Which would be useful in order to systematically estimate conditions under which radiation heat transfer can be neglected.
Assume an absorbing/emitting fluid.
There are several dimensionless criteria which are used to estimate an interaction of thermal radiation with other heat transfer modes (and also the role of thermal radiation).
The simplest of these parameters is the spectral optical thickness of a medium defined as an integral of the transport extinction coefficient along various directions. If the optical thickness over the spectrum is much less than unity for all the directions, there is no any interaction of radiation with both conduction and convection. Of course, it doesn't mean that thermal radiation is negligible. A good example is the radiation of the Sun propagating in space towards the Earth.
The second criterion is the so-called Boltzmann number, Bo, with characterizes a relative role of convective heat transfer with a moving medium and heat transfer due to thermal radiation of this medium. Please note that this criteria doesn't include thermal conductivity of the medium and can be used even in vacuum, as in the case of Liquid Droplet Radiator for space applications.
The third criterion, N, is the ratio of the medium thermal conductivity to the so-called radiative conductivity of an optically thick medium. This criterion (in a combination with the optical thickness) is often used to estimate the relative role of heat conduction and thermal radiation in radiative-conductive problems. This is also successfully used in physical analysis of combined heat transfer in boundary layer flows.
For more details, please read Chapter 4 of the book by
L.A. Dombrovsky and D. Baillis, Thermal Radiation in Disperse Systems: An Engineering Approach, Begell House, New York, 2010: http://www.begellhouse.com/books/6d17e856430c0b8d.html
Hi Omar,
this should be the so called Nusselt number, it gives you the ratio of convective to conductive heat transfer across (normal to) the boundary
Best regards,
Antoni Artinov
Thanks, Antoni Artinov .
But I am actually looking for a measure of thermal radiation relative to convective heat transfer in internal channel flow.
I think it is simply the ratio between the two heat fluxes.
(Radiation heat fux)/(Convection heat flux). When this parameter goes to zero, you can neglect radiation.
Regards
There are several dimensionless criteria which are used to estimate an interaction of thermal radiation with other heat transfer modes (and also the role of thermal radiation).
The simplest of these parameters is the spectral optical thickness of a medium defined as an integral of the transport extinction coefficient along various directions. If the optical thickness over the spectrum is much less than unity for all the directions, there is no any interaction of radiation with both conduction and convection. Of course, it doesn't mean that thermal radiation is negligible. A good example is the radiation of the Sun propagating in space towards the Earth.
The second criterion is the so-called Boltzmann number, Bo, with characterizes a relative role of convective heat transfer with a moving medium and heat transfer due to thermal radiation of this medium. Please note that this criteria doesn't include thermal conductivity of the medium and can be used even in vacuum, as in the case of Liquid Droplet Radiator for space applications.
The third criterion, N, is the ratio of the medium thermal conductivity to the so-called radiative conductivity of an optically thick medium. This criterion (in a combination with the optical thickness) is often used to estimate the relative role of heat conduction and thermal radiation in radiative-conductive problems. This is also successfully used in physical analysis of combined heat transfer in boundary layer flows.
For more details, please read Chapter 4 of the book by
L.A. Dombrovsky and D. Baillis, Thermal Radiation in Disperse Systems: An Engineering Approach, Begell House, New York, 2010: http://www.begellhouse.com/books/6d17e856430c0b8d.html
Thank you very much, Prof. Leonid A. Dombrovsky, for this thorough and very satisfying coverage of the issue and for the shared material!
I think "Boltzmann number" will be useful for this problem.
you can read the below link:
http://www.thermopedia.com/content/207/
king regards
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