Reynolds's analogy gives the interrelationship between fluid friction and newton’s law of viscosity.
The Reynolds analogy is given by,
Nu/RePr = St = Cf/2
Nu = Local Nusselt number, Re = Local Reynolds number, St = Local Stanton number, Pr = Prandtl number, Cf = Skin friction coefficient
Comparison between turbulent thermal conductivity and turbulent viscosity
Equation of motion
The factors that affect the diffusion of gases
- The difference in concentration affects the rate of diffusion. The greater the concentration gradient, the quicker diffusion takes place.
- The temperature affects the rate of diffusion. As the temperature increases, particles gain more kinetic energy and so can diffuse across a membrane more quickly. Therefore, as the temperature increases, the rate of diffusion increases.
- The surface area of the membrane affects the rate of diffusion. As the surface area of the membrane increases, the rate of diffusion also increases, as there is more space for molecules to diffuse across the membrane.
- Distance. The shorter the distance the substances have to move, the faster the rate of diffusion.
Fick’s law of binary diffusion
J is the diffusion flux, of which the dimension is the amount of substance per unit area per unit time. J measures the amount of substance that will flow through a unit area during a unit time interval.
D is the diffusion coefficient or diffusivity. Its dimension is area per unit of time.
φ (for ideal mixtures) is the concentration, of which the dimension is the amount of substance per unit volume.
x is position, the dimension of which is length.
The Boltzmann equation
Significance of Dimensional Analysis
- Preliminary test for the correctness of the given equation
- Convert from one unit to another
- Derive the relationship between the physical quantities.
- Determine the dimensions of constant or unknown physical quantities
- The number of experiments conducted is reduced
Three levels at which transport phenomena can be studied
- Fluid Mechanics
- Heat Transfer
- Mass Transfer