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The paper aims to theoretically study the mathematical model of a steady flow of a heat-conductive incompressible viscous fluid through a spatially periodic plane profile cascade.

Reduction of the infinite periodical problem to one period. Leray-Schauder fixed point principle was used.

This study proves the existence of a weak solution for arbitrarily large given data (i.e. the inflow velocity and the acting specific body force).

The author proposed a special boundary condition on the outflow of the domain not only for the velocity and pressure but also for the temperature.

To the author’s knowledge, the problem has not been studied earlier. More detailed overview is given in the paper in the first part.

In this paper a numerical simulation, based on finite difference techniques, has been developed in order to analyse turbulent natural and mixed convection of air in internal flows. The study has been restricted to two‐dimensional cavities with the possibility of inlet and outlet ports, and with internal heat sources. Turbulence is modelled by means of two‐equation k‐ε turbulence models, both in the simplest form using wall functions and in the more general form of low‐Reynolds‐number k‐ε models. The couple time average governing equations (continuity, momentum, energy, and turbulence quantities) are solved in a segregated manner using the SIMPLEX method. An implicit control volume formulation of the differential equations has been employed. Some illustrative numerical results are presented to study the influence of geometry and boundary conditions in cavities. A comparison of different k‐ε turbulence models has also been presented.

The purpose of this paper is to address various works on mixed convection and proposes 10 unified models (Models 1–10) based on various thermal and kinematic conditions of the boundary walls, thermal conditions and/ or kinematics of objects embedded in the cavities and kinematics of external flow field through the ventilation ports. Experimental works on mixed convection have also been addressed.

This review is based on 10 unified models on mixed convection within cavities. Models 1–5 involve mixed convection based on the movement of single or double walls subjected to various temperature boundary conditions. Model 6 elucidates mixed convection due to the movement of single or double walls of cavities containing discrete heaters at the stationary wall(s). Model 7A focuses mixed convection based on the movement of wall(s) for cavities containing stationary solid obstacles (hot or cold or adiabatic) whereas Model 7B elucidates mixed convection based on the rotation of solid cylinders (hot or conductive or adiabatic) within the cavities enclosed by stationary or moving wall(s). Model 8 is based on mixed convection due to the flow of air through ventilation ports of cavities (with or without adiabatic baffles) subjected to hot and adiabatic walls. Models 9 and 10 elucidate mixed convection due to flow of air through ventilation ports of cavities involving discrete heaters and/or solid obstacles (conductive or hot) at various locations within cavities.

Mixed convection plays an important role for various processes based on convection pattern and heat transfer rate. An important dimensionless number, Richardson number (Ri) identifies various convection regimes (forced, mixed and natural convection). Generalized models also depict the role of “aiding” and “opposing” flow and combination of both on mixed convection processes. Aiding flow (interaction of buoyancy and inertial forces in the same direction) may result in the augmentation of the heat transfer rate whereas opposing flow (interaction of buoyancy and inertial forces in the opposite directions) may result in decrease of the heat transfer rate. Works involving fluid media, porous media and nanofluids (with magnetohydrodynamics) have been highlighted. Various numerical and experimental works on mixed convection have been elucidated. Flow and thermal maps associated with the heat transfer rate for a few representative cases of unified models [Models 1–10] have been elucidated involving specific dimensionless numbers.

This review paper will provide guidelines for optimal design/operation involving mixed convection processing applications.

To investigate the natural convection in open‐ended parallel, convergent, and divergent channels using a fully elliptic procedure without extending the domain outside the channel for the application of the boundary conditions at the inlet and outlet of the channels.

The model is two‐dimensional and fully elliptic in x and y directions, and the equations are solved only inside the channel by the finite volume method using a co‐located arrangement with a segregated procedure and boundary fitted coordinates. The pressure‐velocity coupling is solved by the PRIME algorithm.

The results are shown in terms of velocity vectors, streamlines, isotherms, and the local and the average Nusselt number for all fluids and configurations investigated. For high values of the Rayleigh number, a recirculation region in the outlet of all investigated configurations and Prandtl numbers was observed. Based on the results, a single correlation is proposed to evaluate the average Nusselt number for all fluids and configurations analyzed.

The shown results are based on the following hypothesis: steady‐state, two‐dimensional, laminar flow, and Boussinesq's aproximation. The results are presented in following range of parameters: 10⁵<(S_max/L)Ra_Smax<10⁸, where S_max denotes the maximum distance between the plates and Ra denotes the Rayleigh number; half angle of convergence or divergence (θ): 5° and 15°; and Prandtl numbers: 0.7, 5.0, and 88.

Local and average Nusselt numbers, for Prandtl numbers varying from 0.70 to 88, and a correlation for the average Nusselt number for all fluids and configurations are presented. The results presented in this paper are useful to engineers and researchers involved in thermal design and numerical methods.

Heat and fluid flow through a trapezoidal cooling chamber were studied numerically. Hot fluid is assumed inflow at some depth below the surface into one end of the chamber and withdrawn at another depth from the other end. The top of the chamber is exposed to the surrounding for cooling and the remaining side‐walls are all insulated. Inflow Reynolds number Ro considered is in the range of 100 to 1000 and the inlet densimetric Froude number Fo considered is in the range of 0.5 to 50.0. Numerical experiments show that the flow and temperature fields in the flow‐through trapezoidal chamber are strong function of both Fo and Ro. The submergence ratio D/do, chamber length to depth ratio L/D and chamber wall angles are also significant in influencing the flow fields. Comparisons were also made with available experimental and prototype data.

This paper presents a numerical investigation of the interaction of surfaces radiation with developing laminar free convective heat transfer in a divided vertical channel. The influence of the radiation on the heat transfer and on the air flow is studied for various sizes (width and length) of the plate.

The specifically developed numerical code is based on the utilization of the finite volume method. The SIMPLER algorithm for the pressure‐velocity coupling is adopted. The view factors are determined by using boundary elements to fit the surfaces, an algorithm solving the shadow effect and a Monte Carlo method for the numerical integrations.

Results obtained show that the radiation: plays a very important role on the paces of the isotherms, especially at Ra≥1,600; increases considerably the average wall Nusselt number; and increases the mass flow rate and the average channel Nusselt number at high Rayleigh numbers. The plate location has a significant effect on the heat transfer only in presence of the radiation exchange. The increase of both length and width of the plate causes a decrease of the heat transfer and the mass flow rate.

The use of the code is limited to the flow that is assumed to be incompressible, laminar and two dimensional. The radiative surfaces are assumed diffuse‐gray.

Natural convection in vertical channels formed by parallel plates has received significant attention because of its interest and importance in industrial applications. Some applications are solar collectors, fire research, electronic cooling, aeronautics, chemical apparatus, building constructions, nuclear engineering, etc.

In comparison to the most of the previous studies on natural convection in partitioned channels, the radiation exchange was neglected. This study takes into account the radiation exchange in a divided channel.

This study aims to perform a numerical study of air convection in a rectangular enclosure with two isothermal blocks and oscillating bottom wall temperature under laminar flow conditions. The geometry of the enclosure contains two isothermal blocks placed equidistant along the streamwise direction. The top wall is assumed to be cold (low temperature). The bottom wall temperature is either kept as constant or sinusoidally varied with time. The vertical walls are considered as adiabatic. The flow is diagonally upwards and assisted by the buoyancy force. The inlet is positioned at the bottom of the left wall, and the outlet is placed at the top of the right wall. The parameters considered in this paper are Rayleigh number (104-106), Prantdl number (0.71), amplitude of temperature oscillation (0-0.5) and the period (0.2). The effects of these parameters on heat transfer and fluid flow inside the open cavity are studied. The periodic results of fluid flow are illustrated with streamlines and the heat transfer is represented by isotherms and time-averaged Nusselt number. By virtue of increasing buoyancy, the heat transfer accelerates with an increase in the Rayleigh number. Also, the heat transfer is intensive with an increase in the bottom wall temperature.

The momentum and energy equations are solved simultaneously. The energy equation (3) is initially solved using the alternating direction implicit (ADI) method. The results of the energy equation are updated into the vorticity equation. The unsteady vorticity transport equation is also solved using the ADI method. Dimensionless time step equal to 0.01 is used for high Ra (10⁵ and 10⁶) and 0.001 is used for low Ra (10⁴). Convergence criteria of 10⁻⁵ is used during the vorticity, stream function and temperature calculations, as the sum of error should be very small.

Numerical study of air convection in a rectangular enclosure with two isothermal blocks and oscillating bottom wall temperature is performed under laminar flow condition. The effect of the isothermal blocks on the heat transfer is analyzed for different Rayleigh numbers and the following conclusions are arrived. The hydrodynamic blockage effect is subdued by the isothermal heating of square blocks. Based on the streamline diagrams, it is found that the formation of vortices is greatly influenced by the Rayleigh number when all the walls are exposed to a constant wall temperature. The influence of amplitude on the heat transfer is remarkable on the wall exposed to oscillating temperature and is subtle on the opposite static cold wall. The heat transfer increases with an increase in the Rayleigh number and temperature.

Flow is assumed to be two-dimensional and laminar subject to oscillatory boundary condition. The present investigation aims to study natural convection inside the cavity filled with air whose bottom wall is subject to time-variant temperature. The buoyancy is further intensified through two isothermal square blocks placed equidistant along the streamwise direction at mid-height.

The authors have developed a CFD solver to simulate the situation. Effect of Rayleigh number subject to oscillatory thermal boundary condition is simulated. Streamline contour and isotherm contour are presented. Local and average Nusselt numbers are presented.

This paper aims to deal with characterisation of the thermal performance of a hybrid tubular and cavity solar thermal receiver.

The coupled optical-flow-thermal analysis is carried out on the proposed receiver design. Modelling is performed in two and three dimensions for estimating heat loss by natural convection for an upward-facing cavity. Heat loss obtained in two dimensions by solving coupled continuity, momentum and energy equation inside the cavity domain is compared with the loss obtained using an established Nusselt number correlation for realistic receiver performance prediction.

It is found that radiation emission from a heated cavity wall to the ambient is the dominant mode of heat loss from the receiver. The findings recommend that fluid flow path must be designed adjacent to the surface exposed to irradiation of concentrated flux to limit conduction heat loss.

On-sun experimental tests need to be performed to validate the numerical study.

Numerical analysis of receivers provides guidelines for effective and efficient solar thermal receiver design.

Pressurised air receivers designed from this method can be integrated with Brayton cycles using air or supercritical carbon-dioxide to run a turbine generating electricity using a solar heat source.

The present paper proposes a novel method for coupling the flux map from ray-tracing analysis and using it as a heat flux boundary condition for performing coupled flow and heat transfer analysis. This is achieved using affine transformation implemented using extrusion coupling tool from COMSOL Multiphysics software package. Cavity surface natural convection heat transfer coefficient is obtained locally based on the surface temperature distribution.

A new coupled finite element model has been developed for the joint resolution of both the shallow water equations, that governs the free surface flow, and the groundwater flow equation that governs the motion of water through a porous media. The paper aims to discuss these issues.

The model is based upon two different modules (surface and ground water) previously developed by the authors, that have been validated separately.

The newly developed software allows for the assessment of the fluid flow in natural watersheds taking into account both the surface and the underground flow in the way it really takes place in nature.

The main achievement of this work has dealt with the coupling of both models, allowing for a proper moving interface treatment that simulates the actual interaction that takes place between surface and groundwater in natural watersheds.

The Navier‐Stokes equation and the species continuity equation have been solved numerically in a boundary fitted coordinate system comprising the geometry of a large scale industrial size tundish. The solution of the species continuity equation predicts the time evolution of the concentration of a tracer at the outlet of a single strand bare tundish. The numerical prediction of the tracer concentration has been made with three different turbulence models; (a standard k‐ε, a k‐ε RNG and a Low Re number Lam‐Bremhorst model) which favorably compares with that of the experimental observation for a single strand bare tundish. It has been found that the overall comparison of k‐ε model with that of the experiment is better than the other two turbulence models as far as gross quantities like mean residence time and ratio of mixed to dead volume are concerned. However, it has been found that the initial transient development of the tracer concentration is best predicted by the Lam‐Bremhorst model and then by the RNG model. The k‐ε model predicts the tracer concentration much better than the other two models after the initial transience (t>40 per cent of mean residence time) and the RNG model lies in between the k‐ε and the Lam‐Bremhorst one. The numerical study has been extended to a multi strand tundish (having 6 outlets) where the effect of outlet positions on the ratio of mix to dead volume has been studied with the help of the above three turbulence models. It has been found that all the three turbulence models show a peak value for the ratio of mix to dead volume (a mixing parameter) when the outlets are placed 200 mm away from the wall (position‐2) thus signifying an optimum location for the outlets to get highest mixing in a given multi strand tundish.