Biot number shows how convection and conduction heat tranfer phenomena are related. This time is important in studies because it indicates if the phenomenon is quick or slow.

The Biot number is the ratio of the internal resistance of a body to heat conduction to its external resistance to heat convection. Therefore, a small Biot number represents small resistance to heat conduction, and thus small temperature gradients within the body.

The Biot number (Bi) is a dimensionless quantity used in heat transfer calculations. This ratio determines whether or not the temperatures inside a body will vary significantly in space, while the body heats or cools over time, from a thermal gradient applied to its surface.

Biot number formula h [W/(m² * K)] is the heat transfer coefficient at the material’s surface, k [W/(m * K)] is the thermal conductivity of the material. Bi is the resulting Biot number.

Radiation

Both are dimensionless parameters. Biot number uses thermal conductivity of the body (not fluid), whereas Nusselt number uses thermal conductivity of the fluid. The differences between Biot and Nusselt number is in definition of heat transfer coefficient, which is defined as: h=-k (dT/dn)w/(Tw-T0).

The Prandtl number is a dimensionless quantity that puts the viscosity of a fluid in correlation with the thermal conductivity. It therefore assesses the relation between momentum transport and thermal transport capacity of a fluid.

Nu can not be less than one since it gives relation between conduction and convection of the liquid.

In fluid dynamics, the Nusselt number (Nu) is the ratio of convective to conductive heat transfer at a boundary in a fluid. A larger Nusselt number corresponds to more active convection, with turbulent flow typically in the 100–1000 range.

The use of dimensionless numbers in engineering and physics allows the important task of data reduction of similar problems. This means that a lot of experimental runs are avoided if data is correlated using appropriate dimensionless parameters.

Rayleigh number. Rayleigh number, Ra, is a dimensionless term used in the calculation of natural convection. where g is acceleration due to gravity, β’ is coefficient of thermal expansion of the fluid, ΔT is temperature difference, x is length, ν is kinematic viscosity and κ is thermal diffusivity of the fluid.

(3.50), the Nusselt number is calculated by multiplying the temperature gradient and the thermal conductivity ratio (conductivity of the nanofluid to the conductivity of the base fluid).

The Grashof Number formula for pipes is: GrD=g⋅β(Ts−T∞)D3ν2 G r D = g · β ( T s – T ∞ ) D 3 ν 2 , where: GrD is the Grashof Number for Pipes.

Forced convection: When external sources such as fans and pumps are used for creating induced convection, it is known as forced convection. Examples of forced convection are using water heaters or geysers for instant heating of water and using a fan on a hot summer day.

Example of situation with conduction, convection, and radiation

• Conduction: Touching a stove and being burned. Ice cooling down your hand.
• Convection: Hot air rising, cooling, and falling (convection currents)
• Radiation: Heat from the sun warming your face.

Convection currents are the result of differential heating. It is this movement that creates circulation patterns known as convection currents in the atmosphere, in water, and in the mantle of Earth. In the atmosphere, as air warms it rises, allowing cooler air to flow in underneath.

Three factors contribute to set convection currents in motion:

• heating and cooling of the fluid,
• changes in the fluid’s density, and.
• force of gravity.
• The heat source for these currents is heat from Earth’s core and from the mantle itself.
• Hot columns of mantle material rise slowly.