# Relationship Between Fluid And Newtonian Fluid

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Energy equation

Equation of energy for an electrically conducting, viscous incompressible fluid is ρC_P [∂T/∂t+(q ̅.∇)T]=K∇^2 T+μ(1+1/γ) (1.3) where =2[(∂u/∂x)^2+(∂v/∂y)^2+(∂w/∂z)^2 ]+(∂v/∂x+∂u/∂y)^2+(∂w/∂y+∂v/∂z)^2+(∂u/∂z+∂w/∂x)^2 is the dissipation function which represents the time rate at which energy is being dissipated per unit volume through the action of viscosity. Here, u,v and w are the velocity components of the fluid along thex,y and z directions respectively.C_P is the specific heat at constant pressure, T is the temperature, K is the thermal conductivity and γ is the Casson fluid parameter.

Species Concentration equation

The species concentration equation is given by

∂C/∂t+(q ̅.∇)C=D∇^2 C (1.4)

Here, C is the concentration of the species, D is the molecular diffusivity.

Maxwell’s

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Let n ̂ denote the unit normal drawn to the interface of two media 1 and 2 and [ ] denote the jump in the enclosed quantity in crossing interface from 1 to 2. The boundary conditions on the velocity vector for inviscid fluid flow are simple because here, the normal component of the velocity alone need to be continuous where as for viscous fluid flow both the normal and tangential components of the velocity must be continuous and hence the boundary conditions are given by n ̂ .[q ̅ ]=0 (1.13) n ̂×[q ̅ ]=0 (1.14) If J ̅,ρ_e denote surface current and surface charge density respectively, then the magnetic boundary conditions are n ̂ .[B ̅ ]=0 (1.15) n ̂×[H ̅ ]=J ̅ (1.16) n ̂ .[D ̅ ]=ρ_e (1.17) n ̂×[E ̅ ]=0 (1.18) Physically the above conditions mean that the normal component of the magnetic induction is continuous at the interface, the tangential component is discontinuous on account of sheer current if one or both the medium become infinitely conducting, the normal component of the electric field is discontinuous on account of surface charge density and the tangential component of the electric field is continuous always across the