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This study aims to enhance natural convection heat transfer for a porous thermal cavity. Multi-frequency sinusoidal heating is applied at the bottom of a porous square cavity, considering top wall adiabatic and cooling through the sidewalls. The different frequencies, amplitudes and phase angles of sinusoidal heating are investigated to understand their major impacts on the heat transfer characteristics.

The finite volume method is used to solve the governing equations in a two-dimensional cavity, considering incompressible laminar flow, Boussinesq approximation and Brinkman–Forchheimer–Darcy model. The mean-temperature constraint is applied for enhancement analysis.

The multi-frequency heating can markedly enhance natural convection heat transfer even in the presence of porous medium (enhancement up to ∼74 per cent). Only the positive phase angle offers heat transfer enhancement consistently in all frequencies (studied).

The present research idea can usefully be extended to other multi-physical areas (nanofluids, magneto-hydrodynamics, etc.).

The findings are useful for devices working on natural convection.

The enhancement using multi-frequency heating is estimated under different parametric conditions. The effect of different frequencies of sinusoidal heating, along with the uniform heating, is collectively discussed from the fundamental point of view using the average and local Nusselt number, thermal and hydrodynamic boundary layers and heatlines.

This paper aims to consider numerical analysis of laminar double-diffusive natural convection inside a non-homogeneous closed medium composed of a saturated porous matrix and a clear binary fluid under spatial sinusoidal heating/cooling on one side wall and uniform salting.

The domain of interest is a partially square porous enclosure with sinusoidal wall heating and cooling. The fluid flow, heat and mass transfer dimensionless governing equations associated with the corresponding boundary conditions are discretized using the finite volume method. The resulting algebraic equations are solved by an in-house FORTRAN code and the SIMPLE algorithm to handle the non-linear character of conservation equations. The validity of the in-house FORTRAN code is checked by comparing the current results with previously published experimental and numerical works. The effect of the porous layer thickness, the spatial frequency of heating and cooling, the Darcy number, the Rayleigh number and the porous to fluid thermal conductivity ratio is analyzed.

The results demonstrate that for high values of the spatial frequency of heating and cooling (f = 7), temperature contours show periodic variations with positive and negative values providing higher temperature gradient near the thermally active wall. In this case, the temperature variation is mainly in the porous layer, while the temperature of the clear fluid region is practically the same as that imposed on the left vertical wall. This aspect can have a beneficial impact on thermal insulation. Besides, the porous to fluid thermal conductivity ratio, Rk, has practically no effect on Shhot wall, contrary to Nuinterface where a strong increase is observed as Rk is increased from 0.1 to 100, and much heat transfer from the hot wall to the clear fluid via the porous media is obtained.

The findings are useful for devices working on double-diffusive natural convection inside non-homogenous cavities.

The authors believe that the presented results are original and have not been published elsewhere.

The purpose of this paper is to study thermal (natural) convection in nine different containers involving the same area (area= 1 sq. unit) and identical heat input at the bottom wall (isothermal/sinusoidal heating). Containers are categorized into three classes based on geometric configurations [Class 1 (square, tilted square and parallelogram), Class 2 (trapezoidal type 1, trapezoidal type 2 and triangle) and Class 3 (convex, concave and triangle with curved hypotenuse)].

The governing equations are solved by using the Galerkin finite element method for various processing fluids (Pr = 0.025 and 155) and Rayleigh numbers (10³ ≤ Ra ≤ 10⁵) involving nine different containers. Finite element-based heat flow visualization via heatlines has been adopted to study heat distribution at various sections. Average Nusselt number at the bottom wall ( Nub¯) and spatially average temperature (θ^) have also been calculated based on finite element basis functions.

Based on enhanced heating criteria (higher Nub¯ and higher θ^), the containers are preferred as follows, Class 1: square and parallelogram, Class 2: trapezoidal type 1 and trapezoidal type 2 and Class 3: convex (higher θ^) and concave (higher Nub¯).

The comparison of heat flow distributions and isotherms in nine containers gives a clear perspective for choosing appropriate containers at various process parameters (Pr and Ra). The results for current work may be useful to obtain enhancement of the thermal processing rate in various process industries.

Heatlines provide a complete understanding of heat flow path and heat distribution within nine containers. Various cold zones and thermal mixing zones have been highlighted and these zones are found to be altered with various shapes of containers. The importance of containers with curved walls for enhanced thermal processing rate is clearly established.

The purpose of this paper is to study natural convective flow and heat transfer in a sinusoidally heated wavy porous cavity in the presence of internal heat generation or absorption.

Sinusoidal heating is applied on the vertical left wall of the cavity, whereas the wavy right wall is cooled at a constant temperature. The top and bottom walls are taken to be adiabatic. The Darcy model is adopted for fluid flow through the porous medium in the cavity. The governing equations and boundary conditions are solved using the finite difference method over a range of amplitudes and number of undulations of the wavy wall, Darcy–Rayleigh numbers and internal heat generation/absorption parameters.

The results are presented in the form of streamlines, isotherms and Nusselt numbers for different values of right wall waviness, Darcy–Rayleigh number and internal heat generation parameter. The flow field and temperature distribution in the cavity are affected by the waviness of the right wall. The wavy nature of the cavity also enhances the heat transfer into the system. The heat transfer rate in the cavity decreases with an increase in the internal heat generation/absorption parameter.

The present investigation is conducted for steady, two-dimensional natural convective flow in a wavy cavity filled with Darcy porous medium. The waviness of the right wall is described by the amplitude and number of undulations with a well-defined mathematical function. An extension of the present study with the effects of cavity inclination and aspect ratio will be the interest for future work.

The study might be useful for the design of solar collectors, room ventilation systems and electronic cooling systems.

This work examines the effects of sinusoidal heating on convective heat transfer in a wavy porous cavity in the presence of internal heat generation or absorption. The study might be useful for the design of solar collectors, room ventilation systems and electronic cooling systems.

The purpose of this paper is to model the convective flows in a room equipped by a glass door and a heated floor of length l = 0.8 × H and submitted to a sinusoidal temperature profile and mono alternative temperature profile.

The paper opts for a numerical study of convective flows in a large scale cavity using the Lattice Boltzmann Method (LBM) by considering a two dimensions (2D) square cavity of side H and filled by air (Pr = 0.71). All the vertical walls, the ceiling and the rest of the floor are thermally insulated, the hot portion of length l = 0.8×H is heated with two imposed temperature profiles of amplitude values 0.2 ≤  a  ≤ 0.6 and for two different periods ζ = ζ0 and ζ = 0.4×ζ0. One of the vertical walls has a cold portion θ_c = 0 that represents the glass door.

A systematic study of the flow structure and heat transfer is carried out considering principal control parameters: amplitude “a” and period ζ for Rayleigh number Ra = 10⁸. Effects of these parameters on results are presented in terms of isotherms, streamlines, profiles of velocities, temperature in the cavity, global and local Nusselt number. It has been found that an increase in amplitude or period increases the amplitude of the temperature in the core of cavity. The Nusselt number increases when the amplitude “a” of the imposed temperature increases, but this later is not affected by variation of the period.

The authors used LBM to simulate the convective flows in a cavity at high Ra, heated from below by tow imposed temperature profiles. Indeed, they simulate a local equipped by a solar water heater (SWH). The floor is subjected to a periodic heating: Sinusoidal heating (Case 1) for which the temperature varies sinusoidally (SWH without a supplement), and mono alternation heating (Case 2), the temperature evolves like a redressed signal (SWH with a supplement). The considered method has been successfully validated and compared with the previous work. The study has been conducted using several control parameters such as the signal amplitude and period in the case of turbulent convection. This allowed us to obtain a considerable set of results that can be used for engineering.

The purpose of this study is to numerically analyze the thermal and entropy generation characteristics on two-dimensional, incompressible, laminar single-phase flow of Al₂O₃-water nanofluid in a micro-channel subjected to asymmetric sinusoidal wall heating with varying amplitude, length of fluctuation period and phase difference of applied heat flux for Reynolds number in the range of 25-1000.

The numerical computation is based on the Finite Element Method and the Lagrange finite element technique is used for approximating the flow variables within the computational domain.

The average Nusselt number increases with increasing Reynolds number (Re) for all the volume fractions of nanofluid. However, the total entropy generation decreases up to a critical value of Re and increases thereafter. Increase in volume fraction shifts the critical Re towards the lower Re regime. The average Nusselt number and total entropy generation increase with amplitude and length of fluctuation period of heat flux. The optimal choice of volume fraction for lesser entropy generation and higher heat transfer is found to be 3 per cent independent of the value of amplitude, length of fluctuation period and phase difference of the heat flux.

To the best of authors’ knowledge, the interplay of various parameters concerning non-uniform heating in achieving the maximum heat transfer with minimum irreversibility has not been investigated. Focusing on this agenda, the results of this study would benefit the industrial sector in achieving the maximum heat transfer at the cost of minimum irreversibilities with an optimal choice of inlet Reynolds number, volume fraction of nanofluid, amplitude, length of the period of fluctuation of heat flux and phase difference of applied heat flux.

The purpose of this paper is to investigate numerically mixed convection of Al₂O₃-water nanofluids flowing through a horizontal ventilated cavity heated from below by a temperature varying sinusoidally along its lower wall. The simulations focus on the effects of different key parameters, such as Reynolds number (200 ≤ Re ≤ 5,000), nanoparticles’ concentration (0 ≤ ϕ ≤ 0.1) and phase shift of the heating temperature (0 ≤ γ ≤ π), on flow and thermal patterns and heat transfer performances.

The Navier–Stokes equations describing the nanofluid flow were discretized using a finite difference technique. The vorticity and energy equations were solved by the alternating direction implicit method. Values of the stream function were obtained by using the point successive over-relaxation method.

The simulations were performed for two modes of imposed external flow (injection and suction). The main findings are that the dynamical and thermal fields are affected by the parameters Re, ϕ, γ and the applied ventilation mode; the addition of nanoparticles leads to an improvement of heat transfer rate and an increase of mean temperature inside the enclosure; the heat exchange performance and the better cooling are more pronounced in suction mode; the phase shift of the heating temperature may lead to periodic solutions for weaker values of Re and contributes to an increase or a decrease of heat transfer depending on the value of ϕ and the convection regime.

To the best of the authors’ knowledge, the problem of mixed convection of a nanofluid inside a vented cavity using the injection or suction technics and submitted to non-uniform heating conditions has not been treated so far.

The purpose of this study is to obtain the numerical as well as regularity results for the nonlinear elliptic set of equations arising in the study of fluid flow in microchannel induced by the pressure in the presence of interfacial electrokinetic effects.

For the numerical study, the authors implemented traditional FDM approach, and for the regularity results they used the classical energy estimates. The interfacial electrokinetic effects result in an additional source term in classical momentum equation, hence affecting the characteristics of the flow and heat transfer. The sinusoidal temperature variation is assumed on side walls.

The results were obtained for various combinations of physical parameters appearing in the governing equations. This study concludes that in the presence of electric double layer, the average heat transfer rate reduces along with larger values of Reynolds number. It is observed that the heat transfer increases with the increase in amplitude ratio and phase deviation. The flow behavior and heat transfer rate inside the microchannel are also strongly affected by the presence of κ (kappa).

To the best of the authors’ knowledge, the problem of heat transfer through microchannel in combination with sinusoidal temperature variation at boundary with electric double layer effects has not been considered previously. Hence, this paper focuses on the influence of the sinusoidal boundary temperature distributions on both sidewalls of a rectangular microchannel through parallel plates with electrokinetic effects on the pressure-driven laminar flow. In addition, a detailed mathematical analysis is also to be carried out to verify the regularity of this model with the proposed boundary conditions. The study used the classical energy method to get the regularity results.

The purpose of the present paper is to model a cavity, which is equally divided vertically by a thin, flexible membrane. The membranes are inevitable components of many engineering devices such as distillation systems and fuel cells. In the present study, a cavity which is equally divided vertically by a thin, flexible membrane is model using the fluid–structure interaction (FSI) associated with a moving grid approach.

The cavity is differentially heated by a sinusoidal time-varying temperature on the left vertical wall, while the right vertical wall is cooled isothermally. There is no thermal diffusion from the upper and lower boundaries. The finite-element Galerkin technique with the aid of an arbitrary Lagrangian–Eulerian procedure is followed in the numerical procedure. The governing equations are transformed into non-dimensional forms to generalize the solution.

The effects of four pertinent parameters are investigated, i.e., Rayleigh number (104 = Ra = 107), elasticity modulus (5 × 1012 = E_T = 1016), Prandtl number (0.7 = Pr = 200) and temperature oscillation frequency (2p = f = 240p). The outcomes show that the temperature frequency does not induce a notable effect on the mean values of the Nusselt number and the deformation of the flexible membrane. The convective heat transfer and the stretching of the thin, flexible membrane become higher with a fluid of a higher Prandtl number or with a partition of a lower elasticity modulus.

The authors believe that the modeling of natural convection and heat transfer in a cavity with the deformable membrane and oscillating wall heating is a new subject and the results have not been published elsewhere.

Boussinesq approximation is widely used in solving natural convection problems, but it has severe practical limitations. Using Boussinesq approximation, the temperature difference should be less than 28.6 K. The purpose of this study is to get rid of Boussinesq approximation and simulates the natural convection problems using an unsteady compressible Navier-Stokes solver. The gravity force is included in the source term. Three temperature differences are used namely 20 K, 700 K and 2000 K.

The calculations are carried out on the square and sinusoidal cavities. The results of low temperature difference have good agreement with the experimental and previous calculated data. It is found that, the high temperature difference has a significant effect on the density.

Due to mass conservation, the density variation affects the velocity distribution and its symmetry. On the other hand, the density variation has a negligible effect on the temperature distribution.

The present calculation method has no limitations but its convergence is slow. The current study can be used in fluid flow simulations for nuclear power applications in natural convection flows subjected to large temperature differences.