kinematic viscosity The kinematic viscosity (also called "momentum diffusivity") is the ratio of the dynamic viscosity μ to the density of the fluid ρ. It is usually denoted by the (ν) and has unit m^2/s ν=μ/ρ Dynamic viscosityviscosity is a measure of internal resistance. Dynamic viscosity is the tangential force per unit area required to move one horizontal plane with respect to another plane at an unit velocity - when maintaining an unit distance apart in the fluidτ=μ ∂u/∂yFrom above μ=τ ∂y/∂uμ=kg/m^2 sτ=N/m^2 rate of shear stress∂y/∂u=(m/m)/s change in direction y to change in velocity Peclet number Pe= advective transport rate / diffusive transport rateMass transfer pe=Lu/D=Re*scHeat transfer pe=Lu/∝=Re*PrPe= Peclet number is non-dimensional number L= length (m)u= velocity (m/s)D= diffusion co-efficient (m^2/s)∝= Thermal diffusivity (m^2/s)Nusselt numberNu= convective heat transfer / conductive heat transfer Nu=hl/kNu= Nusselt number is non-dimensional number L= length (m)K= Thermal conductivity, (w/mk)H= heat transfer co-efficient (w/(m^2 k))Momentum FluxMomentum flux is the transport of momentum that acts in a direction perpendicular to the direction of fluid flow. It is considered as the rate of change of horizontal momentum which is moving across a unit area, equal to force per unit area. It is also equivalent to a stress in that it is a force per unit area where the force is acting in a direction within the plane of the area. Momentum Flux = rate of change of flux (N) / area (m*m) = (N/m^2)Fourier's law of heat conductionThe law of heat conduction, also known as Fourier’s law, states that the time rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows q∝A*dt/dxAt x- directionq=-kA dT/dxq is the local heat flux density, Wk is the material's conductivity, W/m·K∆T is the temperature gradient, k/m A is Area m^2Negative sign indicates heat transfer while increase in direction Q= w/m.k * m^2*k/mSo Q= wFick's law of diffusionRate of mass diffusion m ̇ of a chemical species A in stationary medium in direction x is proportional to concentration gradient in that direction dc/dx Mass flux = constant of proportionality * concentration gradient m ̇∝A*dc/dxm ̇=-DA dC/dxWall shear stressWall shear stress is the shear stress in the layer of fluid next to the wall of a pipeτ=μ ∂u/∂yWhere y=0τ=N/(m^2) μ=kg/m^2 s∂u/∂y=(m/s)/m Gradient of Temperature fieldA temperature gradient is a physical quantity that describes in which direction and at what rate the temperature changes the most rapidly around a particular location. The temperature gradient is a dimensional quantity expressed in units of degrees per unit length. (K/m) Consider on 3D mathematically express asT=T(x,y,z) where x, y and z are the coordinates of the location of interest, then the temperature gradient is the vector quantity defined as ∇T=(∂T/∂x,∂T/∂y,∂T/∂z) Unit is (K/m)Divergence of velocity fielddivergent is scalar propertydivergent are given mathematicallydiv v ⃗=∇v ⃗= (█(∂v1/∂x@∂v2/∂y@.@.))div v ⃗= m/s