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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 provide a solution for natural convection in a cavity with a partial heater in case of volumetric heating and analysis of the entropy generation.

The control volume method based on three-dimensional (3D) vorticity-potential vector was applied to solve governing equations of natural convection in a 3D cavity with a fin for different governing parameters as external Rayleigh numbers (103=Ra_E=106), internal Rayleigh numbers 103=Ra_I=106, partition height (0.25=h=0.75) and partition location (0.25=c=0.75). A code was written by using Fortran platform.

The edge of the fin becomes important on entropy generation. The ratio of the Ra_I/Ra_E plays the important role on natural convection and entropy generation. The variation of external Rayleigh number becomes insignificant for the Ra_I/Ra_E>1.

The originality of this work is to analyze the entropy generation and natural convection in a cubical cavity with volumetrically heating.

The purpose of this study is to investigate the effects of heat generation or absorption on heat transfer and fluid flow within two- and three-dimensional enclosure for homogeneous medium filled with different metal liquid. Numerical results are presented and analyzed in terms of fluid flow, thermal field structures, as well as average Nusselt number profiles over a wide range of dimensionless quantities, Grashof number (Gr) (104 and 105), SQ (varied between −500 to 500) and Prandtl number (Pr = 0.015, 0.024 and 0.0321). The results indicate that when the conductive regime is established for a Grashof number Gr = 104, the 2D model is valid and predicts all three-dimensional results with negligible difference. This was not the case in the convective regime (Gr = 105) where the effect of the third direction becomes important, where a 2D-3D difference was seen with about 37 per cent. Also, in most cases, the authors find that the heat absorption phenomena have the opposite effect with respect to the heat generation.

Numerical results are presented and analyzed in terms of fluid flow, thermal field structures, as well as average Nusselt number profiles over a wide range of dimensionless quantities.

Grashof number (Gr) (104 and 105), SQ (varied between −500 to 500) and Prandtl number (Pr = 0.015, 0.024 and 0.0321).

The results indicate that when the conductive regime is established for a Grashof number Gr = 104, the 2D model is valid and predicts all three-dimensional results with negligible difference.

This study aims to numerically scrutinize the entropy generation minimization and mixed convective heat transfer of multi-walled carbon nanotubes–Fe₃O₄/water hybrid nanofluid flow in a lid-driven square enclosure with heat generation in the presence of a porous layer on inner surfaces, considering local thermal non-equilibrium (LTNE) approach and the non-Darcy flow model.

The dimensionless governing equations for hybrid nanofluid and solid phases are solved by applying the finite volume method and semi-implicit method for pressure-linked equations algorithm.

The roles of the internal heat generation in the porous layer, LTNE model and nanoparticles volume fraction on mixed convection phenomenon and entropy generation are introduced for lid-driven cavity hybrid nanofluid flow. Based on the investigation of entropy generation and heat transfer, the minimum total entropy generation and average Nusselt numbers are found at 1 ≤ Ri ≤ 10 where the effect of the forced and free convection flow directions being opposite each other is very significant. When considering various nanoparticle volume fractions, it becomes evident that the minimum entropy generation occurs in the case of φ = 0.1%. The outcomes of LTNE number reveal the operating parameters in which thermal equilibrium occurs between hybrid nanofluid and solid phases.

The analysis of entropy generation under various shear and buoyancy forces plays a significant role in the suitable thermal design and optimization of mixed convective heat transfer applications. This research significantly contributes to the optimization of design and the advancement of innovative solutions across diverse engineering disciplines, such as packed-bed thermal energy storage and thermal insulation.

The purpose of this study is to numerically analyze the mixed convection and entropy generation in an annulus with a rotating heated inner cylinder for single-wall carbon nanotube (SWCNT)–water nanofluid flow using local thermal nonequilibrium (LTNE) model. An examination of the system behavior is presented considering the heat-generating solid phase inside the porous layer partly filled at the inner surface of the outer cylinder.

The discretized governing equations for nanofluid and porous layer by means of the finite volume method are solved by using the SIMPLE algorithm.

It is found that the buoyancy force and rotational effect have an important impact on the change of the strength of streamlines and isotherms for nanofluid flow. The minimum average Nusselt number on the inner cylinder is obtained at Ra$_E$ = 10$^4$, and the minimum total entropy generation is found at Re = 400 for given parameters. The entropy generation minimization is determined in case of different nanoparticle volume fractions. It is observed that at the same external Rayleigh numbers, the LTNE condition obtained with internal heat generation is very different from that without heat generation.

To the best of the authors’ knowledge, there is no previous paper presenting mixed convection and entropy generation of SWCNT–water nanofluid in a porous annulus under LTNE condition. The addition of nanoparticles to based fluid leads to a decrease in the value of minimum total entropy generation. Thus, using nanofluid has a significant role in the thermal design and optimization of heat transfer applications.

The purpose of this paper is to investigate the effects of first‐order homogeneous chemical reaction on a two‐dimensional boundary layer flow past a vertical stretching surface in the presence of internal heat generation.

Using the Boussinesq and boundary‐layer approximations, the fluid equations for momentum, energy balance and concentration governing the problem are formulated. The governing partial differential equations are transformed using similarity transformations into a set of coupled ordinary differential equations that are solved numerically using a shooting technique and a sixth‐order Runge‐Kutta scheme.

It was found that for positive values of the buoyancy parameters, the local skin friction and mass transfer coefficients increase with increasing Eckert and Schmidt numbers while the heat transfer coefficient decreases with both Eckert and Schmidt numbers. Both the velocity and temperature profiles increase significantly when the heat generation parameter increases.

Continuous surface heat and mass transfer problems occur naturally in metallurgical process such as in the aerodynamic extrusion of plastic sheets, hot rolling and the cooling of metallic plates in a cooling bath. This work provides a very useful source of information for researchers on this subject.

This paper illustrates the effects of chemical reaction on boundary layer flow past a vertical stretching surface in the presence of internal heat generation.

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.

This paper aims to present thermal and mechanical stresses in solid and hollow thick-walled cylinders and spheres made of functionally graded materials (FGMs) under the effect of heat generation.

Constant internal temperature and convective external conditions in hollow bodies along with internal heat generation with a combination of outer convective conditions in solid bodies are investigated individually. The effect of the heat convection coefficient on solid bodies is additionally discussed. The variation of the FGM properties in the radial direction is adapted to the Mori–Tanaka homogenization schemes, which produces irregular and two-point linear boundary value problems that are numerically solved by the pseudospectral Chebyshev method.

It has been shown that the selection of the mixtures of FGMs has to be made correctly to keep the thermal and mechanical loads acting on objects at low levels.

In this study, both solid and hollow functionally graded cylinders and spheres for different boundary conditions that are as their engineering applications are examined with the proposed method. The results have demonstrated that the pseudospectral Chebyshev method has high accuracy, low calculation costs and ease of application and can be easily adapted to such engineering problems.

Physical properties of a viscous fluid, e.g. viscosity and thermal conductivity change with temperature and in most of the studies concerned with natural convection, generally, the simultaneous effect of temperature dependent viscosity, thermal conductivity have been neglected. Hence, the purpose of this paper is to investigate the simultaneous effects of varying viscosity and thermal conductivity on free convection flow of a viscous incompressible electrically conducting fluid and heat transfer along an isothermal vertical non‐conducting plate in the presence of exponentially varying internal heat‐generation and uniform transverse magnetic field.

The governing equations of motion and energy are transformed into ordinary differential equations using similarity transformation. The resulting boundary valued, coupled and non‐linear differential equations are converted into system of linear differential equations and solved using Runge‐Kutta fourth order technique along with shooting method.

It was found that: fluid velocity decreases with the increase in magnetic parameter or Prandtl number; fluid temperature increases with the increase in magnetic parameter; velocity and temperature profiles increase due to increase in heat generation parameter; varying viscosity and thermal conductivity modifies the flow and heat transfer characteristic; and skin‐friction and heat transfer are affected by simultaneous change in viscosity and thermal conductivity in presence/absence of exponentially varying heat generation.

The present study is applicable to an incompressible viscous fluid flow and heat transfer with linearly varying viscosity and thermal conductivity.

This paper provides useful information on the physical properties of a viscous fluid with regard to viscosity and thermal conductivity change with temperature.

This work is focused on the numerical modeling of mixed convective heat transfer in a double lid-driven cavity filled with water-CuO nanofluid in the presence of internal heat generation. The paper aims to discuss these issues.

The flow field is modeled using a generalized form of the momentum and energy equations. Discretization of the governing equations is achieved using the penalty finite element scheme based on the Galerkin method of weighted residuals.

The effects of pertinent parameters such as the internal heat generation parameter (Q), the Richardson number (Ri) and the solid volume fraction () on the flow and heat transfer characteristics are presented and discussed. The obtained results depict that the Richardson number plays a significant role on the heat transfer characterization within the triangular wavy chamber. Also, the present results show that an increase in volume fraction has a significant effect on the flow patterns.