absence of a magnetic field, the contribution of both the Marangoni effect and gravitational effect decrease on increasing the relative viscosity.
This article theoretically investigates the entropy generation in unsteady two-dimensional magnetohydrodynamic flow of Maxwell power-law-fluid past a stretching surface in consideration of thermal and solutal Marangoni convection. The heat and mass transport phenomenon of Maxwell power-law-fluid has been expressed using Cattaneo-Christov double diffusion (CCDD) model. Governing equations are modeled by using Navier-Stokes equations under suitable consideration. The developed mathematical model of the problem is in the form of nonlinear and coupled partial differential equations. Using similarity transforms, governing equations are converted into non-linear coupled ordinary differential equations (ODEs) whose numerical solutions have been obtained using Bvp4c routine in MATLAB. Through numerous graphs, a thorough analysis of entropy generation and Bejan number is conducted. It has been observed that the fluid velocity gets accelerated for higher values of thermal and solutal Marangoni parameters in the boundary layer.
Research into hybrid nanofluid flow over a disk surface is growing due to numerous processes in marine or gas turbines, rotating disk reactors for biofuels generation, cooling of spinning equipment components and other industrial applications. The purpose of this research study is to examine the entropy generation for the transient thermocapillary flow of hybrid nanoliquid thin films across a disk surface with different shapes of nanoparticles. To analyze the nanomaterial, the Tiwari–Das hybrid nanofluid flow model is established, and in doing so, Prandtl’s boundary layer theory is incorporated into this model. The energy equation considers the impacts of thermal radiation, two different kinds of heat sources — namely an exponentially space-dependent heat source and a linear thermal heat source — and viscous dissipation. The nonlinear partial differential equations, which explain the flow processes, are transformed into the nondimensional ordinary differential equations (ODEs). Once the ODEs have been constructed, they are next solved using the bvp4c technique. In addition, the surface drag force and the rate of heat transfer are both evaluated as functions of the shape factor of the nanoparticles that are disseminated in the base fluid. The influence of significant parameters on the flow fields is depicted graphically, and adequate physical explanations are provided for each representation. One of the important findings of this study indicates that the largest amount of heat transfer can be accomplished at the disk surface by employing nanoparticles with blade shape, while this physical quantity is the least when nanoparticles with spherical shapes are used. The temperature profile grows as the thermal and exponential heat sources increase. Entropy generation improves with the increase in either the magnetic parameter or the Brinkman number.
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