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Problem 2 of the International Workshop for Eddy Current Code Comparison is a hollow cylinder with its axis perpendicular to a uniform sinuosoidal field. A total of 10 solutions, employing 9 different computer codes, are described and compared with analytic results. Most codes were 2‐D finite element and were found to give satisfactory solutions.

A series of six workshops was held to compare eddy current codes, using the six benchmark problems described in the following six papers. The problems include transient and steady‐state ac magnetic fields, close and far boundary conditions, magnetic and non‐magnetic materials. All the problems are based either on experiments or on geometries that can be solved analytically. The workshops and solutions to the problems are described. Results show that many different methods and formulations give satisfactory solutions, and that in many cases reduced dimensionality or coarse discretization can give acceptable results while reducing the computer time required.

The purpose of this paper is to investigate analytically the steady general three-dimensional stagnation-point flow of an aqueous titania-copper hybrid nanofluid past a circular cylinder that has a sinusoidal radius variation.

First, the analytic modeling of hybrid nanofluid is presented, and using appropriate similarity variables, the governing equations are transformed into nonlinear ordinary differential equations in the dimensionless stream function, which is solved by the well-known function bvp4c from MATLAB.

The current solution demonstrates good agreement with those of the previously published studies in the special cases of regular fluid and nanofluids. Graphical results are presented to investigate the influences of the titania and copper nanoparticle volume fractions and also the nodal/saddle indicative parameter on flow and heat transfer characteristics. Here, the thermal characteristics of hybrid nanofluid are found to be higher in comparison to the base fluid and fluid containing single nanoparticles. An important point to note is that the developed model can be used with great confidence to study the flow and heat transfer of hybrid nanofluids.

Analytic modeling of hybrid nanofluid is the important originality of present study. Hybrid nanofluids are potential fluids that offer better heat transfer performance and thermophysical properties than convectional heat transfer fluids (oil, water and ethylene glycol) and nanofluids with single nanoparticles. In this investigation, titania (TiO₂, 50 nm), copper (Cu, 20 nm) and the hybrid of these two are separately dispersed into the water as the base fluid and analyzed.

This paper aims to develop a numerical study of the steady natural convection in an inclined square porous cavity filled by a nanofluid with sinusoidal temperature distribution on the side walls and adiabatic conditions on the upper and lower walls.

Governing equations transformed in terms of the dimensionless variables using the Darcy–Boussinesq approximation have been solved numerically using a central finite-difference scheme. The Gaus-Siedel iteration technique was used for the system of discretized equations. The two-phase nanofluid model including the Brownian diffusion and thermophoresis effects has been considered for simulation of nanofluid transport inside the cavity.

The numerical results of streamlines, isotherms and isoconcentrations are investigated and the effect of different important parameters, such as inclination angle of the cavity, amplitude ratio of the sinusoidal temperature or phase deviation, is discussed. The results obtained for no inclination of the cavity are compared and successfully validated with previous reported results of the literature. The important findings of the study are focused on the changes made by the inclination angle and the periodic thermal boundary conditions, on the heat and fluid flow.

The originality of the present study is given by the mathematical model presented for an inclined cavity, the numerical solution with new results for inclined cavity and the applications for design of solar energy devices such as solar collectors in which the boundary conditions vary with time because of changes in weather conditions.

The purpose of this paper is to develop a novel type of full‐size flight control iron bird based on a passive electronic hydraulic servo loading system.

On the basis of mathematical modeling of passive loading system math model, the detailed design process of the flight control iron bird is presented. Subsequently, the system digital simulation and physical verification are also given.

Experimental results show that the proposed approach can reduce the redundant forces and improve the system dynamic and force‐tracking accuracy.

This newly‐developed flight control iron bird system has been successfully applied in the flight control system design of some fighters.

The proposed approach for flight control iron bird is new and significant for the design of fighter flight control systems.

The purpose of this study is numerical simulation of magnetohydrodynamics (MHD) water–Al₂O₃ nanofluid mixed convection in a grooved channel with internal heat generation in solid cylinders. Simulations were carried out at Reynolds numbers 50 ≤ Re ≤ 100, Hartmann numbers 0 ≤ Ha ≤ 15, Grashof numbers 5,000 ≤ Gr ≤ 10⁻⁴ and volume fraction 0 ≤ φ ≤ 0.04. The effect of Reynolds number and the influence of magnetic field and pressure drop on convective heat transfer coefficient were studied in different volume fractions of nanoparticles at different Reynolds numbers.

The results show that average Nusselt number increases by increasing Reynolds and Hartman numbers. Also, when Hartman number increases, velocity profile becomes asymmetric. Pressure distribution shows that magnetic field applies Lorentz force at opposite direction of the flow, which causes asymmetric distribution of pressure. As a result, pressure in the upper half of the cylinder is higher than the lower half. Finally, velocity and temperature contours along the channel for different Hartmann numbers, volume fraction 3 per cent, Re = 50 and 100 and Gr = 10,000, are presented.

The effect of Reynolds number and the influence of magnetic field and pressure drop on convective heat transfer coefficient were studied in different volume fractions of nanoparticles at different Reynolds numbers.

Effect of MHD on the flow and heat transfer characteristics of Water–Al₂O₃ nanofluid in a grooved channel with internal heat generation in solid cylinders.

The purpose of this paper is to study the effects of natural convection heat transfer in a cold outer circular enclosure containing a hot inner elliptic circular cylinder. The fluid in the enclosure is Cu-water nanofluid. The main emphasis is to find the numerical treatment for the said mathematical model. The effects of Rayleigh number, inclined angle of elliptic inner cylinder, effective of thermal conductivity and viscosity of nanofluid, volume fraction of nanoparticles on the flow and heat transfer characteristics have been examined.

A very effective and higher order numerical scheme Control Volume-based Finite Element Method (CVFEM) is used to solve the resulting coupled equations. The numerical investigation is carried out for different governing parameters namely; the Rayleigh number, nanoparticle volume fraction and inclined angle of elliptic inner cylinder. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell-Garnetts (MG) and Brinkman models, respectively.

The results reveal that Nusselt number increases with an increase of nanoparticle volume fraction, Rayleigh numbers and inclination angle. Also it can be found that increasing Rayleigh number leads to a decrease in heat transfer enhancement. For high Rayleigh number the minimum heat transfer enhancement ratio occurs at.

To the best of the authors’ knowledge, no such analysis is available in the literature which can describe the natural convection heat transfer in a nanofluid filled enclosure with elliptic inner cylinder by means of CVFEM.

A porous cavity flow field generates entropy owing to energy and momentum exchange within the fluid and at solid barriers. The heat transport and viscosity effects on fluid and solid walls irreversibly generate entropy. This numerical study aims to investigate convective heat transfer together with entropy generation in a partially heated wavy porous cavity filled with a hybrid nanofluid.

The governing equations are nondimensionalized and the domain is transformed into a unit square. A second-order finite difference method is used to have numerical solutions to nondimensional unknowns such as stream function and temperature. This numerical computation is conducted to explore a wide range of regulating parameters, e.g. hybrid nano-particle volume fraction (σ = 0.1%, 0.33%, 0.75%, 1%, 2%), Rayleigh–Darcy number (Ra = 10, 10², 10³), dimensionless length of the heat source (ϵ = 0.25, 0.50,1.0) and amplitude of the wave (a = 0.05, 0.10, 0.15) for a number of undulations (N = 1, 3) per unit length.

A thorough analysis is conducted to analyze the effect of multiple factors such as thermal convective forces, heat source, surface corrugation factors, nanofluid volume fraction and other parameters on entropy generation. The flow and temperature fields are studied through streamlines and isotherms. The average Bejan number suggested that entropy generation is entirely dominated by irreversibility due to heat transport at Ra = 10, and the irreversibility due to the viscosity effect is severe at Ra = 10³, but the increment in s augments irreversibility due to the viscosity effect over the heat transport at Ra = 10².

To the best of the authors’ knowledge, this numerical study, for the first time, analyzes the influence of surface corrugation on the entropy generation related to the cooling of a partial heat source by the convection of a hybrid nanofluid.

This study aims to investigate the flow impinging on a stagnation point of a shrinking cylinder subjected to prescribed surface heat flux in Al₂O₃-Cu/water hybrid nanofluid.

Using similarity variables, the similarity equations are obtained and then solved using bvp4c in MATLAB. The effects of several physical parameters on the skin friction and heat transfer rate, as well as the velocity and temperature profiles are analysed and discussed.

The outcomes show that dual solutions are possible for the shrinking case, in the range λc<λ<−1, where λc is the bifurcation point of the solutions. Meanwhile, the solution is unique for λ≥−1. Besides, the boundary layer is detached on the surface at λc, where the value of λc is affected by the hybrid nanoparticle φhnf and the curvature parameter γ. Moreover, the friction and the heat transfer on the surface increase with the rising values φhnf and γ. Finally, the temporal stability analysis shows that the first solution is stable in the long run, whereas the second solution is not.

The present work considers the problem of stagnation point flow impinging on a shrinking cylinder containing Al₂O₃-Cu/water hybrid nanofluid, with prescribed surface heat flux. This paper shows that two solutions are obtained for the shrinking case. Further analysis shows that only one of the solutions is stable as time evolves.

The purpose of this paper is to examine the effect of magnetic field on ferrofluid convective mode with radiation.

Viscosity of Fe₃O₄ ferrofluid is considered as a function of magnetic field. Solutions of the governing equations are obtained by a powerful numerical method, namely, control volume finite element method (CVFEM). Roles of radiation parameter (Rd), number of undulations (N), Fe₃O₄–water volume fraction (ϕ), Hartmann (Ha) and Rayleigh numbers are illustrated graphically. A correlation for Nu_ave is extracted.

The inner wall temperature decreases with increasing buoyancy forces, but increases with increasing Rd and Ha. Also increasing Rd results in increasing nanofluid motion. This influence is more evident when convection flow is dominant. As nanofluid temperature increases, the nanofluid begins moving from the warm surface to the outer one and dropping along the circular cylinder. At low Rayleigh number, conduction is more significant than convection. |Ψ_max| increases as buoyancy force increases and it decreases as the Lorentz force increases. As Hartmann number increases, the center of the vortices moves to x = 0. As Ra increases, convection becomes stronger. Thus, |Ψ_max| and temperature gradient increase with increasing Ra. As N increases, the distortion of isotherms reduces and vortices become weaker. Increasing Hartmann number results in a reduction in the thermal plume and the heat transfer mechanism changes from convection to conduction. Nusselt number decreases with increasing N ⋅ Nu decreases with increasing Lorentz force. At N = 5 , increasing the Lorentz force causes the main vortices to convert into three smaller ones. As the Lorentz force increases, the two upper vortices merge together and the thermal plume vanishes. The number of extrema in the Nu_loc profile matches the existence of the thermal plume and the number of undulations. Nu_ave increases with increasing Rd. As buoyancy forces increase, the temperature decreases and in turn Nu_ave increases with increasing Ra.

Nanofluids are an innovative way to enhance radiation heat. In this paper, MHD Fe₃O₄–water nanofluid natural convection with radiation source term is examined. Magnetic field-dependent (MFD) viscosity is considered. Using the CVFEM, numerical simulations are carried out for various values of the radiation parameter (Rd = 0 to 0.8), volume fraction of Fe₃O₄–water (ϕ = 0 to 0.04), Rayleigh number (Ra = 10³, 10⁴ and 10⁵), number of undulations (N = 3,4 and 5) and Hartmann number (Ha = 0 to 40).