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The purpose of this paper is to further extend the work of Weng and Chen (2009) by considering heat generation/absorption nature of fluid.

Exact solution of momentum equation is derived separately in terms of Bessel’s function of first and second kind for heat-generating fluid and modified Bessel’s function of first and second kind for heat absorbing fluid.

During the course of numerical computations, it is found that skin friction and rate of heat transfer at outer surface of inner cylinder and inner surface of outer cylinder increases with the increase in heat generation parameter while the reverse trend is found in the case of heat absorption parameter.

In view of the amount of works done on natural convection with internal heat generation/absorption, it becomes interesting to investigate the effect of this important activity on natural convection flow in a vertical annular micro-channel. The purpose of this paper is to further extend the work of Weng and Chen (2009) by considering heat generation/absorption nature of fluid.

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.

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 consider the problem of fully developed laminar mixed convection flow of a couple stress fluid in a vertical channel with the third-kind boundary conditions in the presence or absence of heat source/sink effect.

Through proper choice of dimensionless variables, the governing equations are developed. These governing equations are solved analytically by the differential transform method and numerically by the Runge–Kutta shooting method. Analytical solutions for the velocity and temperature profiles for heat generation and absorption of the problem are reported.

The mass flow rate and Nusselt numbers at both the left and right channel walls on mixed convection parameter, Brinkman number, couple stress parameter and heat generation/absorption parameter for equal and unequal Biot numbers are presented. Favorable comparisons of special cases with previously published work are obtained. It is found that velocity, temperature, mass flow rate and Nusselt number decrease with couple stress parameter and increase with mixed convection parameter and Brinkman number.

The work done in this paper is not done earlier to the authors’ knowledge. This is the first paper in which the sixth-order differential equation is solved using the semi-numerical method, which is a differential method.

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.

This study aims to examine the flow of unsteady mixed convective hybrid nanofluid over a rotating sphere with heat generation/absorption. The hybrid nanofluid contains different shapes of nanoparticles (copper [Cu] and aluminium oxide [Al₂O₃]) in the base fluid (water [H₂O]). The influence of different shapes (sphere, brick, cylinder, platelets and blades) of nanoparticle in water-based hybrid nanofluid is also investigated.

To analyse the nanomaterial, the flow model is established, and in doing so, the Prandtl’s boundary layer theory is incorporated into the present model. The bvp4c approach, i.e. finite difference method, is used to find the numerical solution of differential equations that is controlling the fluid flow. The effect of relevant flow parameters on nanofluid temperature and velocity profile is demonstrated in detailed explanations using graphs and bar charts, whereas numerical results for Nusselt number and the skin’s coefficient for various form parameters are presented in tabular form.

The rate of heat transfer is least for spherical-shaped nanoparticle because of its smoothness, symmetricity and isotropic behaviour. The rate of heat transfer is highest for blade-shaped nanoparticles as compared to other shapes (brick, cylindrical and platelet) of nanoparticles because the blade-shaped nanoparticles causes comparatively more turbulence flow in the nanofluid than other shapes of nanoparticle. Heat generation affects the temperature distribution and, hence, the particle deposition rate. The absorption of heat extracts heat and reduce the temperature across the rotating sphere. The heat generation/absorption parameter plays an important role in establishing and maintaining the temperature around the rotating sphere.

The numerical study is valid with the exception of the fluctuation in density that results in the buoyancy force and the functional axisymmetric nanofluid transport has constant thermophysical characteristics. In addition, this investigation is also constrained by the assumptions that there is no viscosity dissipation, no surface slippage and no chemically activated species. The hybrid nanofluid Al₂O₃–Cu/H₂O is an incompressible and diluted suspension. The single-phase hybrid nanofluid model is considered in which the relative velocity of water (H₂O) and hybrid nanoparticles (Al₂O₃–Cu) is the same and they are in a state of thermal equilibrium.

Study on convective flow across a revolving sphere has its applications found in electrolysis management, polymer deposition, medication transfer, cooling of spinning machinery segments, spin-stabilized missiles and other industrial and technical applications.

The originality of the study is to investigate the effect of shape factor on the flow of electrically conducting hybrid nanofluid past a rotating sphere with heat generation/absorption and magnetic field. The results are validated and provide extremely positive balance with the recognised articles. The results of the study provide many appealing applications that merit further study of the problem.

The purpose of this paper is to perform a numerical study for heat transfer through natural convection in the presence of a constant magnetic field in an incompressible steady nanofluid flow inside an isosceles triangular cavity.

For this flow problem, the left wall of the cavity subjected to uniform/nonuniform heat was considered, while right and bottom walls of the cavity were kept cold. The obtained equations were solved by using the Galerkin weighted residual technique. Results are computed for a wide range of parameters including Rayleigh number (Ra) (10^3 < Ra < 10^7), Hartman number (Ha) (0 < Ha < 60), and heat-generation/-absorption coefficient (q) (−10 < q < 10), while, Prandtl number (Pr) was kept fixed at 6.2. These computed results are presented in terms of stream functions, isotherms, Nusselt numbers and average Nusselt numbers through figures.

It is observed that, in case of uniform heating of the side wall, the strength of stream lines’ circulations increases with an increase in Ra and decreases with an increase in Ha. Similarly, by increasing heat-absorption coefficient q, an increase in the circulation strength is noted and the circulation cell moves towards the left wall in the presence of a heat sink (q < 0) and moves to the cold right wall in the presence of a heat source (q > 0). In the case of nonuniformly heated left wall in the presence of a heat source (q > 0), a higher-temperature gradient is observed in the cavity and isotherms are clustered to the left wall in the lower portion and to right wall in the upper portion; these appear to be straight and parallel to the x-axis near the bottom wall. On the other hand, the heat transfer rate along all the walls of the cavity is observed to be higher for smaller values of q. Whereas, Nusselt number along the bottom wall (Nu-B) increases with an increase in the values of x, while, that along the left wall (Nu-L) first increases and then decreases. But Nusselt number along the right wall (Nu-R) is found to be qualitatively opposite to Nu-L with an increase in distance x. Whereas, average Nusselt number increases with an increase in Rayleigh number Ra and heat-generation/-absorption coefficient q.

The problem is formulated for an incompressible flow; viscous dissipation has been neglected, negligible induced magnetic field has been considered and local thermal equilibrium has been considered.

Results presented in this paper are original and new for the effects of a uniform magnetic field on the natural convection of Cu–water nanofluid in a triangular cavity. Hence, this study is important for researchers working in the area of heat transfer in cavity flows involving the nanofluid to become familiar with the flow behavior and properties.

The purpose of this study is to describe the unsteady three-dimensional magnetohydrodynamic stagnation point flow of nanofluids with heat generation/absorption.

The comprehensive numerical simulations in this study accommodate a physical insight into the heat transfer and flow problem. The use of finite difference method through the bvp4c function in Matlab provides the numerical results and graphical illustrations for the heat transfer rate and shear stress.

Dual solutions are discovered in this study. Thus, stability analysis is implemented and the first solution complies the stability behavior. Silver nanoparticles dominate the highest thermal conductivity. Accretion of the rate of heat transfer is obtained with an increment in the magnitude of heat absorption, suction parameter and nanoparticle volume fraction. A stronger magnetic field and larger unsteadiness parameter contribute to the increase of the surface shear stress.

Many practical fluid mechanics problems involve the time-dependent element. Practically, an unsteady flow of nanofluid can be implemented in the micro-manufacturing, periodic heat exchanges process, nano drug delivery system and nuclear reactors.

In spite of numerous studies on the unsteady flow, none of the researchers combined the effect of heat generation/absorption and magnetic field in the nanofluid model. The behavior of the flow and heat transfer have been analyzed thoroughly with the variations in the unsteadiness parameter, heat source/sink and nanoparticle volume fraction. Moreover, the discovery of dual solutions in this model strengthens the novelty of this study. Subsequently, the implementation of stability analysis leads to a remarkable revelation where the first solution is found to be stable.

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 problem of unsteady laminar fully‐developed flow and heat transfer of an electrically‐conducting and heat‐generating or absorbing fluid with variable properties through porous channels in the presence of uniform magnetic and electric fields is formulated. The general governing equations which include such effects as magnetic field, electric field, porous medium inertia and heat generation or absorption effects are non‐dimensionalized and solved numerically by the implicit finite‐difference methodology. A representative set of numerical results for the transient and steady‐state velocity and temperature profiles, the skin‐friction coefficients at both the upper and lower walls of the channel as well as the heat transfer coefficient at the lower wall are presented graphically and discussed. Favorable comparisons with previously published work are performed and the results are in excellent agreement. A comprehensive parametric study is performed to show the effects of the Hartmann number, electric field parameter, inverse Darcy number, inertia parameter, heat generation or absorption coefficient, exponents of variable properties and the Eckert number on the solutions.