This work analyses the steady natural convection flow of viscous, incompressible, electrically conducting fluid in a vertical parallel plate micro-channels with combined effects of transverse magnetic field and suction/injection in the presence of velocity slip and temperature jump at the micro-channel surfaces. The fully developed solutions of the velocity, temperature, volume flow rate, skin-friction and rate of heat transfer which is expressed as a Nusselt number are derived analytically. The solution obtained for the velocity has been used to compute the skin friction, while the temperature has been used to compute the Nusselt number. The effect of the various flow parameters such as suction/injection parameter, Hartmann number, rarefaction parameter, and fluid-wall interaction parameter are discussed with the aid of line graphs. During the course of numerical computations, results show that as suction/injection, rarefaction and fluid-wall interaction increase, the volume flow rate increases while it decreases with increase in Hartmann number. The implication of this on the flow is that the gas velocity near the wall will decrease.
Microflow has been given great importance in recent research activities due to its new application in microfluidic system devices, such as biomedical sample injection, biochemical cell reaction, microelectric ship cooling, etc. A fundamental understanding of the flow and thermal fields as well as the corresponding characteristics at microscale, which may deviate from those at macroscale, is required for the technological demands. Gaseous flow in microscale devices have been in the vanguard of research activities and have received great deal of attentions in recent years, due to the rapid growth of application in micrototal analysis systems and micro electromechanical systems (MEMS). These applications have raised the interest in understanding the physical aspects of fluid flow and convective heat transfer in both forced and natural forms through micron sized channels, known as micro-channels. A magnetohydrodynamic (MHD) flow, which is the simplest plasma model, has been the subject of a great number of empirical and theoretical investigations in many industrial fields. MHD flows associating with heat transfer have received considerable attention due to the fact that their applications reside in many industrial fields such as electric propulsion for space exploration, crystal growth in liquids, cooling of nuclear reactors, electronic packages, microelectronic devices, etc.
The most common type of body force, which acts on fluid, is attributed to gravity so that the body force vector can be deduced from the gravitational acceleration. On the other hand, when an electrically conducting fluid is subjected to a magnetic field, the fluid motion induces an electric current such that the fluid velocity is reduced on account of interaction between the electric current and the fluid motion. Therefore, in case of free convection of an electrically conducting fluid in the presence of a magnetic field, there should be two body forces, i.e., a buoyancy force and a Lorentz force. They interact with each other, and in turn influence the transport phenomena of heat and mass. Among various studies of MHD free flows, few studies have been accomplished for the confined enclosures. Seki et al. (1979) studied the laminar natural convection of mercury subjected to a magnetic field parallel to gravity in a rectangular enclosure. Numerical results were obtained and compared to their experiment in the consideration of a partially heated vertical wall by uniform heat generator. Rudraiah et al. (1995) performed a numerical simulation about natural convection in a two-dimensional cavity filled with an electrically conducting fluid in the presence of a magnetic field aligned to gravity. They selected the Grashof and Hartmann numbers as controlling parameters to examine the effect of a magnetic field on free convection and associated heat transfer. Some research works were carried out on natural convection in a vertical micro-channel. Example of which are Yu and Ameel (2001), Cheng and Weng (2005) and Jha et al. (2013). Details are given in literature review.
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