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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 present a semi-analytical solution for time-dependent natural convection flow with heat generation/absorption in an annulus partially filled with porous material.

The governing partial differential equations are transformed into the ordinary differential equations using the Laplace transform technique. The exact solution obtained is inverted from the Laplace domain to time domain using the Riemann-sum approximation approach. Justification of the Riemann-sum approximation approach is achieved by comparing the values obtained with those of the implicit finite difference method at both the transient state and the steady state at large time.

If is found that the peak axial velocity always occur in the clear fluid region. In addition, there is an indication that heat generating fluid is desirable for optimum mass flux in the annular gap most importantly when the convection current is enhanced by constant heat flux.

In view of the amount of works done on natural convection with internal heat generation/absorption, it becomes interesting to investigate the influence of this essential activity on natural convection flow in a vertical cylinder partially filled with porous material where the outer surface of the inner cylinder is either heated isothermally or with constant heat flux.

The purpose of this paper is to study the natural convection and radiation heat transfer inside Nonagon inclined cavity with variable heated source length, which contains a porous medium saturated with nanofluid in the presence of uniform heat generation or absorption under the effect of uniform magnetic field with variable direction. The shape factor of nano particles is taking account for the model of nanofluid.

This study is established in two-dimensional space. The 2D numerical study is effectuated with Comsol Multiphysics based on the on the finite element method. The 2D equation system is exposed on dimensionless form taking into account the boundary conditions.

Results obtained show that the convection heat transfer is ameliorated with the augmentation of heated source length. The convection heat transfer is enhanced by increasing Rayleigh, Darcy numbers and the heated source length; however, it is reduced by rising Hartmann number. The presence of radiation parameter lead to improve the convection heat transfer in the presence of both uniform heat generation/absorption. The average Nusselt number reaches a maximum for an inclination of cavity γ = 45° and a minimum for γ = 60°. Both the increase of the shape factor of nano particles and the solid fraction of nano particles improve the convection heat transfer.

Different studies have been realized to study the heat transfer inside cavity contains porous medium saturated with nanofluid under magnetic field effect. In this work, the Nonagon geometric of cavity studied has never been studied. In addition, the effect of radiation parameter with relation of the shape factor of nanoparticles in the presence of uniform heat generation/absorption on the heat transfer performance have never been investigated. Also, the effect of magnetic field direction with relation of the inclination cavity on heat transfer performance.

The purpose of this paper is to know the influence of heat generation/absorption and slip effects on heat and mass transfer flow of carbon nanotubes – water-based nanofluid over a rotating disk. Two types of carbon nanotubes, single and multi-walled, are considered in this analysis.

The non-dimensional system of governing equations is constructed using compatible transformations. These equations together with boundary conditions are solved numerically by using the most prominent Finite element method. The influence of various pertinent parameters such as magnetic parameter (0.4 – 1.0), nanoparticle volume fraction parameter (0.1 – 0.6), porosity parameter (0.3 – 0.6), radiation parameter (0.1 – 0.4), Prandtl number (2.2 – 11.2), space-dependent (−3.0 – 3.0), temperature-dependent (−3.0 – 1.5), velocity slip parameter (0.1 – 1.0), thermal slip parameter (0.1 – 0.4) and chemical reaction parameter (0.3 – 0.6) on nanofluids velocity, temperature and concentration distributions, as well as rates of velocity, temperature and concentration is calculated and the results are plotted through graphs and tables. Also, a comparative analysis is carried out to verify the validation of the present numerical code and found good agreement.

The results indicate that the temperature of the fluid elevates with rising values of nanoparticle volume fraction parameter. Furthermore, the rates of heat transfer rise from 4.8% to 14.6% when carbon nanotubes of 0.05 volume fraction are suspended into the base fluid.

The work carried out in this analysis is original and no part is copied from other sources.

The present investigation aims to deal with the study of unsteady, heat-generating/-absorbing and chemically reacting Casson fluid flow over a vertical cone and flat plate saturated with non-Darcy porous medium in the presence of cross-diffusion effects.

A numerical computation for the governing equations has been performed using implicit finite difference method of Crank–Nicolson type.

The influence of various physical parameters on velocity, temperature and concentration distributions is illustrated graphically, and the physical aspects are discussed in detail. Numerical results for average skin-friction, Nusselt number and Sherwood number are tabulated for the pertaining physical parameters. Results indicate that Soret and Dufour effects have notable influence on heat and mass transfer characteristics of the fluid when the temperature and concentration gradients are high. It is also observed that the consideration of heat generation/absorption plays a vital role in predicting the heat transfer characteristics of moving fluids.

Consider a two-dimensional, unsteady, free convective flow of an incompressible Casson fluid over a vertical cone and a flat plate saturated with non-Darcy porous medium. The fluid properties are assumed to be constant except for density variations in the buoyancy force term. The fluid flow is moderate and the permeability of the medium is assumed to be low, so that the Forchheimer flow model is applicable.

The flow of Casson fluids (such as drilling muds, clay coatings and other suspensions, certain oils and greases, polymer melts and many emulsions), in the presence of heat transfer, is an important research area because of its relevance in the optimized processing of chocolate, toffee and other foodstuffs.

In the heat and mass transfer investigations, the Casson fluid model is found to be accurately applicable in many practical situations in the wings of polymer processing industries and biomechanics, etc.; some prominent examples are silicon suspensions, suspensions of bentonite in water and lithographic varnishes used for printing inks.

The motivation of the present study is to bring out the effects of heat source/sink, Soret and Dufour effects on chemically reacting Casson fluid flow over a vertical cone and flat plate saturated with non-Darcy porous medium. The flow of Casson fluids (such as certain oils and greases, polymer melts and many emulsions) in the presence of heat transfer is an important research area because of its relevance in the optimized processing of chocolate, toffee and other foodstuffs. A numerical computation for the governing equations has been performed using implicit finite difference method of the Crank–Nicolson type.

The purpose of this paper is to investigate the entropy optimization in magnetohydrodynamic hybrid nanomaterials flows toward a stretchable surface. The energy expression is modeled subject to dissipation, heat generation/absorption and Joule heating. Here silicon dioxide (SiO₂) and molybdenum disulfide (MoS₂) as nanoparticles and propylene glycol (C₃H₈O₂) as base fluid, respectively. Furthermore, the authors discussed the comparative study of molybdenum disulfide and silicon dioxide diluted in propylene glycol. The total entropy optimization rate is computed through implementation of the second law of thermodynamics.

The nonlinear partial differential system is reduced to an ordinary one through implementation of transformation. Newton built-in shooting method is used for computational results for the given system. Influences of various flow variables on the temperature, Bejan number, velocity, concentration and entropy generation rate are examined graphically for both nanoparticles (SiO₂ and MoS₂). Gradients of velocity and temperature are computed numerically for various physical parameters. Also, take the comparison between the present and previously published results in tabulated form.

For higher estimation of ϕ both temperature and velocity are enhanced. Entropy optimization and Bejan number have the opposite outcome for viscosity parameter. Temperature and velocity have opposite behaviors for larger values of magnetic parameter. Molybdenum disulfide (MoS₂) is more efficient than silicon dioxide (SiO₂).

No such work is yet published in the literature.

The purpose of this paper is to discuss the flow of Casson nanofluid past a nonlinear permeable stretching sheet in the presence of thermal radiation, chemical reaction, viscous dissipation, heat source, and magnetohydrodynamics.

Appropriate transformations are used to convert the boundary layer equations into nonlinear ODEs which are then solved numerically by using the Runge-Kutta-Fehlberg fourth-fifth order method along with shooting technique.

Solution of this systems is obtained for velocity, temperature, and concentration profiles. Graphical illustrations are added to discuss the effect of evolving parameters against above-mentioned distributions. Tabular values of local skin friction factor, local Nusselt number, and local Sherwood number are also added and studied accordingly.

A good agreement of the present results has been observed by comparing with the existing literature results. It is noted that skin friction coefficient, Nusselt number, and Sherwood number decrease with Casson parameter and increase with suction parameter.

This study aims to analyze the Prandtl fluid flow in the presence of better mass diffusion and heat conduction models. By taking into account a linearly bidirectional stretchable sheet, flow is produced. Heat generation effect, thermal radiation, variable thermal conductivity, variable diffusion coefficient and Cattaneo–Christov double diffusion models are used to evaluate thermal and concentration diffusions.

The governing partial differential equations (PDEs) have been made simpler using a boundary layer method. Strong nonlinear ordinary differential equations (ODEs) relate to appropriate non-dimensional similarity variables. The optimal homotopy analysis technique is used to develop solution.

Graphs analyze the impact of many relevant factors on temperature and concentration. The physical parameters, such as mass and heat transfer rates at the wall and surface drag coefficients, are also displayed and explained.

The reported work discusses the contribution of generalized flux models to note their impact on heat and mass transport.

The purpose of this paper is to study the problem of two‐dimensional unsteady mixed convective flow a dusty fluid over a stretching sheet in the presence of thermal radiation and space‐dependent heat source/sink.

The equations governing the fluid flow and temperature fields for both the fluid and dust phases are reduced to coupled non‐linear ordinary differential equations by using a suitable set of similarity transformations. Numerical solutions of the resulting equations are obtained using the well known RKF45 method.

The numerical results are benchmarked with previously published studies and found to be in excellent agreement. Finally, the effects of the pertinent parameters which are of physical and engineering interest on the flow and heat transfer characteristics are presented graphically and in tabulated form.

The problem is relatively original as the dusty fluid works for this type of problem are lacking.

The purpose of this paper is to study numerically thermosolutal natural convection within an inclined rectangular cavity in the presence of Soret effect and heat generation. The enclosure is heated and salted from its long sides with constant but different temperatures and concentrations. The study focuses on the effects of three main parameters which are, the Soret parameter (Sr = 0 and –0.5), the internal to external Rayleigh numbers ratio 0 ≤ R ≤ 80 and the cavity inclination γ, varied from 0° (vertical position) to 60°. The combined effects of these parameters on fluid flow and heat and mass transfer characteristics are examined for the external Rayleigh number Ra_E = 10⁵, the Prandtl number Pr = 0.71, the buoyancy ratio N = 1, the Lewis number Le = 2 and the aspect ratio of the cavity A = 2.

A hybrid lattice Boltzmann-finite difference method (LBM-FD) was used to tackle the problem under consideration. The LBM with the simple relaxation time was used for the fluid flow in the presence of the gravity force, while the temperature and concentration equations were solved separately using an explicit finite-difference technique at the Boltzmann scale.

The monocellular nature of the flow, obtained for R = 0 is not destroyed by varying the cavity inclination and the Soret parameter but rather by the increase of the parameter R. The Soret parameter and the cavity inclination become perceptible at high values of R. The inclination γ = 60° leads to high mean temperatures compared to the other inclinations. The effect of R on mean concentration is amplified in the presence of Soret effect but limited in the absence of the latter. The negative Soret parameter combined with high internal heat generation and a relatively high inclination is important when the objective is to maintain the fluid at a high concentration of species. The presence of bicellular flow combined with the important elevation undergone by the fluid temperature, makes both the cold and hot walls playing a cooling role with the most important exchanges taking place at the upper part of these walls. The analysis of the mean mass transfer shows that the increase of the inclination may lead to an increase or a decrease of the mass transfer depending on the range of R, in the case of Sr = 0. However, for Sr = −0.5, it is observed that the increase of γ is generally accompanied by a reduction of the mass transfer.

To the best of the authors’ knowledge, the hybrid LBM-FD was not used before to study such a problem. Combined effect of R and inclination may be useful in charging the fluid with species when the objective is to maintain high concentrations in the medium.