**1.2 Magnetohydrodynamics (MHD)**

MHD is the science concerned with the motions of electro fluids and their interactions with magnetic fields. It is a vital branch and comparatively new in the field of fluid dynamics. When a conducting fluid is moving along a magnetic field, it results in induction of an electric field current which in turn produces the body forces. According to Faraday's principle, on passage of electric current in a magnetic area, it experiences a force making to direct it at right angles to the electric field. Similarly, if the conductor has electromagnetic forces of the same order as the hydrodynamical and inertial forces, these forces are taken in the equation of motion along with the other forces. The integration of Navier–Stokes relations of fluid dynamics and Maxwell's expressions of electromagnetism describe magneto hydrodynamics which are to be solved simultaneously. There are many scientific & technical applications in the literature: heating and flow control in metal structures, power production from 2-phase models or seeded high temperature gases, magnetic constraints of extreme temperature plasma and dynamo that develop magnetic field in environmental matters.

The concept of MHD flow of the boundary layer in a vertical channel is greatly considered in present metallurgical and metal processing fields. Most of the metallic materials are manufactured from the molten state. It is significant to determine the heat transfer in metals, which are electric conductors. Therefore, a controlled cooling system is required, so that, it can be regulated through an external magnetic field.

### **1.3 Convective heat and mass transference**

Convection is the movement of molecules within the fluids. It belongs to the fundamental means of heat and mass transference that is carried out by ways of diffusion and random Brownian movement of distinct liquid elements. In our context, convection refers to the totality of advective and diffusive transfer. However, it is taken for only advective phenomena. A mechanism of transfer of heat occurring due to bulk motion of fluids is regarded as convective heat transfer. Emphasis is given to heat that is being passed and distributed.

Extensive research has been done over convective heat and mass transference of the fluid flow in vertical channels and other geometries. The existence of temperature and concentration differences or gradients lead to the convective heat and mass transfer and it is regarded as an area of study for broad examination because it is applied in several engineering issues, which are common in atmospheric buoyancy induced actions, liquid and semi-solid bodies and so on. There are quite a large number of application in the heat and mass transfer flows like, rocket nozzles, nuclear power plants, air craft and its re-entry in atmosphere, chemical and process instruments, mist formation and dispersal, temperature and humidity circulation over cultivation farms, plants destruction because of freezing, etc. Packham [11] considered the steady co-current motion of two immiscible viscous fluids in a parallel tube, the fluid interface being ripple-free

*Convective Heat and Mass Transfer of Two Fluids in a Vertical Channel DOI: http://dx.doi.org/10.5772/intechopen.94529*

and plane. Shail [12] considered the Hartmann flow of a conducting fluid in the pass way between two parallel insulating sheets of unbounded length, there exists a sheet of non-conductive fluid between the conductive fluid and the upper passage layer and given the conclusion that considerable increase could be attained in the conductive fluid velocity for appropriate proportions of the depth and viscosity of the two fluids. Beckermann et al. [13] conducted a numerical and experimental study to analyze the fluid motion and heat transfer in a upright rectangular cover which is occupied partly with a vertical layer of a fluid-saturated absorbent structure, where it is determined that the fluid quantity entering the fluid area to the absorbent layer is dependent on the Darcy & Rayleigh numbers. Lohrasbi and Sahai [14] researched in 2-phase MHD flow and heat transfer with the 1-phase conductive fluid.

### **1.4 Viscous dissipation**

Viscous dissipation relates to the conversion of kinetic to internal energy (heating up the fluid) with respect to viscosity. It plays a significant part in normal convection in numerous units which hold huge deviations of gravitational force Gebhart [15]. Gebhart and Mollendorf [16] examined viscous dissipation in peripheral normal convection by taking in account of exponential deviation of wall temperature using resemblance relation. Fand and Brucker [17] stated that the impact of viscous dissipation is important in case of normal/natural convection in absorbent structure with respect to their investigational correlation for the heat transference in peripheral motions. Fand et al. [18] validated the comment for the Darcy method by experimental and analytical means when predicting the heat transfer coefficient from a parallel chamber implanted in an absorbent medium. Viscous dissipation performs as a heat source and heats the medium considerably. Nakayama and Pop [19] evaluated the influence of viscous dissipation on the Darcy's free convection towards an arbitrary shaped non-isothermal matter placed in a permeable medium. Murthy and Singh [20] observed viscous dissipation on non-Darcy normal convection from an erect flat sheet in a permeable medium saturated with Newtonian fluid. It is deduced that heat transfer decreases significantly with the presence of viscous dissipation effect. El-Amin [21] analyzed the impact of viscous dissipation and Joule heating on magneto fluid dynamics forced convection jointly on a non-isothermal straight container fixed in a fluid saturated permeable membrane. Bejan [22] defined that the calculations are limitedin examining the dissipation effect by means of a stable, 1-D energy relation, based on the analogical form with viscous dissipation effect. Pantokratoras [23] evaluated the viscous dissipation effects in a normal convection using a warmed straight plate. Seddeek [24] investigated viscous dissipation effect and thermophoresis on Darcy Forchheimer mixed convection in a fluid saturated permeable medium. Duwairi et al. [25] studied the effects of viscous dissipation and Joule heating employing an isothermal cone in a saturated porous medium. Various non-Newtonian fluids have high viscosity because the irreparable criterion owing to viscous dissipation sometimes becomes vital. Hence it motivates investigators to analyze the effects of viscous dissipation in a non-Newtonian fluid saturated permeable medium. Cortell [26] analyzed viscous dissipation effect and thermal boundary layer radiation on a nonlinear wide plate. Kairi and Murthy [27] analyzed the viscous dissipation impact over normal convection heat and mass transference from an upright cone in a non-Newtonian fluid saturated non-Darcy absorbent structure. Cortell [28] analyzed the influences of suction, viscous dissipation and thermal radiation over heat transfer of a power-law fluid past a boundless permeable sheet.
