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The purpose of this paper is to explore a model for thermal convection in a plane layer when the density-temperature relation in the buoyancy term is quadratic. A heat source/sink varying in a linear fashion with a vertical height expressed as z was allowed, functioning as a heat sink in an area of the layer and as a heat source in the remainder.

First, the authors present the governing equations of motion and derive the associated perturbation equations. Second, the authors introduce the linear and nonlinear analysis of the system. Third, the authors transform the system to velocity-vorticity-potential formulation and introduce a numerical study of the problem in three dimensions.

First, the linear instability and nonlinear stability thresholds are derived. Second, the linear instability thresholds accurately predict the onset of instability. Third, the required time to arrive at the steady state increases as Ra tends to Ra_L . Fourth, the authors find that the convection has three different interesting patterns.

With the modernday need for heat transfer or insulation devices in industry, particularly those connected with nanotechnology, the usefulness of a mathematical analysis of such resonance became apparent. Thus, this study is believed to be of value.

The purpose of this paper is to develop the numerical simulated methodology for sloshing motion of fluid inside a two dimension rectangular tank, and parametric studies were performed for three parameters – excitation frequency, excitation amplitude, and liquid depth.

A numerically simulated methodology by using the cell‐centered pressure‐based SIMPLE scheme and level set method for the sloshing motion of fluid in a rectangular tank has been developed. The convection term in the Navier‐Stokes equations and the equations used in the level set method were treated by the second‐order upwind scheme. The temporal derivative terms were solved by the three‐level second order scheme. The diffusion term in the Navier‐Stokes equations alone was solved by the central‐difference scheme. All algebraic equations were solved by the point Gauss‐Seidel method. A fully implicit scheme to treat the level set distancing equation, written as the advection equation, was developed. In addition, the level set distancing equation was solved by the iterative procedure to determine the variation of free surface.

For given excitation amplitude together with a liquid depth, the free surface displacement increases when the excitation frequency is less than the resonance frequency of tank. However, the free surface displacement decreases when the excitation is greater than the resonant frequency of the tank. It is noted that the maximum free surface displacement is generated under the circumstance for which the excitation frequency approaches the resonant frequency. The excitation amplitude and the excitation frequency have a substantial effect on the impact pressure on the wall of the tank being investigated.

The sloshing motion of fluid in a rectangular tank has been studied by researchers and scholars using many numerical methods; however, literature employing the level set method to study the sloshing motion of fluid is limited. In this study, the cell‐centered pressure‐based SIMPLE scheme and level set method can be employed to predict the sloshing motion. The numerical methodology can help the engineer to predict sloshing motion of fluid.

The aim of this study is to numerically simulate the density-driven convection in heterogeneous porous media associated with anisotropic permeability field, which is important to the safe and stable long term CO₂ storage in laminar saline aquifers.

The study uses compact finite difference and the pseudospectral method to solve Darcy’s law.

The presence of heterogeneous anisotropy may result in non-monotonic trend of the breakthrough time and quantity of CO₂ dissolved in the porous medium, which are important to the CO₂ underground storage.

The manuscript numerically study the convective phenomena of mixture contained CO₂ and brine. The phenomena are important to the process of CO₂ enhanced oil recovery. Interesting qualitative patterns and quantitative trends are revealed in the manuscript.

Sinusoidal gravity modulation fields imposed on two‐dimensional Rayleigh‐Benard convection flow are studied to understand the effects of periodic source (g‐jitter) on fluids system and heat transfer mechanism. The transient Navier‐Stokes and energy equations are solved by semi‐implicit operator splitting finite element method. Results include two sets. One is considered at normal terrestrial condition and the other one is related to low‐gravity condition. Under low‐gravity condition the research focuses on the effects of modulation frequency and direction in order to find out the critical frequency for heat transfer mechanism transferring from conduction to convection.

The purpose of this paper is to numerically examine the conjugate natural convection in an inclined enclosure with a conducting centred block. This enclosure is filled with an Ethylene Glycol‐copper nanofluid. This study utilises numerical simulations to quantify the effects of pertinent parameters such as the Rayleigh number, the solid volume fraction, the length and the thermal conductivity of the centred block and the inclination angle of the enclosure on the conjugate natural convection characteristics.

The SIMPLE algorithm is utilised to solve the governing equations with the corresponding boundary conditions. The convection‐diffusion terms are discretised by a power‐law scheme and the system is numerically modelled in FORTRAN.

The results show that the utilisation of the nanofluid enhances the thermal performance of the enclosure and that the length of the centred block affects the heat transfer rate. The results also show that the higher block thermal conductivity results in a better heat transfer that is most noticeable at low Rayleigh numbers, and that increasing the inclination angle improves the heat transfer, especially at high Rayleigh numbers.

This paper presents an original research on conjugate natural convection in nanofluid‐filled enclosures.

This paper seeks to increase our understanding on the fluid mechanics and heat transfer in a transitional mixed convection flow between two vertical plates. Direct numerical simulation by the spectral method, with a weak formulation, is used to solve the transient 3–D Navier‐Stokes equations and energy equation. Initial disturbances consist of the finite‐amplitude 2–D Tollmien‐Schlichting wave and two 3–D oblique waves. The transition phenomena in a mixed‐convection flow can be significantly different from the isothermal flow. Disturbance competitions among different modes are also found to be different from those known for an isothermal flow. In a mixed‐convection flow, there exist thresholds for the low‐mode Fourier waves. The intensified vortices are concentrated left of the central surface between the two plates. Hairpin vortices are formed with high Ri. Based on the flow visualization, the λ vortices are found to be staggered on the surfaces parallel to the plates. The Ri number seems to be the main parameter governing the transition mechanism. The Nu number is found to increase during transition.

This paper aims to investigate the fluid structure interaction analysis of conjugate natural convection in a square containing internal solid cylinder and flexible right wall.

The right wall of the cavity is flexible, which can be deformed due to the interaction with the natural convection flow in the cavity. The top and bottom walls of the cavity are insulated while the right wall is cold and the left wall is partially heated. The governing equations for heat, flow and elastic wall, as well as the grid deformation are written in Arbitrary Lagrangian–Eulerian formulation. The governing equations along with their boundary conditions are solved using the finite element method.

The results of the present study show that the presence of the solid cylinder strongly affects the transient solution at the initial times. The natural convection flow changes the shape of the flexible right wall of the cavity into S shape wall due to the interaction of the flow and the structure. It is found that the increase of the flexibility of the right wall increases the average Nusselt number of the hot wall up to 2 per cent.

To the best of the authors' knowledge, the unsteady natural convection in an enclosure having a flexible wall and inner solid cylinder has never been reported before.

The purpose of this paper is to investigate the thermal convection inside a spatially modulated domain.

The governing equations are mapped onto an infinite strip, allowing Fourier expansion of the flow and temperature in the streamwise direction.

Similar to Rayleigh‐Benard convection, conduction is lost to convection at a critical Rayleigh number, which depends strongly on both the modulation amplitude and the wavenumber. The effect of modulation is found to be destabilizing (stabilizing) for conduction for relatively large (small) modulation wavelength. Oscillatory convection sets in as the Rayleigh number is increased.

This paper presents novel results.

The main purpose of this study is to test the performance of the ink-jet printed microwave resonant circuits on Low temperature co-fired ceramics (LTCC) substrates combined with microfluidic channels for sensor applications. Normally, conductive patterns are deposited on an LTCC substrate by means of the screen-printing technique, but in this paper applicability of ink-jet printing in connection with LTCC materials is demonstrated.

A simple microfluidic LTCC sensor based on the microstrip ring resonator was designed. It was assumed the micro-channel, located under the ring, was filled with a mixture of DI water and ethanol, and the operating frequency of the resonator was tuned to 2.4 GHz. The substrate was fabricated by standard LTCC process, and the pattern of the microstrip ring resonator was deposited over the substrate by means of an ink-jet printer. Performance of the sensor was assessed with the use of various volumetric concentrations of DI water and ethanol. Actual changes in concentration were detected by means of microwave measurements.

It can be concluded that ink-jet printing is a feasible technique for fast fabrication of micro-strip circuits on LTCC substrates, including microfluidic components. Further research needs to be conducted to improve the reliability, accuracy and performance of this technique.

The literature shows the use of ink-jet printing for producing various conductive patterns in different applications. However, the idea to replace the screen-printing with the ink-jet printing on LTCC substrates in connection with microwave-microfluidic applications is not widely studied. Some questions concerning accuracy and reliability of this technique are still open.

The purpose of this paper is to study the multi-objective optimization design method of high-power high-frequency magnetic-resonance air-core transformer (ACT).

First, this paper studies the interleaved winding technology, the process of modeling and simulation, the calculation method of high-frequency loss of Litz wire and the design of magnetic shielding in detail. Second, the multi-objective optimization design process of high-frequency magnetic-resonance ACT is established by parametric scanning method and orthogonal experiment method.

An ACT model of 2 kV/100 kW/81.34 kHz was designed. The efficiency, weight power density and volume power density are 99.61%, 21.6 kW/kg and 5.1 kW/kg, respectively. Finally, the multi-physical field coupling simulation method is used to calculate the port excitation voltages and currents and temperature field of ACT. The maximum temperature of the ACT is 95.5 °C, which meets the design requirements.

The above research provides guidance and basis for the optimization design of high-power high-frequency magnetic-resonance ACT.