Search results

This study aims to elucidate the role of curved walls in the presence of identical mass of porous bed with identical heating at a wall for two heating objectives: enhancement of heat transfer to fluid saturated porous beds and reduction of entropy production for thermal and flow irreversibilities.

Two heating configurations have been proposed: Case 1: isothermal heating at bottom straight wall with cold side curved walls and Case 2: isothermal heating at left straight wall with cold horizontal curved walls. Galerkin finite element method is used to obtain the streamfunctions and heatfunctions associated with local entropy generation terms.

The flow and thermal maps show significant variation from Case 1 to Case 2 arrangements. Case 1 configuration may be the optimal strategy as it offers larger heat transfer rates at larger values of Darcy number, Da_m. However, Case 2 may be the optimal strategy as it provides moderate heat transfer rates involving savings on entropy production at larger values of Da_m. On the other hand, at lower values of Da_m (Da_m ≤ 10⁻³), Case 1 or 2 exhibits almost similar heat transfer rates, while Case 1 is preferred for savings of entropy production.

The concave wall is found to be effective to enhance heat transfer rates to promote convection, while convex wall exhibits reduction of entropy production rate. Comparison between Case 1 and Case 2 heating strategies enlightens efficient heating strategies involving concave or convex walls for various values of Da_m.

The purpose of this paper is to apply the numerical methods to study the heap leaching process in a bed of porous and spherical ore particles. This study is performed in two stages: first, modeling the leaching process of a soluble mineral from a spherical and porous ore particle to obtain the distribution of mineral concentrations, leaching solvent concentration and dissolved mineral in the particles (the particle model), and second, modeling the heap leaching of the mineral from a porous bed consisting of spherical and porous ore particles to obtain the distribution of mineral concentrations, leaching solvent concentration and dissolved mineral in the bed (the bed model).

The governing equations are derived for the particle model, and then converted into non‐dimensional form using reference quantities. The non‐dimensional equations are discretised on a uniform spherical grid fitted to the particle using finite difference method. The resulting algebraic equations are solved using Tri‐Diagonal Matrix Algorithm, and the governing equations are derived for the bed model, and then converted into non‐dimensional form using reference quantities. The non‐dimensional equations are discretised explicitly on a one‐dimensional and uniform grid fitted to the bed. The unknown quantities are evaluated using the corresponding values at the previous time interval.

The results obtained from numerical modeling show that, when the particle has a low diffusion resistance or a high chemical resistance, the reaction takes place slowly and homogeneously throughout the ore particle. On the other hand, when the bed has a low convection resistance, the reaction takes place homogeneously throughout the bed. As the convection resistance increases, the non‐homogeneous (local) behavior predominates. It is also noticed that, when the chemical reaction resistance is high, the reaction takes place homogeneously throughout the bed.

The dynamic diffusion and movement of solution in the ore particles and ore bed are not modeled and volumetric ratio of solution in the particles and the bed and also vertical velocity of solution in the bed are assumed to be fixed constants.

This study shows that the reaction takes place homogeneously throughout the bed when the convection resistance is low, the diffusion resistance is high, the concentration resistance is low, and the chemical reaction resistance is high.

Homogeneous reaction conditions being suitable for heap leaching operations are identified. Thus, it is recommended to approach the above conditions when preparing ore heaps and designing the relevant operation.

This study aims to numerically analyze natural convection of alumina-water nanofluid in a differentially-heated square cavity partially filled with a heat-generating porous medium. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been considered for the description of the nanoparticles transport effect in the present study. Local thermal non-equilibrium approach for the porous layer with the Brinkman-extended Darcy model has been used.

Dimensionless governing equations formulated using stream function, vorticity and temperature have been solved by the finite difference method. The effects of the Rayleigh number, Ostrogradsky number, Nield number and nanoparticles volume fraction on nanofluid flow, heat and mass transfer have been analyzed.

It has been revealed that the dimensionless heat transfer coefficient at the fluid/solid matrix interface can be a very good control parameter for the convective flow and heat transfer intensity. The present results are original and new for the study of non-equilibrium natural convection in a differentially-heated nanofluid cavity partially filled with a porous medium.

The results of this paper are new and original with many practical applications of nanofluids in the modern industry.

It is well known that the mixed convection process is the combined effect of the presence of both the forced and the free convection processes. In several applications such as environmental chambers, IC engines, etc. the forced convection is brought in by multiple suction/injection (S/I) effect. Study of mixed convection in a vertical square fluid saturated porous cavity with multiple S/I effect greatly contributes to such an understanding. So far, not much research work has reported in this direction. Hence, the purpose of this paper is to investigate such a mixed convection process in a fluid saturated vertical porous square cavity.

In this study, the authors numerically solved the couple partial differential equations governing the mixed convection process in a fluid saturated vertical square porous cavity by finite element method. The study is parametric in nature wherein the authors cover a large range of values for different parameters arising the mathematical model governing the problem under consideration.

The influence of multiple S/I effects on mixed convection is analyzed for a wide range of controlling parameters such as S/I flow velocities (a), S/I window size (D/H) and Rayleigh number (Ra). Both the flow and temperature fields are highly sensitive to magnitude of S/I velocity, S/I window slit size and “Ra”. While heat fluxes along the isothermal left vertical wall decrease with increasing S/I velocities they are formed to increase with increasing “(D/H)” and “Ra”. Nusselt numbers increase with increasing “Ra” and increasing size of S/I window slit size. Multi‐cellular circulation pattern and thermal boundary layers are seen to manifest in flow and temperature fields, respectively.

The study is based on 2D model, but the model is generic in nature; also it is fully numerical in nature. Due to lack of apt literature no experimental support is provided. The mathematical model used in the study is based on certain assumptions such as isotropic porous medium, fluid is viscous in nature and follows Newtonian laws and the porous structure is saturated with fluid, etc. Regarding future work, 3D modelling and simulation is in progress and attempts are also being made to collaborate with experimental groups on the problem under investigation.

The results from the work are relevant to the context of heat and fluid flow studies in IC engines, influence of mixed convection process on bacterial growth process in environmental chambers and cooling of electronic devices, etc.

The paper describes a mathematical model, especially the boundary treatment, for describing the influence of multiple S/I effects on mixed convection flow in a vertical square enclosure filled with a Darcian fluid saturated homogeneous porous medium. To understand the physics behind the mixed convection process in the proposed configuration, extensive numerical simulations have been carried out for the first time for different values of the important governing parameters arising from the model.

The purpose of this paper is to analyze the natural convection heat transfer and irreversibility characteristics in a quadrantal porous cavity subjected to uniform temperature heating from the bottom wall.

Brinkmann-extended Darcy model is used to simulate the momentum transfer in the porous medium. The Boussinesq approximation is invoked to account for the variation in density arising out of the temperature differential for the porous quadrantal enclosure subjected to uniform heating on the bottom wall. The governing transport equations are solved using the finite element method. A parametric study is carried out for the Rayleigh number (Ra) in the range of 10³ to 10⁶ and Darcy number (Da) in the range of 10⁻⁵-10⁻².

A complex interaction between the buoyant and viscous forces that govern the transport of heat and entropy generation and the permeability of the porous medium plays a significant role on the same. The effect of Da is almost insignificant in dictating the heat transfer for low values of Ra (10³, 10⁴), while there is a significant alteration in Nusselt number for Ra ≥10⁵ and moreover, the change is more intense for larger values of Da. For lower values of Ra (≤10⁴), the main contributor of irreversibility is the thermal irreversibility irrespective of all values of Da. However, the fluid friction irreversibility is the dominant player at higher values of Ra (=10⁶) and Da (=10⁻²).

From an industrial point of view, the present study will have applications in micro-electronic devices, building systems with complex geometries, solar collectors, electric machinery and lubrication systems.

This research examines numerically the buoyancy driven heat transfer irreversibility in a quadrantal porous enclosure that is subjected to uniform temperature heating from the bottom wall, that was not investigated in the literature before.

By means of dip‐ or spray‐coating with polythene powder, a complete protective covering can be applied in one operation to metal articles of the most complex shape, such as the soap and sponge rack shown overleaf. Dip‐coating in particular is a process which can be carried out with very simple equipment, yet on the other hand it is adaptable to mass production requirements.

This paper aims to discuss the dynamic adsorption processes of carbon dioxide in a porous fixed bed on the industrial scale, using a multiple-relaxation-time lattice Boltzmann (LB) model.

A multiple-relaxation-time LB model is developed to predict the dynamic adsorption processes of carbon dioxide in a porous fixed bed on the industrial scale. The breakthrough curves from the simulation results are compared with the experimental data to validate the reliability of this model, and the effects of flow velocity, porosity and linear driving force mass transfer coefficient on the adsorption behaviors of carbon dioxide are explored further.

The numerical results show that the improved fluid flux leads to the reduction in the time required for completion of adsorption processes nonlinearly, and the differential pressure significantly raises with the decreasing porosity of porous fixed bed for fixed values of Reynolds number and total adsorption capacity. The maximum adsorption ratio of carbon dioxide was found at Re = 12 in this work. In addition, the higher mass transfer resistance of adsorbent particles advances the appearance time of the breakthrough point and delays the completion time of the adsorption processes.

This work will provide a way to study the adsorption technology of carbon dioxide in the fixed-bed using the LB method.

The purpose of this paper is to report a novel formulation of convective heat transfer source term for the case of flow through porous medium.

The novel formulation is obtained by analytical solution of an idealized dual problem. Computations are performed by dedicated tool for fixed bed combustion named GRATECAL and developed by the authors. However, the proposed method can also be applied to other porous media flow problems.

The new source term formulation is unconditionally stable and it respects exponential decay of temperature difference between the fluid and porous solid medium.

The results of this work are applicable in the simulation of convective heat transfer between the fluid and porous medium. Applications include e.g. fixed bed combustion, catalytic reactors and lime kilns.

The reported solution is believed to be original. It will be useful to all involved in numerical simulations of fluid flow in porous media with convective heat transfer.

Regularities imposed by an external wall on the random distribution of particles in a packed bed lead to anisotropic wall effects of the bed. The resulting deviations of near—wall porosity from the average bed—porosity markedly affect the average velocity profile, not only near the wall but also some distance into the bed itself. The effect of wall channelling due to such variations in porosity near external boundaries is predicted by means of two different numerical solution methods for a unified model for granular porous media. The results are shown to compare favourably to experimental and numerical results reported in the literature.

The purpose of this paper is to investigate thermally and hydrodynamically fully developed convection in a duct of rectangular cross-section containing a porous medium and fluid layer.

The Darcy–Brinkman–Forchheimer flow model is adopted. A finite difference method of second-order accuracy with the Southwell-over-relaxation method is deployed to solve the non-dimensional momentum and energy conservation equations under physically robust boundary conditions.

It is found that the presence of porous structure and different immiscible fluids exert a significant impact on controlling the flow. Graphical results for the influence of the governing parameters i.e. Grashof number, Darcy number, porous media inertia parameter, Brinkman number and ratios of viscosities, thermal expansion and thermal conductivity parameters on the velocity and temperature fields are presented. The volumetric flow rate, skin friction and rate of heat transfer at the left and right walls of the duct are also provided in tabular form. The numerical solutions obtained are validated with the published study and excellent agreement is attained.

To the author’s best knowledge this study original in developing the numerical code using FORTRAN to assess the fluid properties for immiscible fluids. The study is relevant to geothermal energy systems, thermal insulation systems, resin flow modeling for liquid composite molding processes and hybrid solar collectors.