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The purpose of this study is simultaneous dyeing and mordanting of wool yarns with extracted cochineal dye and aluminum sulfate to the reduction of consuming energy, water and time.

The dyeing process was optimized using the response surface methodology (RSM) approach. pH, dyeing duration and the presence of additives were chosen as variables and the color strength of samples as a response. The color characteristics and fastness attributes of samples dyed in the best condition were evaluated and compared to pre-mordant dyeing outcomes on wool yarns.

The best conditions for deep dyeing wool with cochineal dye were as follows: pH 2.5, time 110 min and the ratio of aluminum: additives 1:0 at 100 °C. Color strength of dyed wool yarns by one-bath and pre-mordant dyeing methods were approximately the same. Wool yarns can dye to the on-bath dyeing method such that the dyed samples have similar color strength and fastness properties to pre-mordant dyeing.

Wool dyeing processes that use one-bath dyeing consume less water and produce fewer effluents. As a result, this strategy conserves water and energy for a higher quality of life. The findings of this study, in general, aid environmental protection.

A novel one-bath process for dyeing wool with cochineal dye at heavy depths is introduced. RSM was used to optimize the procedure and determine effective parameters on the color strength of dyed wools. Using extracted cochineal dye and aluminum sulfate in a simultaneous dyeing technique, good color fastness qualities on wool fibers were achieved.

The purpose of this study is to investigate the applicability of volume average which is extensively used for analyzing the heat and fluid flow (both for single-phase and solid/liquid-phase change) in a closed cell porous medium numerically.

Heat conduction equations for the solid frame and fluid (or phase change material) are solved for pore scale and volume average approaches. The study mainly focuses on the effect of porosity and the number of porous media unit cell on the agreement between the results of the pore scale and volume average approaches.

It is observed for the lowest porosity values such as 0.3 and the number of porous media unit cell as 4 in heat transfer direction, the results between two approaches may be questionable for the single-phase fluid. By increasing the number of porous media unit cell in heat transfer direction, the agreement between two approaches becomes better. In general, for high porosity values (such as 0.9) the agreement between the results of two approaches is in the acceptable range both for single-phase and solid/liquid-phase change. Two charts on the applicability of volume average method for single-phase and solid/liquid-phase change are presented.

The authors’ literature survey shows that it is the first time the applicability of volume average which is extensively used for analyzing the heat and fluid flow in a closed cell porous medium is investigated numerically.

The purpose of this work is the study of the steady free convection in a square differentially heated cavity filled by a Brinkman bidisperse porous medium. An appropriate mathematical model considering the Brinkman, momentum and energy interphase terms is proposed. The dependence of the stream functions, isotherms and of the Nusselt numbers on the governing parameters is analysed.

The both phases of flow and heat transfer are solved numerically using a modified finite difference technique. The algebraic system obtained after discretization is solved using the SOR method. The results are found to be in a significant agreement with the ones presented by the literature for a Darcy bidisperse porous medium and a Brinkman monodisperse porous medium.

The effects of the governing parameters on stream functions, isotherms and Nusselt numbers are discussed. It has been found that in the case of the Brinkman bidisperse model, the Nusselt numbers decrease compared to the Darcy model, and this behaviour is significant in comparison to the Brinkman monodisperse case.

A mathematical model for the free convection inside a cavity filled by a non-Darcy bidisperse porous medium, based on the Brinkman equation, is used. The effect of Darcy number, Rayleigh number, modified inter-phase heat transfer parameter, modified thermal conductivity ratio and the inertial parameters is studied. To the best of the authors’ knowledge, this problem has not been studied before, and the results are new and original.

The purpose of this paper is to improve the volume-averaged models for free convection flow in porous media.

A pore scale simulation is conducted against which an independent volume-averaged solver is fine-tuned.

Micro and macro scale results can merge if proper choice of local thermal non-equilibrium and thermal dispersion models are selected. This depends on the range of Ra values investigated.

This is the first time a work like this is published in the literature.

The lattice Boltzmann simulation of fluid flow in partial porous geometries with curved porous-fluid interfaces has not been investigated yet. It is mainly because of the lack of a method in the lattice Boltzmann framework to model the hydrodynamic compatibility conditions at curved porous-fluid interfaces, which is required for the two-domain approach. Therefore, the purpose of this study is to develop such a method.

This research extends the non-equilibrium extrapolation lattice Boltzmann method for satisfying no-slip conditions at curved solid boundaries, to model hydrodynamic compatibility conditions at curved porous-fluid interfaces.

The proposed method is tested against the results available from conventional numerical methods via the problem of fluid flow through and around a porous circular cylinder in crossflow. As such, streamlines, geometrical characteristics of recirculating wakes and drag coefficient are validated for different Reynolds (5 ≤ Re ≤ 40) and Darcy (10⁻⁵ ≤ Da ≤ 5 × 10⁻¹) numbers. It is also shown that without applying any compatibility conditions at the interface, the predicted flow structure is not satisfactory, even for a very fine mesh. This result highlights the importance of the two-domain approach for lattice Boltzmann simulation of the fluid flow in partial porous geometries with curved porous-fluid interfaces.

No research is found in the literature for applying the hydrodynamic compatibility conditions at curved porous-fluid interfaces in the lattice Boltzmann framework.

The purpose of this paper is to analyze two different approaches (Models A and B) for an adiabatic boundary condition at the wall of a channel filled with a porous medium. The analytical solutions for the velocity distribution, the fluid and solid phase temperature distributions are derived and compared with numerical solutions. The phenomenon of heat flux bifurcation for Model A is demonstrated. The effects of pertinent parameter C on the applicability of the Models A and B are discussed. Analytical solutions for the overall Nusselt number and the heat flux distribution at the channel wall are derived and the influence of pertinent parameters Da and k on the overall Nusselt number and the heat flux distribution is discussed.

Two approaches (Models A and B) for an adiabatic boundary condition in porous media under local thermal non-equilibrium (LTNE) conditions are analyzed in this work. The analysis is applied to a microchannel which is modeled as a porous medium.

The phenomenon of heat flux bifurcation at the wall for Model A is demonstrated. The effect of pertinent parameter C on the applicability of each model is discussed. Model A is applicable when C is relatively large and Model B is applicable when C is small. The heat flux distribution is obtained and the influence of Da and k is discussed. For Model A, ϕ_Afin increases and ϕ_Asub, ϕ_Acover decrease as Da decreases and k is held constant, ϕ_Asub increases and ϕ_Afin, ϕ_Acover decrease as k increases while Da is held constant; for Model B, ϕ_Bfin increases and ϕ_Bsub decreases either as Da decreases or k decreases. The overall Nusselt number is also obtained and the effect of Da and k is discussed: Nu increases as either Da or k decrease for both models. The overall Nusselt number for Model A is larger than that for Model B when Da is large, the overall Nusselt numbers for Models A and B are equivalent when Da is small.

Proper representation of the energy equation and the boundary conditions for heat transfer in porous media is very important. There are two different models for representing energy transfer in porous media: local thermal equilibrium (LTE) and LTNE. Although LTE model is more convenient to use, the LTE assumption is not valid when a substantial temperature difference exists between the solid and fluid phases.

Fluid flow and convective heat transfer in porous media have many important applications such as thermal energy storage, nuclear waste repository, electronic cooling, geothermal energy extraction, petroleum processing and heat transfer enhancement.

This work has important fundamental implications.

In this work the microchannel is modeled as an equivalent porous medium. The analytical solutions for the velocity distribution, the fluid and solid phase temperature distributions are obtained and compared with numerical solutions. The first type of heat flux bifurcation phenomenon, which indicates that the direction of the temperature gradient for the fluid and solid phases is different at the channel wall, occurs when Model A is utilized. The effect of pertinent parameter C on the applicability of the models is also discussed. The analytical solutions for the overall Nusselt number and the heat flux distribution at the channel wall are derived, and the effects of pertinent parameters Da and k on the overall Nusselt number and the heat flux distribution are discussed.