Convective--Diffusive Transport with Chemical Reaction in Natural Convection Flows

The problem of steady, laminar, double-diffusive natural convection boundary-layer flow of a micropolar fluid over a vertical permeable semi-infinite plate embedded in a uniform porous medium in the presence of non-Darcian and thermal dispersion effects is investigated. Also, the model problem allows for possible heat generation or absorption and first-order chemical reaction effects. Both the wall temperature and wall concentration are assumed to have linear variations with the distance along the plate. Appropriate transformations are employed to transform the governing differential equations into a non-similar form that can be solved as an initial-value problem. The resulting equations are solved numerically by an efficient implicit, iterative, finite-difference scheme. The obtained results are checked against previously published work on special cases of the problem and are found to be in good agreement. A parametric study illustrating the influence of the microrotation material parameter, concentration to thermal buoyancy ratio, chemical reaction parameter, Schmidt number, heat generation or absorption and the surface suction or injection effects on the fluid velocity, microrotation, temperature and solute concentration as well as the local skin-friction coefficient, local wall microrotation coefficient and the local wall heat and mass transfer coefficients is conducted. The results of this parametric study are shown graphically and the physical aspects of the problem are highlighted and discussed. Greek Symbolseffective thermal diffusivity of the porous medium; α d thermal diffusivity of the porous medium due to thermal dispersion;Introduction Double-diffusive convection is referred to buoyancy-induced flow due to the combined effects of both temperature and concentration gradients. Double-diffusive convection from different geometries embedded in porous media has a wide range of engineering and geophysical applications such as geothermal reservoirs, drying of porous solids, thermal insulation, enhanced oil recovery, packed-bed catalytic reactors, cooling of nuclear reactors, and underground energy transport. Most early studies on porous media have used the Darcy law which is a linear empirical relation between the Darcian velocity and the pressure drop across the porous medium and is limited to relatively slow flows. However, for relatively higher velocity flow situations, the Darcy law becomes inadequate for representing the flow behavior correctly since it does not account for the resulting inertia effects of the porous medium. In this situation, the pressure drop has a quadratic relationship with the volumetric flow rate. The high flow situation is established when the Reynolds number based on the pore size is greater than unity. Vafai and Tien (1981) [1] discussed the importance of inertia effects for high velocity flows in porous media. Double-diffusive convection flow of a Newtonian fluid along a vertical surface embedded in a uniform porous medium was considered by Bejan (1984) [2] based on scale ...

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“…The last term in Eq. (5) is employed according to Rahman and Mulolani (2000) [30] for a first-order chemical reaction.…”

Section: Problem Formulationmentioning

confidence: 99%

Double-Diffusive Convective Flow of a Micropolar Fluid Over a Vertical Plate Embedded in a Porous Medium with a Chemical Reaction

Chamkha

Al-Mudhaf

Al-Yatama

2004

Inter J Fluid Mech Res

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“…Researchers also used the finite difference method and found the solution of some special problem, composed of mixed convection flow over a vertical cylinders, such as Lee et al, 8 Merkin and Mahmood et al, 9,10 Wang and Kleinstreuer, 11 Kumari and Nath, 12 Ali and Al-Yousef, 13 Rahman and Mulolani. 14 Note that the mixed convection flow problems have been solved for other geometries and such flow along a horizontal circular cylinder placed in porous medium with constant wall temperature was studied by Nazar et al 15 The mixed convection flow of nano-fluid within momentum and thermal boundary layers was examined by Nazar et al, 16 Patial et al, 17,18 Prakash et al, 19 Swati, 20 and Wang. 21 Most recently, the forced convection flows along a vertical and heated cylinder has been studied by Pandey and Kumar, 22 Khan and Malik, 23 Hayat et al, 24 Sinha et al, 25 and Khan et al 26 In this paper, a generalize model problem of forced convection flow is simulated over a variably porous and heated cylinder of non-uniform radius.…”

Section: Introductionmentioning

confidence: 99%

Forced convection flow over a moving porous and non-uniform cylinder of variable thickness

Jan

Marwat

Rehman

2022

Advances in Mechanical Engineering

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Forced convection flow of viscous fluid over a moving, porous, and heated cylinder of variable thickness is studied in this paper. The non-uniform cylinder is placed vertically in a quiescent fluid. All the field quantities (the normal and axial velocities and temperature), defined at the wall or surface of cylinder, are variable and may have non-linear form. An appropriate set of transformations is developed on the analogies of systematic classical symmetries for a system of partial differential equations (PDE’s), whereas, they are equipped with the representative of each velocity component, temperature function, and similarity variable. However, the PDE’s along with the boundary conditions (BC’s) are reduced into a system of boundary value problem (BVP) of ordinary differential equations (ODE’s) by using these new and unseen similarity variables. The system of non-linear coupled ODE’s, combined with the BC’s is solved, whereas, the numerical results are obtained for different values of the existing governing parameters. All the field quantities, skin friction, rate of heat transfer at the surface of the cylinder are evaluated with the help of [Formula: see text] package of MATLAB and the results are shown in different graphs. The present simulation generalizes all types of forced convection flow problems, over a porous and heated cylinder of variable (uniform) radius, when it is stretched (shrunk) with linear and non-linear (uniform) velocity. However, the simulated problem gives rise to a new set of problems and that they are valid for non-linear (linear and uniform) injection (suction) velocity.

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“…There are many industrial and environmental applications for the buoyancyinduced flows from heated horizontal cylinders confined in an enclosure, such as space heating, heat exchangers, solar energy collectors, nuclear and chemical reactors, energy storage systems, electronic equipment, and so on [1][2][3][4][5]. A literature survey shows that numerous experimental and numerical studies have been conducted on natural convection in enclosures with the presence of a body with various thermal conditions.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Unsteady Natural Convection from Heated Horizontal Circular Cylinders in a Square Enclosure

Karimi¹,

Xu²,

Wang³

et al. 2014

Numerical Heat Transfer, Part A: Applications

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In this article, a 2-D numerical study is carried out to investigate the effect of this interaction on natural convection from two heated horizontal cylinders confined in a square enclosure with isothermal walls at the heat sink temperature. The simulations are carried out for Rayleigh numbers between 10 3 and 10 7 , and dimensionless horizontal distances of cylinders between 0.1 and 0.4. The results show that the variation of the area-averaged Nusselt number strongly depends on the distance between the two cylinders if Rayleigh numbers are less than 10 4 . In contrary, the effect of cylinder spacing on heat transfer was found to be nearly negligible when the Rayleigh number is between 10 4 and 10 7 . It is also observed that steady state flow and heat transfer undergo periodical oscillation, and ultimately chaotic oscillation in special positions of cylinders can occur.

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Convective--Diffusive Transport with Chemical Reaction in Natural Convection Flows

Cited by 23 publications

References 16 publications

Double-Diffusive Convective Flow of a Micropolar Fluid Over a Vertical Plate Embedded in a Porous Medium with a Chemical Reaction

Double-Diffusive Convective Flow of a Micropolar Fluid Over a Vertical Plate Embedded in a Porous Medium with a Chemical Reaction

Forced convection flow over a moving porous and non-uniform cylinder of variable thickness

Numerical Simulation of Unsteady Natural Convection from Heated Horizontal Circular Cylinders in a Square Enclosure

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