Search results

This study aims to analyze entropy generation and magnetohydrodynamic (MHD) natural convection of hybrid nanofluid in a square cavity, with a heated elliptical block placed at the center, in presence of a periodic-variable magnetic field.

In this paper, simulations were performed with a FORTRAN home code. The numerical methodology used to solve Navier–Stokes, energy and entropy generation equations with corresponding boundary conditions, is essentially based on the finite volume method and full multigrid acceleration.

The cavity is filled with Ag–Tio₂/Water hybrid nanofluid. The main objective of this investigation is to predict the effects of body’s size (6 cases), type of applied magnetic field (variable or uniform), the non-dimensional period number of the variable magnetic field (VMF) (0.2 ≤ Λ ≤ 0.8), the inclination angle of the VMF (0 ≤ χ ≤ 90), Rayleigh number (5 × 103 ≤ Ra ≥ 105) and Hartmann number (5 ≤ Ha ≥ 100) on thermal performance, heat transfer rate, entropy generation and flow patterns.

To the authors’ best knowledge, this paper is the first numerical investigation deals with the entropy generation and natural convection of hybrid nanofluid in a two-dimensional cavity, with specific thermal boundary conditions, containing an elliptical block under periodic-variable magnetic field. Different combinations between flow-governing parameters were made to find optimal thermal performance.

This study aims to numerically scrutinize the entropy generation minimization and mixed convective heat transfer of multi-walled carbon nanotubes–Fe₃O₄/water hybrid nanofluid flow in a lid-driven square enclosure with heat generation in the presence of a porous layer on inner surfaces, considering local thermal non-equilibrium (LTNE) approach and the non-Darcy flow model.

The dimensionless governing equations for hybrid nanofluid and solid phases are solved by applying the finite volume method and semi-implicit method for pressure-linked equations algorithm.

The roles of the internal heat generation in the porous layer, LTNE model and nanoparticles volume fraction on mixed convection phenomenon and entropy generation are introduced for lid-driven cavity hybrid nanofluid flow. Based on the investigation of entropy generation and heat transfer, the minimum total entropy generation and average Nusselt numbers are found at 1 ≤ Ri ≤ 10 where the effect of the forced and free convection flow directions being opposite each other is very significant. When considering various nanoparticle volume fractions, it becomes evident that the minimum entropy generation occurs in the case of φ = 0.1%. The outcomes of LTNE number reveal the operating parameters in which thermal equilibrium occurs between hybrid nanofluid and solid phases.

The analysis of entropy generation under various shear and buoyancy forces plays a significant role in the suitable thermal design and optimization of mixed convective heat transfer applications. This research significantly contributes to the optimization of design and the advancement of innovative solutions across diverse engineering disciplines, such as packed-bed thermal energy storage and thermal insulation.

This paper aims to introduce the decomposed harmonic balance finite element method (HBFEM) to decrease the memory requirement in large‐scale computation of the DC‐biasing magnetic field. Harmonic analysis of the flux density and flux distribution was carried out to investigate the DC biased problem in a laminated core model (LCM).

Based on the DC bias test on a LCM, the decomposed HBFEM is applied to accurately calculate the DC‐biasing magnetic field. External electric circuits are coupled with the magnetic field in the harmonic domain. The reluctivity matrix is decomposed and the block Gauss‐Seidel algorithm solves each harmonic solution of magnetic field and exciting current sequentially.

The calculated exciting currents and flux density are compared with that obtained from measurement and time domain finite element analysis, respectively, which demonstrates consistency. The DC bias leads to the significant saturation of the magnetic core and serious distortion of the exciting current. The flux density varies nonlinearly with DC bias excitation.

The harmonic balance method is only applicable in solving the steady state magnetic field. Future improvements in the method are necessary in order to manage the hysteresis effects in magnetic material.

The proposed method to solve the DC biased problem significantly reduces the memory requirement compared to the conventional HBFEM. The decomposed harmonic balance equations are solved efficiently by the block Gauss‐Seidel algorithm combined with the relaxation iterative scheme. An investigation on DC bias phenomena is carried out through the harmonic solution of the magnetic field. The decomposed HBFEM can also be applied to solve 3‐D DC‐biasing magnetic field and eddy current nonlinear problems in a practical power transformer.

Discrete differential operators of periodic base functions have been examined to solve boundary-value problems. This paper aims to identify the difficulties of using those operators to solve ordinary linear and nonlinear differential equations with Dirichlet and Neumann boundary conditions.

This paper presents a promising approach for solving two-dimensional (2D) boundary problems of elliptic differential equations. To create finite differential equations, specially developed discrete partial differential operators are used to replace the partial derivatives in the differential equations. These operators relate the value of the partial derivatives at each point to the value of the function at all points evenly distributed over the area where the solution is being sought. Exemplary 2D elliptic equations are solved for two types of boundary conditions: the Dirichlet and the Neumann.

An alternative method has been proposed to create finite-difference equations and an effective method to determine the leakage flux in the transformer window.

The proposed approach can be classified as an extension of the finite-difference method based on the new formulas approximating the derivatives. This method can be extended to the 3D or time-periodic 2D cases.

This paper presents a methodology for calculations of the self- and mutual-leakage inductances for windings arbitrarily located in the transformer window, which is needed for special transformers or in any case of the internal asymmetry of windings.

The presented methodology allows us to obtain the magnetic vector potential distribution in the transformer window only, for example, to omit the magnetic core of the transformer from calculations.