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The purpose of this study is the application of the following concepts to the time discrete form. Variational Calculus, potential and kinetic energies, velocity proportional Rayleigh dissipation function, the Lagrange and Hamilton formalisms, extended Hamiltonians and Poisson brackets are all defined and applied for time-continuous physical processes. Such processes are not always time-continuously observable; they are also sometimes time-discrete.

The classical approach is developed with the benefit of giving only a short table on charge and flux formulation, as they are similar to the classical case just like all other formulation types. Moreover, an electromechanical example is represented as well.

Lagrange and Hamilton formalisms together with the velocity proportional (Rayleigh) dissipation function can also be used in the discrete time case, and as a result, dissipative equations of generalized motion and dissipative canonical equations in the discrete time case are obtained. The discrete formalisms are optimal approaches especially to analyze a coupled physical system which cannot be observed continuously. In addition, the method makes it unnecessary to convert the quantities to the other. The numerical solutions of equations of dissipative generalized motion of an electromechanical (coupled) system in continuous and discrete time cases are presented.

The formalisms and the velocity proportional (Rayleigh) dissipation function aforementioned are used and applied to a coupled physical system in time-discrete case for the first time to the best of the author’s knowledge, and systems of difference equations are obtained depending on formulation type.

The purpose of this paper is to analyze the dynamical state of a discrete time engineering/physical dynamic system. The analysis is performed based on observability, controllability and stability first using difference equations of generalized motion obtained through discrete time equations of dissipative generalized motion derived from discrete Lagrange-dissipative model [{L,D}-model] for short of a discrete time observed dynamic system. As a next step, the same system has also been analyzed related to observability, controllability and stability concepts but this time using discrete dissipative canonical equations derived from a discrete Hamiltonian system together with discrete generalized velocity proportional Rayleigh dissipation function. The methods have been applied to a coupled (electromechanical) example in different formulation types.

An observability, controllability and stability analysis of a discrete time observed dynamic system using discrete equations of generalized motion obtained through discrete {L,D}-model and discrete dissipative canonical equations obtained through discrete Hamiltonian together with discrete generalized velocity proportional Rayleigh dissipation function.

The related analysis can be carried out easily depending on the values of classical elements.

Discrete equations of generalized motion and discrete dissipative canonical equations obtained by discrete Lagrangian and discrete Hamiltonian, respectively, together with velocity proportional discrete dissipative function are used to analyze a discrete time observed engineering system by means of observability, controllability and stability using state variable theory and in the method proposed, the physical quantities do not need to be converted one to another.

The purpose of this paper is to carry out an in-depth analysis of heat dissipation performance by natural convection phenomenon inside light-emitting diode (LED) lamps containing hot pin-fins because of its significant industrial applications.

The problem is assimilated to heat transfer inside air-filled rectangular cavity with various governing parameters appraised in ranges interesting engineering application and scientific research. The lattice Boltzmann method is used to predict the dynamic and thermal behaviors. Effects of monitoring parameters such as Rayleigh number Ra (10³-10⁶), fin length (0-0.25) and its position, pin-fins number (1-8), the tilting-angle (0-180°) and cavity aspect ratio Ar (0.25-4) are carried out.

The rising behaviors of the dynamic and thermal structures and heat transfer rate (Nu), the heatlines distribution and the irreversibility rate are appraised. It was found that the flow is constantly two contra-rotating symmetric cells. The heat transfer is almost doubled by increasing Ra. A lack of cooling performance was identified between Ar = 0.5 and 0.75. The inclination 45° is the most appropriate cooling case. At constant Ra, the maximum stream-function and the global entropy generation remain almost unchanged by increasing the pin number from 1 to 8 and the entropy generation is of thermal origin for low Ra, so that the fluid friction irreversibility becomes dominant for Ra larger than 10⁵.

Improvements may include three-dimensional complex geometries, accounting for thermal radiation, high unit power and turbulence modelling. Such factors effects will be conducted in the future.

The cooling performance/heat dissipation in LED lamps is a key manufacturing factors, which determines the lifetime of the electronic components. The best design and installation give the opportunity to increase further the product shelf-life.

Both cooling performance, irreversibility rate and enclosure configuration (aspect ratio and inclination) are taken into account. This cooling scheme will give a superior operating mode of the hot components in an era where energy harvesting, storage and consumption is met with considerable attention in the worldwide.

The purpose of this study is to present a comprehensive hydrothermal analysis on an inclined mini-channel using numerical and experimental techniques. The fin array acts as heat source within the channel, and a wavy wall located at the top of the channel is heat sink. The side walls are insulated with curved profiles. Also, the channel is inclined with four known inclination angles. To solve the governing equations, the dual-multi-relaxation-time lattice Boltzmann method with D2Q9 and D2Q5 lattice models for flow and temperature fields is used, respectively. Also, the channel is filled with SiO2-glycol nanofluid.

Identifying the behavior of a thermal component during natural convective flow is a challenging topic due to its complexities. This paper focuses on analyzing the thermal and hydrodynamic aspects of a narrow channel equipping with fin array.

Two correlations are proposed considering temperature and volume fraction ranges for thermal conductivity and dynamic viscosity according to measured experimental data which are used in the numerical phase. Finally, the structure of flow, temperature distribution of fluid, local thermal and viscous dissipations, volume-averaged entropy production, Bejan number and heat transfer rate are extracted by numerical simulations. The results show that the average Nusselt number enhances about 57% (maximum enhancement percentage) when volume fraction increases from 1% to 3% at Ra = 10⁶ and θ = 90°. In addition, the value of entropy generation is maximum at φ = 1%, Ra = 10⁶ and φ = 90°. Also, the maximum enhancement of entropy generation in range of Ra = 103 to 106 is about 4 times at φ = 1% and θ = 90°.

The originality of the present study is combining a modern numerical method (i.e. dual/multi-relaxation-time LBM) with experimental observation on characteristics of SiO₂-glycol nanofluid to study the thermal and hydrodynamic properties of the studied mini-channel.

The purpose of this paper is to carry out a comprehensive review of some latest studies devoted to natural convection phenomenon in the enclosures because of its significant industrial applications.

Geometries of the enclosures have considerable influences on the heat transfer which will be important in energy consumption. The most useful geometries in engineering fields are treated in this literature, and their effects on the fluid flow and heat transfer are presented.

A great variety of geometries included with different physical and thermal boundary conditions, heat sources and fluid/nanofluid media are analyzed. Moreover, the results of different types of methods including experimental, analytical and numerical are obtained. Different natures of natural convection phenomenon including laminar, steady-state and transient, turbulent are covered. Overall, the present review enhances the insight of researchers into choosing the best geometry for thermal process.

A comprehensive review on the most practical geometries in the industrial application is performed.

This study aims to employ a modern numerical approach for conducting the simulations, which uses the smoothed-profile lattice Boltzmann method. Two separate distribution functions for flow and temperature fields are used to solve the Navier–Stokes equations in the most efficient manner. In addition, the Koo–Kleinstreuer–Li model is used to calculate the dynamic viscosity and thermal conductivity in the desired volume fractions, and the effect of Brownian motion is taken into consideration.

Nowadays, because of enhanced global price of oil and critical issue of global warming, a significant demand for using renewable energy exists. The solar energy is one of the most popular forms of renewable energy. The solar collector can be used to collect and trap the energy received from the sun. The present work focuses on introducing and investigating a parabolic-trough solar collector.

To analyze all hydrodynamic and thermal views of the solar collector, the structure of nanofluid stream, distribution of temperature, local dissipations because of flow and heat transfer, volumetric entropy production, Bejan number vs Rayleigh number and volume fraction are presented. Also, three different configurations for profile of solar receiver are designed and studied.

The originality of the present work is in using a modern numerical approach for a well-known application. Also, the effect of Brownian motion is taken into account which significantly enhances the accuracy.

The purpose of this study is analysis of the natural convection and entropy production in a two-dimensional section of the considered heat exchanger. For this purpose, the lattice Boltzmann method which is equipped with Bhatnagar–Gross–Krook model is used. This model proposes a significant accurate prediction for thermal and hydro-dynamical behaviors over free convection phenomenon. The heat exchanger is filled with Fe₂O₃-water nanofluid. To improve the accuracy of prediction, it is neglected to use the theoretical models for properties of nanofluid. At this end, some experimental observations are conducted, and the required rheological and thermal properties of nanofluid are measured based on laboratory work..

The present work focuses on the influence of different factors on the thermal behaviors and entropy production of a heat exchanger. The heat exchanger is consisted by an inner tube, an outer tube and some fins which are implanted at the surface of inner tube.

The effects of various factors like structure of inner fins, nanoparticle concentration and Rayleigh number over the heat transfer rate, local and volumetric entropy production, Bejan number, flow configuration and temperature distributions are provided.

The originality of this work is using a new-developed numerical method for treating natural convection and experimental measurements for thermal and rheological properties of nanofluid.

The purpose of this paper is to describe a variational multiscale finite element approximation for the incompressible Navier‐Stokes equations using the Boussinesq approximation to model thermal coupling.

The main feature of the formulation, in contrast to other stabilized methods, is that the subscales are considered as transient and orthogonal to the finite element space. These subscales are solution of a differential equation in time that needs to be integrated. Likewise, the effect of the subscales is kept, both in the nonlinear convective terms of the momentum and temperature equations and, if required, in the thermal coupling term of the momentum equation.

This strategy allows the approaching of the problem of dealing with thermal turbulence from a strictly numerical point of view and discussion important issues, such as the relationship between the turbulent mechanical dissipation and the turbulent thermal dissipation.

The treatment of thermal turbulence from a strictly numerical point of view is the main originality of the work.

This study aims to numerically study the buoyant convective flow of two different nanofluids in a porous annular domain. A uniformly heated inner cylinder, cooled outer cylindrical boundary and adiabatic horizontal surfaces are considered because of many industrial applications of this geometry. The analysis also addresses the comparative study of different porous media models governing fluid flow and heat transport.

The finite difference method has been used in the current simulation work to obtain the numerical solution of coupled partial differential equations. In particular, the alternating direction implicit method is used for solving transient equations, and the successive line over relaxation iterative method is used to solve time-independent equation by choosing an optimum value for relaxation parameter. Simpson’s rule is adopted to estimate average Nusselt number involving numerical integration. Various grid sensitivity checks have been performed to assess the sufficiency of grid size to obtain accurate results. In this analysis, a general porous media model has been considered, and a comparative study between three different models has been investigated.

Numerical simulations are performed for different combinations of the control parameters and interesting results are obtained. It has been found that the an increase in Darcy and Rayleigh numbers enhances the thermal transport rate and strengthens the nanofluid movement in porous annulus. Also, higher flow circulation rate and thermal transport has been detected for Darcy model as compared to non-Darcy models. Thermal mixing could be enhanced by considering a non-Darcy model.

The present results could be effectively used in many practical applications under the limiting conditions of two-dimensionality and axi-symmetry conditions. The only drawback of the current study is it does not include the three-dimensional effects.

The results could be used as a first-hand information for the design of any thermal systems. This will help the design engineer to have fewer trial-and-run cases for the new design.

A pioneering numerical investigation on the buoyant convective flow of two different nanofluids in an annular porous domain has been carried out by using a general Darcy–Brinkman–Forchheimer model to govern fluid flow in porous matrix. The results obtained from current investigation are novel and original, with numerous practical applications of nanofluid saturated porous annular enclosure in the modern industry.

This paper aims to perform the lattice Boltzmann simulation of natural convection heat transfer in cavities included with active hot and cold walls at the side walls and internal hot and cold obstacles.

The cavity is filled with double wall carbon nanotubes (DWCNTs)-water nanofluid. Different approaches such as local and total entropy generation, local and average Nusselt number and heatline visualization are used to analyze the natural convection heat transfer. The cavity is filled with DWCNTs-water nanofluid and the thermal conductivity and dynamic viscosity are measured experimentally at different solid volume fractions of 0.01 per cent, 0.02 per cent, 0.05 per cent, 0.1 per cent, 0.2 per cent and 0.5 per cent and at a temperature range of 300 to 340 (K).

Two sets of correlations for these parameters based on temperature and solid volume fraction are developed and used in the numerical simulations. The influences of different governing parameters such as Rayleigh number, solid volume fraction and different arrangements of active walls on the fluid flow, heat transfer and entropy generation are presented, comprehensively. It is found that the different arrangements of active walls have pronounced influence on the flow structure and heat transfer performance. Furthermore, the Nusselt number has direct relationship with Rayleigh number and solid volume fraction. On the other hand, the total entropy generation has direct and reverse relationship with Rayleigh number and solid volume fraction, respectively.

The originality of this work is to analyze the two-dimensional natural convection using lattice Boltzmann method and different approaches such as entropy generation and heatline visualization.