A dimensionless number defined as the ratio of the momentum diffusivity to the species diffusivity, and used to characterize fluid flows marked by simultaneous momentum and species diffusion, along with convection.

The ratio of the internal forces to the external forces will depend upon its speed, and the viscosity of the fluid, and the size of the body. But the ratio of the internal to the viscous forces is dimensionless, so it must depend on some combination of the viscosity, speed V and linear size l that is dimensionless.

The Prandtl number is an example of a dimensionless number that is an intrinsic property of a fluid. Fluids with small Prandtl numbers are free-flowing liquids with high thermal conductivity and are therefore a good choice for heat conducting liquids.

The Reynolds ( Re ) number is a quantity(unit-less) which engineers use to estimate if a fluid flow is laminar or turbulent. This is important, because increased mixing and shearing occur in turbulent flow. This results increase viscous losses which affects the efficiency of hydraulic machines.

The Reynolds number (Re) helps predict flow patterns in different fluid flow situations. These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation. Reynolds numbers are an important dimensionless quantity in fluid mechanics.

The purpose of the Reynolds number is to get some sense of the relationship in fluid flow between inertial forces (that is those that keep going by Newton’s first law – an object in motion remains in motion) and viscous forces, that is those that cause the fluid to come to a stop because of the viscosity of the fluid.

Reynolds number (Rn) is defined as Rn=(ρVL)/μ=(VL)/ν, where V is the fluid velocity relative to the body and L is a typical length.

Flow with Reynolds number less than 2000 is considered as laminar flow whereas flow with Reynolds number greater than 4000 is considered as turbulent flow.

Therefore, in the present work, a chord-based Reynolds number range between 104 and 105 is defined as the low-Reynolds-number range. Note that this range is two orders of magnitude lower than that of large-scale conventional aircraft, which typically operate at a Reynolds number of over 106.

In physics, a characteristic length is an important dimension that defines the scale of a physical system. In computational mechanics, a characteristic length is defined to force localization of a stress softening constitutive equation. The length is associated with an integration point.

The Reynolds number (Re) of a flowing fluid is calculated by multiplying the fluid velocity by the internal pipe diameter (to obtain the inertia force of the fluid) and then dividing the result by the kinematic viscosity (viscous force per unit length).

The characteristic length is L = 0.18 m.

The Grashof number is a way to quantify the opposing forces. ν is the kinematic viscosity. For gases β = 1/T where the temperature is in K. For liquids β can be calculated if variation of density with temperature at constant pressure is known.