Heat and mass transfer in magneto-biofluid flow through a non-Darcian porous medium with Joule effect

Abstract

In the present study, a mathematical model for the hydromagnetic non-Newtonian biofl uid fl ow in the non-Darcy porous medium with Joule effect is proposed. A uniform magnetic fi eld acts perpendicularly to the porous surface. The governing nonlinear partial differential equations are transformed into linear ones which are solved numerically by applying the explicit fi nite difference method. The effects of various parameters, like Reynolds number and hydro-magnetic, Forchheimer, and Darcian parameters, Prandtl, Eckert, and Schmidt numbers, on the velocity, temperature, and concentration are presented graphically. The results of the study can fi nd applications in surgical operations, industrial material processing, and various heat transfer processes. Introduction. Mathematical modeling of heat transfer in biofl uid engineering was initiated in the late 1940s in a seminal paper by Pennes (1) who laid the foundations for investigating heat transfer in tissues. Subsequently the fi eld of studies has expanded rapidly to embrace convection fl ows in hemodynamics, as well as radiative heat transfer in thermal ablation biotechnologies. The pulsatile fl uid fl ow with heat transfer fi nds applications in fi elds like mechanical and industrial thermal engineering systems. Extensive studies have been carried out by Lagendijk (2), Chato (3), Beg and Sajid (4), Kolios, Sherar, and Hunt (5), and Chakravarty and Sen (6). Barozzi and Dumas (7), calculating heat transfer in the entrance region, considered the rheological properties of the blood stream and a cell-free peripheral plasma layer at the vessel wall. Baish (8) studied heat transport by countercurrent blood vessels in the presence of an arbitrary pressure gradient. Deng and Liu (9), Craciiunescu and Clegg (10), Consiglieri, Santos, and Haemmerich (11), and Davalos, Rubinsky, and Mir (12) carried out theoretical analysis of the heat convection coeffi cient in large vessels. An analytical study of heat transfer in fi nite tissue with two blood vessels and uniform Dirichlet boundary conditions was performed by Shrivastava, McKay, and Romer (13). All these studies were confi ned to Newtonian blood fl ow models. Although many Newtonian models based on the Navier-Stokes equations were studied, the rheological nature of biofl uids, like blood, plasma, bile, etc., has also been recognized in a great quantity of studies. It is required to develop a non-Newtonian model that can give more accurate results in the fi eld of study of physiological fl uids. Due to the pumping action of the heart in the human circulation system, a pulsatile feature of blood also should be considered. Skalak and Chien (14) presented an investigation of the non-Newtonian fl ow of blood, considering erythrocytes as soft tissues. An excellent summary of a number of rheological models for blood was provided by Cokelet (15). The results of the study of biofl uids in the presence of magnetic fi eld with Joule dissipation fi nd applications in various upcoming fi elds like innovative drug targeting, surgical operations, etc. Various surgical operations require control of the fl uid fl ow and heat transfer of biological fl uids. The presence of electromagnetic fi elds during such operations can have an impact on the human circulation system. The electric nature of a biofl uid, like blood, has already been confi rmed by previous studies. The presence of iron oxides in the hemoglobin molecule has been shown to produce strong magnetic properties of blood (16). Under oxygenated conditions blood exhibits diamagnetic properties, and under deoxygenated conditions it behaves as a paramagnetic fl uid. Several authors studied heat transfer in biomagnetofl uid fl ows, including Tzirtzilakis and Tanoudis (17) who investigated biomagnetic convective heat transfer over a stretching surface, and Louckopoulos and Tzirtzilakis (18) who studied biomagnetic fl ow and heat transfer in a parallel-plate system. The presence of a porous medium during the fl ow presents a more physically realizable situation. This approach can be applied to the blood vessels and pulmonary systems due to the presence of fatty deposits and artery blockages. Khaled