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 .

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 .

Dear Abhishek

Prof. Arunn Narasimhan explained the same in his online notes very clearly

please go through

https://home.iitm.ac.in/arunn/nusselt-biot-numbers-and-ozisik.html

thanks to ozisik and arunn.

There is an additional comment to be made to prof. Arun's nice explanation.

In the Nusselt number, the characteristic lenght is generally bounded to the flow field, while, in the Biot number, the same is linked to the solid material.

Dear prof. Carlomagno, in my perspective and according to arunn's comments on the issue is the concept of non-dimesionalization only.

Please comment on my perspective

thanks in advance

Dear Mr. Raja, since prof. Arunn correctly pointed out that the thermal conductivity once is the one of the fluid and the other one that of the solid, I just wanted to specify that, to perform the right non-dimesionalization, this applies also to the characteristic lenght. In fact, both numbers arise from ratios of temperature gradients and average temperature gradients.

Biot number in a body relates conductive heat transfer within a body and the convective heat transfer on the surface of said body, this is determined by the geometry and properties of the body, while the number of Nusselt determining the extent enhances heat transfer from a surface through which a fluid flows (heat transfer by convection) compared to the heat transfer only if this conduction occurs.

Example on characteristics length: assume a cylinder in cross flow, the characteristics length for Nusselt id the cylinder diameter. for Biot number is the volume of the cylinder divided the surface area of the cylinder.

1. Assume the case for a short cylinder when fluid flow over the cylinder surface and both ends of the cylinder. in this case the total surface area should include area for both end of the cylinder.

2. Assume a long cylinder when both side are out side the pipe of the main flow. in this case the surface area is the cylinder surface only. the characteristics length will same ad the cylinder diameter which also used for Nusselt number.

Dear Mr. Hamad,

for your first case, we have a problem The h on the end of the short cylinder is generally different from the average one around it. Which one we have to use? . Probably, an intermediate one which, however, depends on the cylinder aspect ratio.

Going back to Biot number significance, I am attaching a very short note that, probably, has a more direct physical significance.

Regards

Dear Professor Hamad,

Can you explain, what will be the effect of increasing magnitude of Biot number on the Nusselt number? Will heat transfer rate at the surface of body through fluid enhance or reduce if Biot number is augmented?

 with regards

The Nu number is used in the criterion equations for calculating the heat transfer coefficients (bulk-wall or wall-bulk). Biot numbers (Bim and Bih) are mainly used in the description of external mass transfer and external heat transfer (bulk phase-surface of catalyst grain). Regards,

Although both numbers have apparently the same definition, their meanings are very different. Biot Number is the ratio of heat transfer resistance at the surface of a "Body" (for example a body inmersed in a fluid or in contact with another solid) to the heat transfer resistance inside the body. For small Biot number the temperature gradient inside the body is very small during cooling or heating.

Nusselt number is the ratio of heat transfer in a "fluid" by convection and conduction across a boundary ( for example the wall of a cooling channel). A very small Nu-number means that the heat flows just by conduction and convection is very small or negligible (for example by very small Reynolds number= laminar flow). For very high Nu-number the heat flow is high convective ( for example in a turbulent flow) and conduction is negligible.

Truth. The definitions are mathematically the same, but different physical meaning and other application.

In the denominator of Nu - the thermal conductivity in the fluid, in the denominator of Bih - the thermal conductivity in the body - porous (effective thermal conductivity) or not and in Bim denominator - effective diffusivity related to the porous body. Also there is a possibility of different characteristic dimensions. Bih and Bim numbers can be used, among others, in the equations (boundary conditions) describing external transport phenomena (interparticle mass and heat transfer) in catalytic processes. Regards,

Dear Abhishek Gupta

Both are the ratio of convection heat transfer to conduction heat transfer.

Nu number is about the convection and conduction in a single fluid, but Bi is about the conduction in a solid and convection in a fluid.

Hi

Nusselt number shows you whether conductive or convective heat transfer dominates across the fluid-solid interface. Biot number shows you whether significant thermal gradients will develop inside a solid by showing you the ratio of heat transfer away from the surface of a solid to heat transfer within the solid.

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).