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The purpose of this paper is to investigate the impact of time-periodic thermal boundary conditions on natural convection flow in a vertical micro-annulus.

Analytical solution in terms of Bessel’s function and modified Bessel’s function of order 0 and 1 is obtained for velocity, temperature, Nusselt number, skin friction and mass flow rate.

It is established that the role of Knudsen number and fluid–wall interaction parameter is to decrease fluid temperature, velocity, Nusselt number and skin friction.

No laboratory practical or experiment was conducted.

Cooling device in electronic panels, card and micro-chips is frequently cooled by natural convection.

In view of the amount of works done on natural convection in microchannel, it becomes interesting to investigate the effect that time-periodic heating has on natural convection flow in a vertical micro-annulus. The purpose of this paper is to examine the impact of time-periodic thermal boundary conditions on natural convection flow in a vertical micro-annulus.

The purpose of this paper is to investigate fully developed mixed convection flow in the steady-periodic regime for a Newtonian fluid in a vertical microtube in the presence of velocity slip and temperature jump, which has not been accounted for in the literature.

To achieve this objective, the governing equations for the problem are separated into steady and oscillatory components using separation of variable method; this gives a pair of independent boundary value problems. This is then solved along with its boundary conditions and constraint equations using the method of undetermined coefficient. The exact solutions of momentum and energy equations are obtained under the velocity slip and temperature jump conditions.

The significant result from the study is that increase in rarefaction parameter as well as fluid–wall interaction parameter decreases the oscillation amplitude of the dimensionless velocity. Furthermore, it was found that the product of dimensionless frequency and Prandtl number initiate a strong convection current inside the microtube.

Such type of study may be used on the determination of the thermal and tangential momentum accommodation coefficients and be applicable to the designs and fabrications of microheat exchanger. Moreover, it provides the possibility to get a bench mark for numerical solvers with reference to basic flow configuration.

These solutions generally deserve great attention, since the application of a magnetic field has been found to be effective tool in controlling the convection current. The current work is aimed as an extension of the previous analytical studies to prove some insight into a number of industrial applications, which use similar configurations.

Most compact heat exchangers and heat dissipating components rely on convection enhancement mechanisms that reduce the continuous growth of boundary layers. Usually surface irregularities, in the form of interruptions and/or vortex generators, are introduced in the flow passages. The resulting geometric configurations are periodic in space and, after a short distance from the entrance, induce velocity and thermal fields that repeat themselves from module to module. The numerical models presented here consider the space‐periodicity and allow flows that are stationary at sub‐critical values of the Reynolds number, but become time‐periodic, or quasi periodic, above the critical value of the Reynolds number. Space discretizations are achieved by an equal order finite element procedure based on a projection algorithm. Two‐dimensional schematizations are employed to analyze the effects of surface interruptions and transverse vortex generators, while three‐dimensional schematizations are employed for longitudinal vortex generators.

Three‐dimensional laminar forced convective heat transfer in ribbed square channels is investigated. In these channels, transverse and angled ribs are placed on one or two of the walls to form a repetitive geometry. After a short distance from the entrance, also the flow and the dimensionless thermal fields repeat themselves from module to module allowing the assumption of periodic, or anti‐periodic, conditions at the inlet/outlet sections of the calculation cell. Prescribed temperature boundary conditions are assumed at all solid walls, including the ribs. Pressure drop and heat transfer characteristics are compared for rib angles ranging from 90° (transverse ribs) to 45°, and different values of the Reynolds number. The influence of rib geometries is investigated below and above the onset of the self‐sustained flow oscillations that precede the transition to turbulence. Numerical simulations are carried out employing an equal order finite‐element procedure based on a projection algorithm.

Carbonate-based heterogeneous reacting systems are investigated for the applications of thermochemical carbon dioxide capture and energy storage. This paper aims to review recent progress in numerical modeling of thermal transport phenomena in such systems.

Calcium oxide looping is selected as the model carbonate-based reacting system. Numerical models coupling heat and mass transfer to chemical kinetics are reviewed for solar-driven calcium oxide looping on the sorbent particle, particle bed, and reactor levels.

At the sorbent particle level, a transient numerical model of heat and mass transfer coupled to chemical kinetics has been developed for a single particle undergoing cyclic calcination and carbonation driven by time-periodic boundary conditions. Modeling results show cycle times impact the maximum sorbent utilization and solar-to-chemical energy efficiency. At the reactor level, a model of heat and mass transfer coupled to chemical kinetics of calcination of a packed-bed reactor concept has been developed to estimate the reactor’s performance. The model was used to finalize reactor geometry by evaluating pressure drops, temperature distributions, and heat transfer in the reactor.

Successful solar thermochemical reactor designs maximize solar-to-chemical energy conversion by matching chemical kinetics to reactor heat and mass transfer processes. Modeling furthers the understanding of thermal transport phenomena and chemical kinetics interactions and guides the design of solar chemical reactors.

By neglecting the influence of tubes, this paper adopts a simplified two‐dimensional approach to deal with laminar convection of air through wavy finned‐tube exchangers. Pressure drop and heat transfer characteristics are investigated in the fully developed region of the flow channels between adjacent fins. The solutions are presented for several space ratios (height over length of a module) and two corrugation angles. They concern laminar flows both below and above the onset of the self‐sustained oscillations that precede the transition to turbulence. Fully developed velocity and thermal fields are computed by imposing anti‐periodic conditions at inlet/outlet sections of a single calculation cell. In the range of Reynolds numbers investigated, Nusselt numbers and friction factors first increase with space ratios (up to a value depending on the corrugation angle), then start decreasing with increasing space ratios.

The purpose of this paper is to analyse the convective heat transfer of an unsteady pulsed, laminar, incompressible flow in axisymmetric tubes with periodic sections. The flow is supposed to be developing dynamically and thermally from the duct inlet. The wall is heated at constant and uniform temperature.

The problem is written with classical homogeneous boundary conditions. We use a shift operator to impose non‐homogeneous boundary conditions. Consequently, this method introduces source terms in the Galerkin formulation. The momentum equations and the energy equation which govern this problem are numerically solved in space by a spectral Galerkin method especially oriented to this situation. A Crank‐Nicolson scheme permits the resolution in time.

From the temperature field, the heat transfer phenomenon is presented, discussed and compared to those obtained in straight cylindrical pipes. This study showed the existence of zones of dead fluid that locally have a negative influence on heat transfer. Substantial modifications of the thermal convective heat transfer are highlighted at the entry and the minimum duct sections.

Pulsated flows in axisymmetric geometries can be applied to medical industries, mechanical engineering and technological processes.

One of the original features of this study is the choice of Chebyshev polynomials basis in both axial and radial directions for spectral methods, combined with the use of a shift operator to satisfy non‐homogeneous boundary conditions.

The paper adopts a simplified two‐dimensional approach to deal with convective heat and mass transfer in laminar flows of humid air through wavy finned‐tube exchangers. The computational domain is spatially periodic, with fully developed conditions prevailing at a certain distance from the inlet section. Both the entrance and the fully developed flow region are investigated. In the fully developed region, periodicities in the flow, temperature and mass concentration fields are taken into account. The approach is completely general, even if the finite element method is used for the discretizations. In the application section, velocity, temperature, and mass concentration fields are computed first. Then apparent friction factors, Nusselt numbers, Colburn factors for heat and mass transfer, and goodness factors are evaluated both in the entrance and in the fully developed region.

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.

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.