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This paper’s goal is to investigate the oscillatory flow of double-diffusive convection in a Voigt fluid. We re-design the basic equations of the channel flow, which initially appear dimensional, in a dimensionless manner using non-dimensional variables. The oscillation technique transforms the governing equations into coupled ordinary differential equations (CODEs). We have derived the analytical expressions for velocity, temperature, and concentration distribution by solving the CODEs using the direct analytical method. The study focuses on how physical factors, like the thermal Grashof number, the solutal Grashof number, the Prandtl number, the Lewis number, and the Voigt fluid parameter, affect different aspects of flow, such as speed, temperature, concentration, rate of heat transfer, and mass transfer. Notably, the study finds that skin friction increases on both channel plates with increasing injection on the heated plate. The significance of double-diffusive oscillatory flow lies in its ability to improve heat and mass transfer rates, as well as its impact on pattern formation and stability, which influences a wide range of applications from engineering design to environmental studies. [ABSTRACT FROM AUTHOR]

AbstractEnclosures that contain both fluid and porous regions are utilized in various industries and geophysical processes to enhance heat and mass transfer. These enclosures find applications in fields such as geothermal engineering, drying of porous solids, cooling of electronics, metal solidification, and many others. In line with the motivation behind these applications, the present study explores double diffusion in the naturally convective flow of water-based nano fluid saturated in the trapezoidal porous enclosure and containing Copper (Cu) nano particles. The impact of uniformly applied radiative heat flux and nano particle shape factor is also accounted. A numerical investigation was carried out using a finite difference methodology integrated into a computational MATLAB code for numerical simulation. The simulation aimed to study the effect of nanoparticle shape factor on the effectiveness of a porous medium, which is exposed to two distinct objectives: enhancing heat transfer and optimizing mass transfer within a fluid-saturated porous medium. This research conducts a meticulous parametric exploration, underscoring the pivotal roles played by Darcy number (Da), nanofluid shape factor (m), Rayleigh number (Ra), thermal radiation (Rd), buoyancy ratio (Nr), and Lewis number (Le) in shaping the dynamics of flow, heat, and concentration transfer. The analysis of Nusselt and Sherwood numbers reveals that changing the shape of nano-particles from spheres to bricks increases the heat flux and mass flux coefficients by approximately 0.33% and 1.37% respectively. The results show a significant increase in Nusselt and Sherwood numbers, with blade-shaped nanoparticles demonstrating approximately a 2.97% and 10.82% improvement, respectively, compared to sphere-shaped nanoparticles. The outcome of this analysis yields an exhaustive dataset encompassing Nusselt and Sherwood numbers can be written as mathematical functions based on the parameters we talked about earlier. [ABSTRACT FROM AUTHOR]

This article explains the heat and mass transfer of electrically conducting Newtonian fluid in double‐diffusive magnetoconvective flow. We have considered two infinite horizontal plates at a constant distance apart under the concentration‐modulated boundary condition. A constant magnetic field is considered in vertically upward directions, which generates an induced magnetic field. We have used the weakly nonlinear analysis to obtain the heat and mass transfer rate using the Ginzburg–Landau equation. The software MATHEMATICA is used to determine the solution of the Ginzburg–Landau equation by inbuilt function. The effects of physical parameters that occurred in the study on the Nusselt number and Sherwood number have been examined graphically. Modulation has a negligible effect on the threshold value of the thermal Rayleigh number, that is, on stationary convection. Moreover, it was found that the Chandrasekhar number, magnetic‐Prandtl number, amplitude of modulation, and frequency of modulation are proportional to the heat and mass transports. [ABSTRACT FROM AUTHOR]

The present analysis mathematically investigates the thermohaline convection problem in viscoelastic fluid layer saturating porous media by utilizing the modified Boussinesq approximation. By performing linear stability analysis, the Darcy–Rayleigh numbers for stationary and oscillatory modes of convection are derived. The effects of different parameters describing the problem are studied numerically. In nonlinear stability analysis, the heat and mass transfer rates in the form of Nusselt and Sherwood numbers, respectively, are obtained for oscillatory convection using the derived Ginzburg–Landau equation. From the results, it is observed that overstability is the preferred mode of instability in linear stability. It is found that in linear double‐diffusive convection problems, the stress relaxation imparts a destabilizing effect whereas the strain retardation time, the coefficient of specific heat variation due to temperature, and the concentration gradient have a stabilizing effect on the system's stability. The numerical values of heat and mass transfer rates varied with the coefficient of specific heat showing that the heat transport decreases while the mass transport increases. Also, the stress relaxation time, the concentration gradient, and the gravity modulation's amplitude increase while the strain retardation time decreases the heat and mass transfer rates. The wavelength of oscillations remains unaltered with the variation of specific heat variation due to temperature. The modulation frequency does not affect the heat/mass transfer rate; though, the wavelength of oscillations decreases with increasing frequency. [ABSTRACT FROM AUTHOR]

A three-dimensional computational study of double-diffusive natural convection was conducted to explore the impact of tilt on the thermal and solutal performance of a floating pyramidal solar still filled with an air-steam mixture. In the present work, the still is cooled from the upper walls and is maintained at a low vapor concentration. The bottom wall of the still is maintained at a hot temperature and high concentration. Four different models of baffles placed in the upper region of the solar still have been studied. The mathematical formulation of the equations governing the problem is based on the vector current potential -vorticity formalism. The numerical method of finite volumes is used. The effect of Rayleigh and tilt angle of the floating solar still on the flow structure, iso-temperatures, iso-concentrations, and heat and mass transfer rates were examined. The most relevant results of this study are (i) an uncooled air-vapor mixture outlet was observed during tilting for the solar still equipped with a small, flat baffle, (ii) triangular and curvilinear baffle configurations are suitable to guide the air-vapor mixture towards the cold walls during the tilting of the solar still floating on the sea, and (iii) the triangular baffle configuration is the most relevant design, enhancing thermal and solutal performance by 20%. [ABSTRACT FROM AUTHOR]

• The Soret and Dufour effects of double-diffusive convection over a rough surface are studied by using a TRT-LB model. • A sudden enhancement or attenuation in heat and mass transfer causes changes in the state and structure of flow. • Unexpected changes in the flow structure from reversal to period were identified after its long-term evolution. • Heat and mass transfer as well as the flow structure are most intimately related to the compactness of rough elements. This study examines the Soret and Dufour effects of double-diffusive convection (DDC) over a rough surface by using a lattice Boltzmann (LB) model with two-relaxation-time (TRT) collision operators, where the cross-diffusion terms are modeled by introducing additional collision operators that can be used to avoid the need for special treatment of the gradient terms. The TRT model is applied to improve the stability of the LB method for flows at high Rayleigh numbers. We investigate how rough surfaces with different distributions and compactness of rough elements affect heat and mass transfer as well as the flow structure of the DDC system with the Soret and Dufour effects. We examined five rough models with different spatial distributions of the triangular rough elements as well as different values of the Rayleigh number (R a = 10 6 and 10 9), Prandtl number (P r = 0.7), Lewis number (L e = 1 and 2), buoyancy ratio (− 2 ≤ N c ≤ 6.5), Soret factor (0 ≤ S T C ≤ 1), Dufour factor (0 ≤ D C T ≤ 1), and the height of the roughness (1 / 96 ≤ h ≤ 1 / 2). Specifically, the influence of the buoyancy ratio on the DDC system was investigated, and the relationship of heat and mass transfer with the buoyancy ratio was divided into four stages: conduction-dominated, transition, steady convection-dominated, and oscillatory convection-dominated stages. The rough surfaces reduced heat and mass transfer at low Rayleigh numbers and low height of the roughness, and the third rough model (Model III) yielded the highest reduction. The flow showed periodic behavior after long-term reversals in some cases, which appear to have not been observed in previous research. Moreover, the effects of the Soret and Dufour factors were examined, and it was found that mass and heat transfer could be enhanced in most cases by increasing their values. To enhance heat and mass transfer, the height of the roughness should be increased as well. Model III delivered the best performance, with a scenario completely opposite to that in case of a low roughness height. Finally, approximate values of the critical height of the roughness with different rough models were obtained such that heat and mass transfer were enhanced only when the height of the roughness was greater than a critical value. [ABSTRACT FROM AUTHOR]

This paper reports a numerical study of double-diffusive natural convection through an annular space delimited by a square cylinder on the outside and a cylindrical cylinder on the inside covered by a porous layer. The Darcy-Brinkmann-Forchheimer is used for modeling flow in both fluid and porous areas. The annular space is partially or completely filled with an isotropic porous medium. A finite volume method, using the Patankar-Spalding technique is used for solving the discretization of the dimensionless equations governing the problem. The effects of simultaneously applied thermal and solutal buoyancy forces on heat and mass transfer are shown in the results for a large range of buoyancy ratios, Rayleigh number, and thermal conductivity. Streamlines, isotherms, and iso-concentrations are presented to analyze the flow structure transition from mass species dominated to thermal dominated flow. Results show that the buoyancy ratio can change the flow pattern and the increased thermal conductivity ratio can improve heat and mass transfer. A good agreement was obtained between the present results and those published were found. [ABSTRACT FROM AUTHOR]

The motion of the humid air inside a solar still is due to double-diffusive natural convection, where convective heat and mass transfer phenomena are encountered. The humid air, an intermediate medium between the evaporating and the condensing surfaces of the solar still, is regarded as a heat engine that absorbs heat from the free surface of the warmed brackish or saline water and converts it into work to carry up the water vapor molecules to the inner surface of the glass cover. Like all heat engines, the humid air work is accompanied by a degraded energy due to the presence of irreversibilities. The aim of the present study is to give answers about the internal irreversibility origins and the associated work fluxes of the humid air inside the solar still due to double-diffusive natural convection. It is for the first time that the internal entropy generation and the work fluxes formulations are developed and investigated for the humid air inside a solar still. It is found that the irreversibility rate due to fluid friction is the major contributor of the total entropy generation for N > 0.3. The increase in the temperature and the concentration gradients enhances the augmentation of all irreversibility rates. The second law efficiency is an important parameter that should be evaluated to assess the system performance. The mean value of the irreversibility percentage is found equal to 6.83%. The reversible and the lost work fluxes increase with the increase in the humid air temperature. [ABSTRACT FROM AUTHOR]

The stationary Darcy–Brinkman equations in the double-diffusive convection, which model the heat and mass transfer phenomena, are considered in this paper. Based on a suitable contractive operator, the existence and uniqueness of the problem are firstly proved by using the fixed point theorem. The regularities of the weak solution are also derived. Then, the Newton iterative method is studied for solving the nonlinear discrete system generated from the finite element approximation, including the stability and the optimal error estimates regarding the spatial mesh size and the iterative factor. The analysis indicates that the viscosity coefficient has more impact on the numerical algorithm than the thermal conductivity and the mass diffusivity coefficients. Finally, many numerical examples are shown to confirm the correctness of the theoretical prediction. [ABSTRACT FROM AUTHOR]

The nonlinear stability of stationary and oscillatory double-diffusive convection in an Oldroyd-B fluid layer is investigated using a perturbation method. The cubic Landau equations are derived and based on which the stability of stationary and oscillatory bifurcating solutions in the neighborhood of their critical values is discussed. The boundary between stationary and oscillatory convection demarcated by identifying a codimension-two points in the viscoelastic parameters plane. The bifurcating solution is found to be subcritical depending on the choices of physical parameters. Heat and mass transport are estimated in terms of Nusselt numbers. The effect of Prandtl number is observed only in the case of oscillatory motions and increase in its value is to decrease the heat and mass transfer. Besides, increasing relaxation and retardation parameters is to decrease and increase the amount of heat and mass transfer, respectively in the stationary case, while these parameters found to exhibit an opposing kind of behavior in the case of oscillatory motions. [ABSTRACT FROM AUTHOR]

In this research article, we investigated the weakly non-linear effect of gravity modulation for the temperature dependent viscous fluid in a horizontal porous layer in the presence of internal heat source. We use power series expansion in terms of the amplitude of gravity modulation, which is considered to be small for double-diffusive convection in porous media. We graphically show the effect of internal heat source, solute Rayleigh number, Lewis number, Vadász number, thermo-rheological parameter, the amplitude of gravity modulation, the frequency of modulation on the heat and mass transfer using Ginzburg-Landau equation. The effect of gravity modulation is found significant and is more effective for the low values of frequency of modulation. [ABSTRACT FROM AUTHOR]

A numerical study of the 3-D double-diffusive natural convection in an inclined solar distiller was established. The flow is considered laminar and caused by the interaction of thermal energy and the chemical species diffusions. The governing equations of the problem, are formulated using vector potential-vorticity formalism in its 3-D form, then solved by the finite volumes method. The Rayleigh number is fixed at Ra = 105 and effects of the buoyancy ratio and inclination are studied for opposed temperature and concentration gradients. The main purpose of the study is to find the optimum inclination angle of the distiller which promotes the maximum mass and heat transfer. [ABSTRACT FROM AUTHOR]

In this work, the heat and mass transfers in 3D lid driven cavity is analyzed. Double-diffusive convective flow in a cubic enclosure with moving left side in −y (Case I) or +y (Case II) directions is studied numerically. The cavity is heated from left side and cooled from right and constant different concentration is imposed, while remaining surfaces are adiabatic. The FVM based on the 3D vector-potential – vorticity formalism is used as numerical method. Prandtl number and Lewis number are fixed at 10, 0.7 and 2, respectively. The study covers a wide range for Richardson number 0.1 ≤ Ri ≤ 10 and Buoyancy ratio −10 ≤ Ri ≤ 10. Results are presented by particle trajectories, isotherms, Iso-concentration and local and mean Nusselt and Sherwood numbers. [ABSTRACT FROM AUTHOR]

• A comprehensive and detailed solution of double-diffusive natural convection of Casson fluids in an enclosure is obtained. • The influence of the governing parameters on fluid flow, morphology of yielded/unyielded regions, and heat and mass transfer are thoroughly examined. • The unyielded regions grow with decreasing buoyancy ratio and increasing the yield number. • The Lewis number has different effects on unyielded areas depending on the flow parameters. • Correlations for average Nusselt and Sherwood numbers are provided. This study investigates the double-diffusive natural convection of the non-Newtonian Casson fluid in a square cavity based on the original viscoplastic stress model without simplification. Therefore, yield stress plays an essential role in understanding fluid behavior. The finite element approach provided a numerical solution to continuity, momentum, energy, and species governing equations. The governing parameters for this problem are Rayleigh number, Ra , yield number, Y , buoyancy ratio number, Nr , and Lewis number, Le. The influence of these parameters on heat and mass transfer, the morphology of yielded/unyielded regions, and fluid flow are thoroughly examined. The results show that unyielded regions increase at high Rayleigh numbers, despite the increase in buoyancy force and consequently increased heat and mass transfer. On the other hand, as the buoyancy ratio drops, the flow's strength and heat and mass transmission diminish, leading to an increase in plug regions. Accordingly, the mechanisms influencing the growth of unyielded regions are complex and follow different patterns. However, the plug regions always grow with increasing Y. The results indicate that increasing the Lewis number (mass transfer) reduces the effect of the buoyancy ratio on flow, heat transfer, and the unyielded regions in every case. Quantitative analysis of the results indicates that, while buoyancy ratio affects heat and mass transfer almost equally, the Lewis number increases mass transfer up to three times the heat transfer. Meanwhile, changing the buoyancy ratio can increase the maximum yield stress to 400%, while changing the Lewis number has a maximum effect of 20%. [Display omitted] [ABSTRACT FROM AUTHOR]

Double diffusive flow in a cavity has attracted lots of attention due to its importance in many engineering fields such as ocean circulation, crystal growth, pollution transportation in air, metal manufacturing process and so on. When heat and mass transfer occur simultaneously in the double diffusive flow, the fluid flow is not only driven by the temperature gradient but also by the concentration gradient as well. In some cases, the Dufour and Soret effects will play a significant role in the double diffusive flow process. The energy flux created by the concentration gradient is called Dufour effect and the temperature gradient can cause the mass flux which is Soret effect. When taking the Soret and Dufour effects into account, the temperature and concentration equations become coupled with each other. However, the coupling diffusivities matrix can be diagonalized. The coupled system can then be transformed to two uncoupled diffusion–advection equations of two independent species. The temperature and concentration can be obtained by the inverse transformation of these two independent species. As a numerical method developed in the past two decades, lattice Boltzmann method (LBM) is powerful in simulating complex heat transfer and fluid mechanics problems. In the current study, a lattice Boltzmann model was developed and implemented for the double-diffusive convection with Soret and Dufour effects. Three distribution functions were used to compute the fluid velocity, specie 1, and specie 2, respectively. Specifically, a rectangular enclosure with horizontal temperature and concentration gradients was investigated. On the other hand, the graphics processing units (GPU) computing becomes popular since the advent of the NVIDIA’s CUDA platform, which includes both hardware components and software programming environment. The developed LBM code was adapted on the CUDA platform to accelerate the computation for parametric studies. The GPU is responsible for the parallel tasks while CPU tackles the sequential steps in the computation. To verify the improvement on computation ability by using GPU, the ratio of the computational time between CPU code and CUDA code is presented by simulating the classical natural convection process in a cavity. The computational speed can be accelerated by more than 20 times when large number of nodes is used. The fluid flow, temperature field and concentration field are presented for different Rayleigh numbers, buoyancy ratios, Prandtl numbers, Lewis numbers, aspect ratios, as well as Soret and Dufour coefficients. In addition, the results of Nusselt and Sherwood numbers are shown for different parametric conditions. As a result, lattice Boltzmann method was demonstrated as a good option to study the complex double-diffusive convection with Soret and Dufour effects in a vertical cavity. [ABSTRACT FROM AUTHOR]

The onset of double diffusive convection in a couple stress fluid saturated porous layer with an internal heat source is studied using linear and weak nonlinear stability analyses. The linear analysis is based on the classical normal mode technique. The modified Darcy equation that includes the time derivative term is used to model the momentum equation. In the present context, double diffusive convection is of particular interest in the study of extraction of metals from ores where a mushy layer is formed during solidification of a metallic alloy. Further, internal heating of the system is used as an external means to influence the transport process, thereby controlling the quality and structure of the resulting solid. The expressions for stationary, oscillatory and finite-amplitude Rayleigh number are obtained as a function of governing parameters such as internal Rayleigh number, couple stress parameter, solute Rayleigh number, Darcy-Prandtl number, normalized porosity and Lewis number and their effects on the stability of a system are shown graphically. It is observed that the onset of both stationary and oscillatory convection is advanced by the internal Rayleigh number. The nonlinear analysis is based on the truncated representation of Fourier series which provides the quantification of heat and mass transfer. Heat transport is reinforced while mass transport is suppressed by the internal Rayleigh number. The transient behavior of Nusselt and Sherwood numbers is studied by solving numerically a fifth order Lorenz type system using Runge–Kutta method. Some known results are recovered as the particular cases of the present study. [ABSTRACT FROM AUTHOR]

Abstract: Double-diffusive convection in a vertical annulus filled with a fluid-saturated porous medium is numerically investigated with the aim to understand the effects of a discrete source of heat and solute on the fluid flow and heat and mass transfer rates. The porous annulus is subject to heat and mass fluxes from a portion of the inner wall, while the outer wall is maintained at uniform temperature and concentration. In the formulation of the problem, the Darcy–Brinkman model is adopted to the fluid flow in the porous annulus. The influence of the main controlling parameters, such as thermal Rayleigh number, Darcy number, Lewis number, buoyancy ratio and radius ratio are investigated on the flow patterns, and heat and mass transfer rates for different locations of the heat and solute source. The numerical results show that the flow structure and the rates of heat and mass transfer strongly depend on the location of the heat and solute source. Further, the buoyancy ratio at which flow transition and flow reversal occur is significantly influenced by the thermal Rayleigh number, Darcy number, Lewis number and the segment location. The average Nusselt and Sherwood numbers increase with an increase in radius ratio, Darcy and thermal Rayleigh numbers. It is found that the location for stronger flow circulation is not associated with higher heat and mass transfer rates in the porous annular cavity. [Copyright &y& Elsevier]

This article reports a numerical study of double-diffusive convection in a fluid-saturated vertical porous annulus subjected to discrete heat and mass fluxes from a portion of the inner wall. The outer wall is maintained at uniform temperature and concentration, while the top and bottom walls are adiabatic and impermeable to mass transfer. The physical model for the momentum equation is formulated using the Darcy law, and the resulting governing equations are solved using an implicit finite difference technique. The influence of physical and geometrical parameters on the streamlines, isotherms, isoconcentrations, average Nusselt and Sherwood numbers has been numerically investigated in detail. The location of heat and solute source has a profound influence on the flow pattern, heat and mass transfer rates in the porous annulus. For the segment located at the bottom portion of inner wall, the flow rate is found to be higher, whereas the heat and mass transfer rates are higher when the source is placed near the middle of the inner wall. Further, the average Sherwood number increases with Lewis number, while for the average Nusselt number the effect is opposite. The average Nusselt number increases with radius ratio ( λ); however, the average Sherwood number increases with radius ratio only up to λ = 5, and for λ > 5 , the average Sherwood number does not increase significantly. [ABSTRACT FROM AUTHOR]

The double-diffusive convection in a horizontal fluid-saturated porous layer, which is heated and salted from below in the presence of Soret and Dufour effects, is studied analytically using both linear and nonlinear stability analyses. The linear analysis is based on the usual normal mode technique, while the nonlinear analysis is based on truncated representation of Fourier series. The generalized Darcy model that includes the time derivative is employed for the momentum equation. The critical Rayleigh number, wavenumber for stationary and oscillatory modes, and frequency of oscillations are obtained analytically using linear theory. The effects of solute Rayleigh number, Lewis number, normalized porosity parameter, Vadasz number, Soret and Dufour parameters on the stationary, oscillatory convection, and heat and mass transfers are shown graphically. The Vadasz number has dual effect on the threshold of the oscillatory convection. Some known results are recovered as special cases of the present problem. [ABSTRACT FROM AUTHOR]

The article deals with nonlinear thermal instability problem of double-diffusive convection in a porous medium subjected to temperature/gravity modulation. Three types of imposed time-periodic boundary temperature (ITBT) are considered. The effect of imposed time-periodic gravity modulation (ITGM) is also studied in this problem. In the case of ITBT, the temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent periodic part. The temperature of both walls is modulated in this case. In the problem involving ITGM, the gravity field has two parts: a constant part and an externally imposed time-periodic part. Using power series expansion in terms of the amplitude of modulation, which is assumed to be small, the problem has been studied using the Ginzburg-Landau amplitude equation. The individual effects of temperature and gravity modulation on heat and mass transports have been investigated in terms of Nusselt number and Sherwood number, respectively. Further the effects of various parameters on heat and mass transports have been analyzed and depicted graphically. [ABSTRACT FROM AUTHOR]

Abstract: A stability analysis is carried out to investigate the onset of thermosolutal convection in a horizontal porous layer when the solid and fluid phases are not in a local thermal equilibrium, and the solubility of the dissolved component depends on temperature. To study how the reaction and thermal non-equilibrium affect the double-diffusive convection, the effects of scaled inter-phase heat transfer coefficient H and dimensionless reaction rate k on thermosolutal convection are discussed . The critical Rayleigh number and the corresponding wave number for the stability and overstability convections are obtained. Specially, asymptotic analysis for both small and large values of H and k is presented, and the corresponding asymptotic solutions are compared with numerical results. At last, a nonlinear stability analysis is presented to study how H and k affect the Nusselt number. [ABSTRACT FROM AUTHOR]

Abstract: Double-diffusive convection in vertical annuluses with opposing temperature and concentration gradients is of fundamental interest and practical importance. However, available literature especially for higher Rayleigh numbers beyond is sparse. In this study, we investigated double diffusion induced convection up to using a simple lattice Boltzmann model. Thanks to the good stability of the present model, a modest grid resolution is sufficient for the present simulations. The influences of the ratio of buoyancy forces , the aspect ratio and the radius ratio on heat and mass transfer characteristics are discussed in detail. [Copyright &y& Elsevier]

Solar stills are convenient, cheap and ambient friendly but has the drawback of low production of potable fresh water. To explore better the concept and make more attractive for use some more research is necessary to improve the productivity and thermal performance of these units. In this paper a numerical study on an inclined type solar still is performed to investigate the influence of the water film thickness on the heat transfer and fluid flow inside the device cavity. The solar still system temperatures are calculated for four film thicknesses, 0.14, 0.5, 1.0 and 3.0 mm, through the Runge-Kutta method for the ambient conditions of Campinas, southeast of Brazil. The temperatures of the film and the glass are input to the computational fluid dynamics investigation. The radiative transfer and double-diffusive convection of air and vapor mixture are simulated considering the nongray Spectral Line Based Weighted-Sum-of-Gray-Gases method. The results indicate that the use of film thickness δ w = 3.0 mm increased the temperature difference between the water film and the glass from 2.14 °C to 9.15 °C when compared to the film flowing over the bare plate, δ w = 0.14 mm, and increased the rate of fresh water yield more than 2.0 times, for summer conditions and peak insolation hours. The use of transparent gas approach slightly overpredicted radiative and convective heat transfer inside the solar still cavity. • An inclined solar still is numerically simulated considering nongray gas approach • Thick water films increase temperature and vapor concentration in the cavity core. • A film thickness of 3 mm is adequate for increased fresh water yield. • The moving water film does not induce a clockwise moving mixture. • The transparent gas approach results in errors up to 39% in temperature and vapor profiles. [ABSTRACT FROM AUTHOR]

• The combined effect of cross gradients results in enhancement in heat transfer at lower thermal Rayleigh numbers. • Relative location of obstacles w.r.t the boundary layer influences its role on heat transfer. • Obstacles results in higher heat and mass transfer even though the average flow velocity decreases. • At lower buoyancy ratio, the mass transfer at the horizontal walls are highly enhanced with the increase in Lewis number. We investigate natural convection driven by a horizontal temperature gradient and a vertical concentration gradient in fluid-filled enclosures with obstructions inside it. Within the domain, nine adiabatic and impermeable cylinders are placed, occupying 30% of the domain volume. The Boussinesq approximation is used to account for density variations within the fluid and the flow is fully resolved. The solutal Rayleigh number has been fixed at R a C = 10 6 and the Prandtl number at P r = 5.4. The Lewis number has been varied in the range of 1 ≤ Le ≤ 100 and the buoyancy ratio in the range of 0.1 ≤ | N | ≤ 10. The rate of heat and mass transfer are compared to those found in single-scalar natural convection, i.e solely thermal or concentration driven convection. Besides, the obtained heat and mass transfer rate in the cylinder-packed enclosure have been compared to those found in a fluid-only domain. We observe that the addition of a destabilizing concentration gradient to a side-heated enclosure results in heat transfer enhancement, which decreases with Lewis number and thermal Rayleigh number. Similarly, the temperature gradient increases the mass transfer, especially at high Lewis numbers and lower concentration buoyancy force over its thermal counterpart. Although the presence of the cylindrical obstacles reduced the flow velocity, the mass transfer was enhanced at lower buoyancy ratio. [ABSTRACT FROM AUTHOR]

The onset of Darcy-Brinkman convection in a binary viscoelastic fluid-saturated sparsely packed porous layer with an internal heat source is studied using both linear and nonlinear stability analyses. The Oldroyd-B model is employed to describe the rheological behavior of binary fluid. An extended form of the Darcy-Oldroyd law incorporating Brinkman's correction and time derivative is used to describe the flow through a porous layer. The onset criterion for stationary, oscillatory, and finite amplitude convection is derived analytically. There is a competition between the processes of thermal diffusion, solute diffusion, and viscoelasticity that causes the convection to set in through an oscillatory mode rather than a stationary mode. The effect of internal Rayleigh number, relaxation and retardation parameters, solute Rayleigh number, Darcy number, Darcy-Prandtl number, and Lewis number on the stability of a system is investigated and is shown graphically. The nonlinear theory based on the truncated representation of the Fourier series method is used to find heat and mass transfer. The transient behavior of the Nusselt and Sherwood numbers is obtained using numerical methods. Some known results are recovered for the particular cases of the present study. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 42(8): 676-703, 2013; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21056 [ABSTRACT FROM AUTHOR]