**1.5 Diffusion effects**

The diffusion effects namely thermal-diffusion (Soret) and diffusion-thermo (Dufour) are highly important in fluid mechanics. Soret is the transfer of mass formed by temperature gradients, i.e. species diversity evolving in a primary homogeneous blend directed to a thermal gradient. Diffusion-thermo effect is the heat transfer or the heat flux formed by concentration gradient. The problems concerned to heat and mass transference and density variations with temperature and concentration lead to integrated buoyancy convected force. The diffusion impacts influence the flow field in boundary membrane on an upright channel.

Chapman and Cowling [29] developed the diffusion-thermo and thermaldiffused heat and mass effects. Eckert and Drake [30] suggested that Dufour effect has widened magnitude and so this effect should not be ignored. Kafoussias and Williams [31] included the boundary layer flows with Soret and Dufour effects for the combined forced-normal convection problem. Anghel et al. [32] analyzed the Dufour and Soret effects of a free convection boundary layer on a vertical field inserted in a permeable membrane. Postelnicu [33] evaluated the effects of thermaldiffusion and diffusion-thermo on combined heat and mass transference in natural convection boundary layer flow in a Darcian porous media under transverse magnetic effect. Alam and Rahman [34] analyzed the effects of thermal-diffusion and diffusion-thermo on combined and free convection heat and mass transference flow past an erect permeable flat sheet inserted in a porous membrane with or without flexible suction. In many studies, Dufour and Soret effects are ignored based on a minor magnitude order than Fourier's and Fick's laws effect. The effect of thermaldiffusion and diffusion-thermo influences over the motion area in mixed convection boundary-layer on an upright surface kept in a permeable medium and on mixed convection flow past a vertical permeable even sheet with varying suction. Chamkha and Ben-Nakhi [35] studied the combined convection flow in the existence of thermal radiation with an erect porous layer embedded in an absorbent media considering thermal-diffusion and diffusion-thermo effects. El-Aziz [36] examined the Dufour and Soret effects on MHD heat and mass transference on a porous widening layer in the presence of thermal radiation in a combined manner. Maleque [37] considered only the diffusion-thermo effect on convective heat and mass transference past a rotating permeable disk, in where the thermal-diffusion effect is ignored. Anwar Beg et al. [38] described the thermal-diffusion and diffusion-thermo impacts by numerically studying the free convection MHD heat and mass transfer over a stretching layer with saturated permeable structure. Pal and Chatterjee [39] study shows combined convected magneto hydrodynamic heat and mass transference past a stretching plate considering Ohmic dissipated thermal-diffusion and diffusion-thermo impacts with micro-polar fluid. MHD flow of a pair of immiscible and conducting fluids within isothermal and insulated moving sheets under an applied electric and inclined magnetic effect and with an induced magnetic field has been investigated by Stamenkovic et al. [40].

#### **1.6 Two fluid flow**

For many years, Scientists and Engineers have been showing interest in two phase flows, which arise in many industrial applications. The two-phase fluid flow phenomena are important in pipe flows, fluidized beds, sedimentation, gas purification, transport processes and shock waves. The study of dynamics of two phase fluid system is concerned with the motion of a liquid or gas containing immiscible, suspended stokesian solid particles. In the equations of motion of two phase fluid

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

flows, which are the modified form of Navier-Stoke's equations, the presence of dust adds an extra force term which represents the interaction between the dust and the fluid particles. The modified form of Navier–Stokes equations coupled with Euler equations of motion for perfect fluids are used as the equations of motion of fluid phase and particle phase, respectively. Practical application of these flows may be found in heat exchanges utilizing liquid metal or liquid sodium coolants in the area of thermal instability in boiling heat transfer studies. Malashetty and Leela [41, 42] studied two-fluid flow and heat transference in a parallel fluid passage in both conductive phases. Such investigations are beneficial to understand the slag layer effects over heat transfer features of a coal-fired magneto hydrodynamic generator. Vajravelu et al. [43] dealt with the hydromagnetic unstable motion of two immiscible conducting fluids between two porous media of different porosity. Malashetty and Umavathi [44] studied 2-phase magnetohydrodynamic flow and heat transference in a sloped passage, where 1-phase is conductive and the transport characteristics of the fluids are assumed to be unvarying. Srinivasan et al. [45] theoretically studied the two immiscible fluid models in a permeable membrane by considering the impacts of non-Darcian boundary and inertia. Malashetty et al. [46] explored the complexities of completely established 2-fluid magneto hydrodynamic flow including and excluding applied electric field in an slant pass way and described the solution of energy and momentum equations, using perturbation method for smaller value product of Prandtl and Eckert number in completely progressed free convection 2-fluid MHD flow of a tilted passage.
