Conjugated effect of joule heating and magneto-hydrodynamic on double-diffusive mixed convection in a horizontal channel with an open cavity

https://doi.org/10.1016/j.ijheatmasstransfer.2011.04.010Get rights and content

Abstract

A finite element analysis is performed on the conjugated effect of joule heating and magneto-hydrodynamic on double-diffusive mixed convection in a horizontal channel with an open cavity. Homogeneous flows are imposed throughout the channel. Consistent high temperatures and concentrations are imposed at the bottom wall of the cavity. The other sides of the cavity along with the channel walls are considered as adiabatic. The effects of the various parameters (Richardson number, Hartmann number, joule heating, buoyancy ratio and Lewis number) on the contours of streamline, temperature, concentration and density have been depicted. Moreover, the average Nusselt and Sherwood numbers as well as bulk temperature is presented for the aforementioned parameters. The results show that the aforesaid parameters have noticeable effect on the flow pattern and heat and mass transfer.

Introduction

Mixed convection is that type of heat transfer in which there is a noteworthy interaction between free and forced convection. Mixed convective heat transfer in open cavities has long been studied and has received increases attention due to its application of practical interest, such as nuclear reactors, solar receiver, thermal storage and open cavity packaging of semiconductors. Studies associated with mixed convection in open cavities have received increasing consideration. Pavlovic and Penot [1] performed an experimental investigation of the mixed convection heat transfer in an open isothermal cubic cavity. They concluded that the convective heat loss for the central solar receiver. Fusegi [2] carried out a numerical study on convective heat transfer from periodic open cavities in a channel with oscillatory through flow. Khanafer et al. [3] made a numerical investigation on mixed convection heat transfer in open-ended enclosures for three different flow angles. They found that, thermal insulation of cavity can be achieved through the use of high horizontal velocity flow. A numerical analysis of laminar mixed convection in a channel with an open cavity and a heated wall bounded by a horizontally insulated plate was presented by Manca et al. [4], where the authors considered three heating modes: assisting flow, opposing flow and heating from below. Later, a similar problem for the case of assisting forced flow configuration was tested experimentally by Manca et al. [5]. Leong et al. [6] performed a numerical study on the mixed convection from an open cavity in a horizontal channel. Authors found that the heat transfer rate was reduced, and the flow became unstable in the mixed convection regime. Aminossadati and Ghasemib [7] performed a numerical study on the mixed convection in a horizontal channel with a discrete heat source in an open cavity. They considered three different heating modes and found noticeable differences among the indicated three heating modes. Wong and Saeid [8] numerically investigated the opposing mixed convection arises from jet impingement cooling of a heated bottom surface of an open cavity in a horizontal channel filled with porous medium.

Magneto-hydrodynamics (MHD) is that branch of science, which studies the dynamics of electrically conducting fluids in the presence of electromagnetic fields. MHD is usually regarded as a very up to the date subject, because it has many engineering applications such as liquid–metal cooling of nuclear reactors and electromagnetic casting, etc. MHD studies are mostly focused on convection heat transfer in closed cavities. Piazza and Ciofalo [9] carried out a numerical investigation on buoyancy-driven magneto-hydrodynamic flow in a liquid–metal filled in a cubic enclosure. The authors found that increasing Hartmann number suppressed the convective motions. Chamkha [10] made a study for mixed convection in a square cavity in the presence of magnetic field and an internal heat generation and absorption. He concluded that the flow behavior inside the cavity and heat transfer rate is strongly affected by the magnetic field. Sarries et al. [11] performed a numerical study on unsteady natural convection of an electrically conducting fluid in a laterally and volumetrically heated square cavity under the influence of a magnetic field. Xu et al. [12] completed an experimental study on natural convection of a molten metal contained in a rectangular enclosure in the presence of an external magnetic field. Oztop et al. [13] studied the effects of sinusoidal temperature boundary conditions on magneto-hydrodynamic buoyancy-induced flow in a non-isothermally heated square enclosure. Rahman et al. [14] made a numerical investigation on the conjugate effect of joule heating and magneto-hydrodynamics mixed convection in an obstructed lid-driven square enclosure. Recently, Rahman et al. [15] numerically studied magneto-hydrodynamic mixed convection in a horizontal channel with an open cavity. They used Galerkin weighted residual method for the numerical simulation and showed a significant effect of the considered parameters on the flow and thermal fields inside the cavity. Bhuvaneswari et al. [16] carried out a computational study of convective flow and heat transfer in a cavity in the presence of uniform magnetic field. Ogot [17] made an analysis of heat and fluid flow transport due to natural convection and magneto-hydrodynamic flows in a square enclosure with a finite length heater using differential quadrature technique. Sposito and Ciofalo [18] studied fully developed mixed magneto-hydrodynamic convection in a vertical square duct.

The double-diffusive mixed convection in a channel with an open enclosure has also found wide applications in engineering, such as cooling of electronic components, finned heat exchangers, cavity of solar central receivers, chemical processing, thermal and pollution control, evaporative cooling and fire control in buildings. There are several studies related to mixed convection for combined heat, and mass transfer. Deng et al. [19] made a numerical study for a laminar double diffusive mixed convection in a two-dimensional ventilated enclosure with discrete heat and contaminant sources. They investigated the characteristics of the airflow and heat/contaminant transport structures in the indoor air environment by means of a convection transport visualization technique. Costa [20] carried out a numerical study for double-diffusive natural convection in parallelogrammic enclosures filled with moist air. Chamkha and Naser [21] studied the problem of unsteady, laminar double-diffusive convective flow of a binary gas mixture in an inclined rectangular enclosure filled with a uniform porous medium. A numerical simulation of double diffusive natural convection in rectangular enclosure in the presence of magnetic field and heat source was performed by Teamah [22]. Teamah and El-Maghlany [23] numerically simulated double-diffusive mixed convective flow in a rectangular enclosure with insulated moving lid. Brown and Lai [24] numerically investigated a horizontal channel with an open cavity and obtained correlations for combined heat and mass transfer which covered the entire convection regime from natural, mixed to forced convection. Chamkha and Naser [25] made an examination on hydromagnetic double-diffusive convection in a rectangular enclosure with opposing temperature and concentration gradients.

A detailed literature survey reveals that the majority of existing numerical investigations are restricted in cavities with or without a magnetic field in detail. In view of the abovementioned statements, it is also seemed that the conjugate effect of joule heating and magneto-hydrodynamic double-diffusive mixed convection in a horizontal channel with an open cavity has not been addressed yet. In the present study, we undertake this task varying the Hartmann number Ha (10  Ha  100), joule heating parameter J (0.0  J  3.0), buoyancy ratio Br (0.5  Br  5.0) and Lewis number Le (2.0  Le  10.0) for Reynolds number Re = 100, Richardson number Ri = 1.0 and Prandtl number Pr = 0.7. A comprehensive study of the flow field, temperature and concentration distribution with detailed analysis on heat and mass transfer evaluation will be done. The results are shown in terms of parametric presentations on the contours of streamlines, isotherms, concentration and density for the considered pertinent dimensionless parameters.

Section snippets

Physical model and mathematical formulation

Fig. 1 shows the considered two-dimensional model with boundary conditions and coordinates. It is a horizontal channel with an open square cavity of length L. The heat source of high temperature, Th and a contaminant source of high concentration, ch are considered on the bottom surface of the cavity. The rest of the walls of the cavity along with the channel walls are also adiabatic and impermeable. In addition, the incoming fluid through the channel is at a uniform velocity, ui, at the ambient

Solution procedure

The non-dimensional Eqs. (2), (3), (4), (5) are discretized by the finite element method. The equation of continuity is used as a constraint due to mass conservation and this constraint may be used to find the pressure distribution. In order to discretize Eqs. (2), (3), (4), (5), the Penalty finite element method [26], [27], [28] is used where the pressure, P is eliminated by a penalty constraint γ. The incompressibility criteria given by Eq. (1) consequences inP=-γUX+VY.

The continuity

Results and discussion

In this paper, a numerical study has been performed to determine the effects of joule heating on the double-diffusive mixed convection flow of an electrically conducting fluid in a horizontal channel with an open cavity. For the intention of discussing the results, the numerical calculations are presented in the form of streamlines, isotherms, concentration and density contours. With this aim, different parameters such as Reynolds number (Re), Prandtl number (Pr), Richardson number (Ri), Lewis

Conclusion

This work deals with the conjugate effect of joule heating on MHD double-diffusive mixed convection in a horizontal channel along with an open cavity. The finite element method is engaged for numerical simulation. Graphical results of the flow structure, temperature, concentration and fluid density levels for Hartmann number Ha, joule heating parameter J, buoyancy ratio Br and Lewis number Le are presented and discussed. The subsequent conclusions may be drawn from the above mentioned study:

  • The

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