Formally both of them are  indeed an dimensionless group h L / k, where h is the convective heat transfer coefficient between the wall of a solid body and an external flow, L is a characteristic length and k a thermal conductivity.

The difference lies in k :

• In the case of the Biot number, k is the thermal conductivity of the solid. 
• In the case of the Nusselt number, k is the thermal conductivity of the fluid flowing around the body.

The Biot number will help you to know if your solid body can be considered to have an homogenous temperature (a "small body"). If Bi

Formally both of them are  indeed an dimensionless group h L / k, where h is the convective heat transfer coefficient between the wall of a solid body and an external flow, L is a characteristic length and k a thermal conductivity.

The difference lies in k :

• In the case of the Biot number, k is the thermal conductivity of the solid. 
• In the case of the Nusselt number, k is the thermal conductivity of the fluid flowing around the body.

The Biot number will help you to know if your solid body can be considered to have an homogenous temperature (a "small body"). If Bi

Biot number is an indicator of spatial variation of temperature inside the body or how uniformly the heat will be dissipated inside the body.

Nusselt number indicates the heat transfer enhancement due to convection phenomenon. Its non dimensional temperature gradient at the surface of the solid.

Based on a physical point of view, Nusselt number is general rate of heat transferred between a surface, a fluid flow and surrounding area in assisting or opposing directions.

However Biot number is a quantity of heat transferred to a body of surface via convection and it is distributed throughout the body through conduction which is subjected to the body capacity to store the thermal energy. 

Nusselt number is conduction heat transfer of fluid / convection heat transfer of fluid. Biot number is conduction heat transfer of solid / convection heat transfer of fluid.

Usually, Nusselt number indicates which is dominant between conduction vs. convection heat transfer in a fluid.

Biot number indicates how much solid temperature can change quickly based on the convection heat transfer in fluid.

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).

When we use the Biot number, then k is thermal conductivity of the solid and the temperature gradient (dT/dn)w is defined from temperature distribution in solid. If we use the Nusselt number, then temperature gradient is defined from temperature distibution in fluid, which includes knowing the temperature distribution in the boundary layer around the solid body, and in that case k is thermal conductivity of the fluid.

i agree with the above definitions

All the above explanations are excellent. I might add one more insight. The Biot number can be perceived as the ratio of internal (conductive) resistance of solid to external (convective resistance), while Nusselt number may be perceived as the ratio of the external conductive resistance if the fluid were at rest (imagine an extended no-slip layer!) to its external convective resistance. 

I have to express dismay that such a question was even raised. Answers are there in every basic book on Heat Transfer, if the teacher (or research supervisor) is unable to clarify. Can't we use the resources offered by Research Gate in a better way!

The Nusselt number is all on the fluid side, as pointed above.

For the Biot number, you can find a physical suggestion in the attached document, even if it has some little bugs.

Nusselt number (Nu) is a dimensionless number used in heat transfer operations. It represents the ratio between the convective heat transfer and conductive heat transfer across an interface (often fluid / solid). If conduction is the main mode of transfer, then the Nusselt number is of the order of unity. In the presence of convection (eg by the movement of a fluid in turbulent), the heat transfer is made primarily by fluid movement and will result to reach the Nusselt number to infinity.

The Biot number (Bi) is a dimensionless number used in the heat transfer calculations in the transition phase. It compares the resistance to heat transfer within and on the surface of a body.

Biot number uses thermal conductivity of the body (not fluid), whereas Nusselt number uses thermal conductivity of the fluid.

Dear all

Good day 

I agree with all answers too. A very good explanation is given by Olivier Louisnard!

Nusselt number, through the non-dimensionalization of the heat transfer coefficient in , quantifies how much the convection heat transfer could be higher when compared with the conduction heat transfer, if the fluid were stationary.

The Biot number provides a way to compare the conduction resistance within a solid body to the convection resistance external to that body (offered by the surrounding fluid) for heat transfer.

I agree with 

@ Olivier 

@ Rizwan

Above  definitions are good.

@Rizwan, your answer makes sense to me, but it may not do so to several young people who do not have the same deep knowledge that we have.

(i) Instead of "sum of two laws (Fourier law of heat conduction plus newton law of cooling)"

it would have been better to say "equating the two laws (Fourier law of heat conduction applied to the solid   equated to   newton law of cooling applied to the liquid)".

Similarly,

(ii) In "in Nusselt number we just use Fourier law of heat conduction at the surface", better to say "we just use Fourier law of heat conduction in the no-slip layer of the liquid".

Dear colleagues

Good day,

Please, look at:

https://www.researchgate.net/post/What_is_the_difference_between_BIOT_number_and_NUSSELT_number

Brian G Higgins · 69.86 · 66.3 · University of California, Davis

In the context of problems involving the transfer of heat, the Biot Number and the Nusselt Number have the same group of physical parameters: h L/k, where L is a characteristic length scale , h is a heat transfer coefficient, and k is the thermal conductivity. The Nusselt Number is used to characterize the heat flux from a solid surface to a fluid. In that case the thermal conductivity is for the fluid. Normally in engineering applications one can find correlations for the Nusselt number in terms of other dimensionless parameters that characterize the flow environment near the surface of the plate: The Rayleigh number if free convection is important, a Prandtl number and a Reynolds number ( if force convection is important ) 

The Biot number is used the characterize the heat transfer resistance "inside" a solid body. In that case k is the thermal conductivity of the solid body, and h is the heat transfer coefficient that describes the heat transferred from the "surface of the solid body" to the surrounding fluid. The Biot Number can be thought of as the ratio of internal diffusion resistance to external convection resistance. Note that 1/h is the external convection resistance and L/k is the internal diffusion resistance.

One can also define a Biot number for mass transfer: h_m L/D, where now D is the 

molecular diffusivity and h_m is the mass transfer coefficient. Again it can be thought of as the ratio of internal diffusion resistance to external convection resistance.

Best regards

Fateh

Nu and Sh numbers are used in the criterion equations of unit processes except for reactor processes. The Biot numbers (Bim and Bih) are mainly used in the description of external mass and heat transfer (bulk - catalyst pellet surface). Regards

Biot number relates the ratio of the external convection to the internal heat conduction. For the calculation of Biot one uses the thermal conductivity of the solid and the smallest distance between the surface and the interior of the solid . Nüsselt number expresses the external heat transfer by convection in the boundary layer and allows to deduce the convection coefficient. For the calculation of Nüsselt number, we use the thermal conductivity of the fluid (gas or liquid) and an external characteristic distance.

It is obvious that Biot number determines the relationship between the resistance due to thermal conductivity in body and the resistance due to convective heat transport. However, Biot's number does not only concern heat exchange processes (Bih) but also mass exchange processes (Bim). The Biot number is used, among others, in the description of the catalytic process in the reactors. It can be interparticle heat transfer, but it can be intraparticle mass transfer. It is also worth remembering that in the case of porous catalysts, in the Bih and Bim the effective thermal conductivity coefficient and the effective diffusion coefficient, respectively are used. Regards,

Dear all,

Thank you for your kind replies.

Please remember that both the Nusselt and Biot numbers are the dimensionless parameters. We might things such dimensionless parameters as ratio between something to anything which have the same dimensions. Thus, we might interpret the same dimensionless parameter with difference meaning such as Nusselt and Biot number.

Thank you.