HEAT EXCHANGE OF ELECTRIC CONDUCTIVE LIQUID IN THE SUPPLY OF HEAT TO THE INNER SURFACE OF THE SPHERICAL LAYER AT SMALL VALUES OF THE REYNOLD'S MAGNETIC NUMBER

Представлены результаты численного моделирования нестационарного теплообмена и магнитной гидродинамики электропроводной жидкости в сферическом слое. Исследовано влияние малых значений магнитного числа Рейнольдса и теплоты джоулевой диссипации на эволюцию структуры течения жидкости, поле температуры, магнитной индукции и распределение чисел Нуссельта. The results of numerical simulation of unsteady heat transfer and magneto hydrodynamics of an electrically conductive fluid in a spherical layer are presented. The influence of small values of the magnetic Reynolds number and the heat of Joule dissipation on the evolution of the structure of the fluid flow, the field of temperature, magnetic induction and the distribution of Nusselt numbers is investigated.

Dynamics of water conveying zinc oxide through divergent-convergent channels with the effect of nanoparticles shape when Joule dissipation are significant

Aim of study The shape effects of nanoparticles are very significant in fluid flow and heat transfer. In this paper, we discuss the effects of nanoparticles shape in nanofluid flow between divergent-convergent channels theoretically. In this present study, various shapes of nanoparticles, namely sphere, column and lamina in zinc oxide-water nanofluid are used. The effect of the magnetic field and joule dissipation are also considered. Research methodology The system of nonlinear partial differential equations (PDEs) is converted into ordinary differential equations (ODES). The analytical solutions are successfully obtained and compared with numerical solutions. The Homotopy perturbation method and NDsolve method are used to compare analytical and numerical results respectively. Conclusion The results show that the lamina shape nanoparticles have higher performance in temperature disturbance and rate of heat transfer as compared to other shapes of nanoparticles.

Insight into the significance of Joule dissipation, thermal jump and partial slip: Dynamics of unsteady ethelene glycol conveying graphene nanoparticles through porous medium

In the production of ethelene glycol, graphene nanoparticles is inevitable and even suggested due to monomolecular layer of carbon atoms which are bounded like honey comb structure is known as graphene due to this structure, graphene has several types of exceptional and unique structural, optical and electronic properties. However, little is known on the enhancement of the transport phenomenon when Joule dissipation, inclined magnetic field, thermal jump and partial slip are apparent. With emphasis to the inherent aforementioned concepts together with heat source/sink and thermal radiation, this paper presents insight into the dynamics of unsteady Ethelene glycol conveying graphene nanoparticles through porous medium. The dimensional governing equation was non-dimenzionalized using fitting similarity variables and solved the dimensionless equations using Runge-Kutta Fehlberg algorithms along with the shooting technique. Also, a statistical method was implemented for multiple quadratic regression estimation analysis on the numerical figures of wall velocity gradient and local Nusselt number to establish the connection among heat transfer rate and physical parameters. Our numerical findings reveal that the magnetic field and porosity parameters boost the graphene Maxwell nanofluid velocity while Maxwell parameter has a reversal impact on it. The regression analysis confers that Nusselt number is more prone to heat absorption parameter as compared to Eckert number. The rate of heat transfer is higher in case of with slip compare to without slip flow in the presence of thermal radiation, viscous dissipation and unsteady parameter. The fluid velocity and temperature distribution is higher in without slip compare to with slip flow.

Effect of nonuniform heat source/sink, and viscous and Joule dissipation on 3D Eyring–Powell nanofluid flow over a stretching sheet

The aim of this paper is to explore the effect of heat source/sink, and space- and temperature-dependent viscous and Joule dissipation on 3D magnetohydrodynamic radiating Eyring–Powell nanofluid streamline flow with convective conditions past a stretching sheet. The coupled nonlinear flow, thermal, and species phenomena equations are transformed into a system of coupled nonlinear ordinary differential equations through suitable similarity transformations with corresponding boundary conditions. The transformed dimensionless equations are then solved analytically with the Adomian decomposition method. A comprehensive study is conducted on the influence of sundry physical dimensionless parameters governing the flow velocity, temperature, and concentration distributions. For parameters of engineering interest, the computed numerical results are presented with the aid of tables. Furthermore, the present solutions agree with the earlier reported results in specific cases, and an excellent correlation is witnessed. The present analysis is of great interest germane to cooling of metallic plates, polishing of artificial heart valves, oil pipeline friction reduction in the oil industry, flow tracers, enhanced oil recovery, and separation processes in chemical industries and petroleum extraction.

Simulation of electrically conductive liquid convection in a spherical layer when heat is applied to the inner sphere

Представлены результаты численного моделирования конвективного теплообмена электропроводящей жидкости между концентрическими сферами при подводе тепла к внутренней сфере. Исследовано влияние числа Грасгофа и джоулевой диссипации на структуру течения жидкости, поля температуры, магнитной индукции и распределение локальных чисел Нуссельта. Получено уравнение подобия теплообмена, когда ускорение свободного падения направлено к центру сферического слоя. The Boussinesq approximation is used for modelling a large class of problems of convective heat transfer in spherical concentric layers in which the gravity vector is directed vertically downwards. But for problems of geophysics and astrophysics there is a fundamental difference, the gravity vector is directed along the radius to the center of the spherical layer. Therefore, the study of convective heat transfer in spherical layers, when the vector of gravitational acceleration is directed along the radius to the center of the spherical layer, is of independent interest. In this paper, the influence of the Grashof number, the Joule dissipation heat on the fluid flow structure, temperature field, magnetic induction, and the distribution of Nusselt numbers when heat is applied from below are studied. To solve the problem, the finite element method is used. In a dimensionless formulation, the problem is solved taking into account both the heat of the Joule dissipation, magnetic, inertial, viscous and lifting forces in a spherical coordinate system and the symmetry in longitude. The stationary fields of temperature, stream functions, vortex strength, radial and meridional components of magnetic induction and the distribution of local Nusselt numbers of electro conductive liquid in a concentric spherical layer for different Grashof numbers with and without accounting for the heat of Joule dissipation are obtained when heat is applied to the inner sphere. Two critical values of the Grashof number are numerically determined. The equation of heat exchange similarity is obtained, when the acceleration of gravity is directed to the center of the spherical layer. The mathematical model and the presented results may be useful for the study of convective heat exchange of electrically conducting fluid in space technologies and in the geophysical and astrophysical problems.

Perturbation theory for metal pad roll instability in cylindrical reduction cells

We propose a new theoretical model for metal pad roll instability in idealized cylindrical reduction cells. In addition to the usual destabilizing effects, we model viscous and Joule dissipation and some capillary effects. The resulting explicit formulas are used as theoretical benchmarks for two multiphase magnetohydrodynamic solvers, OpenFOAM and SFEMaNS. Our explicit formula for the viscous damping rate of gravity waves in cylinders with two fluid layers compares excellently to experimental measurements. We use our model to locate the viscously controlled instability threshold in cylindrical shallow reduction cells but also in Mg–Sb liquid metal batteries with decoupled interfaces.