Thermal analysis of an Eyring-Powell fluid flow through a constricted channel

Sufian Munawar, Najma Saleem
2018 Thermal Science  
This paper is aimed to investigate the entropy generation in a magnetohydrodynamic convective flow of Eyring-Powell fluid through a mildly constricted channel. The constriction is assumed to be of regular or irregular shape and is presented inside the channel wall. Mathematical model is developed using the basic laws of conservation of mass, momentum and energy. The governing equations are normalized using appropriate set of dimensionless variables and solutions are obtained by regular
more » ... by regular perturbation technique. The solutions are further used to calculate the entropy expression associated with the second-law of thermodynamics. The heat transfer characteristics, like, temperature, isotherms, entropy generation number entropy lines and the Bejan number are analyzed for the variation in magnetic field, shape parameter and material constants. It is observed that entropy production is maximum in the narrow part of the channel. Moreover, entropy generation rate is higher for the regular parabolic shape as compared to irregular shapes of constriction. Powell fluid passage of time and make the arteries stiffer and narrower and leads to serious problems such as angina, blood pressure, heart attack, stroke or even death. These plaques may have different shapes and sizes. Some mathematical models of blood flow through stenosis have been developed in the noteworthy articles [1] [2] [3] [4] [5] . Due to the presence of electromagnetic fields in blood flow most of investigators assumed magnetohydrodynamic in blood flow problems. In this regards, Sud et al. [6] showed that under the appropriate strength of moving magnetic field the flow velocity accelerates. Mekheimer and El Kot [7] examined the effects of magnetic field and Hall current on the physiological flow of micropolar through stenotic artery and concluded that large values of the Hartmann number have increasing effects on impedance and decreasing effects on blood flow velocity. Kumar et al. [8] proposed a study dealing with the oscillatory MHD blood flow through an artery carrying mild stenosis and critically studied the effects of magnetic force on different shapes of stenosis. The study of entropy is extremely useful in biological thermodynamics to understand the flow characteristics at flow transitions such as constricted regions. The break downing of foodstuff in to constituents, and then developing cells, tissues and muscles increase the order in the body and thus reduce entropy. However, the human body convects heat to the environment due to the change in the temperature of the body and the environment. It consumes energy-comprising substances in the form of food and emits heat into space by excreting waste in the form of carbon dioxide, water, urine, and feces. Consequently, the overall entropy of the human body rises. This increase in the entropy of body affects the physiological fluids inside human body such as blood flow, transport of semen, passage of urine from kidney to bladder through ureter, swallowing food through esophagus, transport of lymph in lymphatic vessels, etc. Thermodynamically, in a closed system, entropy is produced by various factors. Bejan [9] identified different factors that cause entropy production in four different convective heat transfer configurations. The two major sources of entropy in a convective heat transfer phenomenon, the heat transfer rate and fluid friction, were discovered by Bejan [10]. Readers are referred to a worth reading book by Bejan [11] on the subject for deep understanding of the subject. Afterwards, numerous investigators [12-19] further explored the phenomenon of heat transfer and entropy generation in convective heat flow problems under various physical assumptions. Souidi et al. [20] conducted an entropy analysis for a peristaltic pump in a contracting tube. Recently, Munawar et al. [21] investigated production of entropy associated with second-law in a biological flow of variable viscosity fluid. Most of the biological fluids are non-Newtonian fluids in nature. In this regard, Eyring-Powell (EP) fluid [22] gained the importance among scientists because of its accuracy and consistency in calculating the fluid time scale at different polymer concentration. This was used by Yoon and Ghajar [23] to estimate the fluid time scale by experimental shear viscosity measurement. A few recent investigations dealing with EP fluid flow are mentioned here for the interested readers [24] [25] [26] [27] . The flow analysis of EP fluid in a constricted artery has recently been investigated by Saleem and Munawar [28] . Yet there is a room to study the thermodynamical aspects of EP fluid in constricted channel flow. In this study we intended to accomplish this task by investigating the heat transfer and second-law analyses of Eyring-Powell fluid flow through a constriction of regular/irregular shapes in the presence constant magnetic field. The governing equations of the current convective heat transfer problem are modeled and simplified
doi:10.2298/tsci180125308m fatcat:ccqgxo6rbnhixkvw6qm6rofzye