I should go with Mr. Pisipaty Srinivas Kishore , where he explained the role of the shape factor when the two bodies don't facing exactly each other. We have mathematical models and ready tables for such factor.

Shape factor is a very important factor. It's a measure of the facing heat transfer areas. This leads to determine the amount of heat exchanged. As you indicated, this importance cannot be ignored and should be taken into consideration. Radiation heat transfer is so oriented on the relative positions of such surfaces.

Since Radiation Heat Transfer between surfaces depends on the orientation of the surfaces relative to each other , we have to take this into account with the Shape Factor. This is to account for the effects of orientation and shapes of the surfaces involved

The Shape Factor also named View Factor has to be consider in the Stefan-Boltzmann law as :

Q_dot_rad = (A_sup)*(sigma)*(epsilon)*(F_12)*[ (T_sup)^4 - (T_inf)^4 ]

Where:

Q_dot_rad: is the heat flux via Radiation Heat Transfer [kW]

A_sup: Is the surface area of Radiation Heat Transfer [m2]

sigma : Stefan-Boltzmann constant

epsilon: is the surface's Emissivity (optical property of the surface) [no units]

F_12: is the Shape Factor of the surface 2 viewed from surface 1 [no units]

T_sup : is the absolute temperature of the surface emitting the heat flux

T_inf : Is the free stream Temperature, or a temperature very far away from the emitting body , as T_sky , or another surface which is receiving part of the emitted head flux.

So the Shape Factor is purely geometric and is independent of the surface properties and its temperatures,

You can find tables with formulas to compute the Shape Factor for different configuration of surfaces

Best Regards !

https://www.sciencedirect.com/search?qs=radiation%20heat%20transfer&show=25&sortBy=relevance

I extend Elhadi I. Dekam, Franklin Uriel Paras Hernandez and Md. Washim Akram thanks for providing answers. However, any discussion on radiation shape factor be continued to get useful answers.

Dear Pisipaty:

Can you tell us the reason of your question (i.e. the context of your interest on Radiation' Heat Transfer) ?

For me, Radiation in Heat Transfer becomes interesting since it is almost not considered in the design of phononic devices.

In Phononics; design and fabrication of devices as thermal diodes, thermal transistors, etc, when working with solid state devices at the nanoscale, the only considered part of Heat Transfer is Conduction. But I believe there could be (perhaps) also enhancing effects if we get to consider the Heat Radiation part as well. Studies on this have not been well addressed so far.

In the future I would like to explore more the ways we could exploit the part of Heat transfered by Radiation in Nanodevices (Nanophononics).

Kind Regards !

I am interested to know the opinion on significance of shape factor from different researchers.

Thank you Franklin Uriel Parás Hernández for your useful answer.

Shape factor or configuration factor or view factor is the commonly used term for heat transfer between any two bodies participating in radiation. The heat coming from a source of the first may not completely touch the second body since the orientation of two bodies are different. Hence shape factor is used.

When two bodies are participating in radiation which are at two different orientations and at two different temperatures, the radiation completely does'nt fall on other body. Hence shape factor is used in addition to others to calculate radiation heat transfer.

Shape factor is also called as configuration factor or view factor and used in radiation heat transfer to evaluate heat transfer for any two bodies participating in radiation. If the two bodies are kept at two different orientations, only a part of radiation from one body falls on other body and hence shape factor is multiplied in order to get correct radiation heat transfer.

Interesting topic! Following

Thank you Hassan Izzeddin Sarsak for following.

When two bodies are at different orientations, the amount of heat radiation falling is determined by multiplying shape factor. Since, only a part of radiation falls on second body out of the total radiation emitted by first body.

Shape factor is also termed as view factor or configuration factor. As the name indicates, how first body is viewing the second body or vice versa is taken into consideration while evaluating radiation heat transfer. The amount of radiation emitting from a body to the other body with different orientations is got by multiplying shape factor. In other sense, one can say that the above describes that a part of radiation coming from first body is taken by second body.

Shape factor comes when two bodies are participating in radiation being at two different orientations. This is a factor, which multiples to the total radiation emitted by first body falling or which is available to second body.

Shape factor is used in radiation heat transfer. As it is also named view factor, this comes application or finds use when two bodies are at different orientations emitting radiation.

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Thank you Afraa Ibrahim for following.

If two bodies are subjected to radiation, shape factor is considered to be a factor multiplied for total radiation emitted by first body falling on second and vice-versa. This is mainly due to two bodies can be at different orientations, different angles or at different planes.

Determination of shape factor which is very much dependent on geometry is very much essential and primary in order to evaluate of radiation heat transfer between two bodies subjected to different orientations.

Shape factor also called as view factor depends on geometry of the object. This is used only when radiation considered between two bodies are at different orientations with one another. This factor is to be multiplied to get effective radiation.

Shape factor is quite necessary and important in solving or attempting any radiation problem. This is used when two bodies are at two different orientations and the shape factor is taken at a time for any two bodies only at a time participating in radiation.

Radiation travels and goes from one body to other body by electromagnetic waves. Radiation is carried by photons which has no mass but has energy. When the radiation is emitted by first body and falling on to the second body and if these two bodies are at two different orientations, radiation shape factor is multiplied to get radiation received by second body.

Heat transfer consists of three modes, namely conduction, convection and radiation. Radiation generally considered when temperature difference between two bodies are high. If two bodies are participating in radiation, with two different orientations, shape factor is multiplied to get actual radiation heat transfer.

Radiation shape factor is considered and used when two bodies are at different orientations since when, radiation is emitted by first body, only part of radiation falls on second body and hence multiplied with shape factor.

Shape factor should be used in evaluating radiation heat transfer between the two bodies, when the two bodies are at two different orientations. The radiation coming from first body may not be falling on to the second body fully and since part of the radiation is absorbed by the second body and hence radiation shape factor is multiplied. Shape factor depends on geometry.

Radiation coming from one body falling on second body is determined by thermal radiation taking temperatures. Apart from these, if two bodies are at different orientations, radiation received by second body is less. Hence, radiation shape factor which depends on geometry multiplied to get radiation received by second body.

Radiation heat transfer may occur from one body to other body, but in evaluation, radiation heat transfer is considered between only two bodies at a time. Shape factor known as configuration factor or view factor is used when two bodies participate in radiation with two different orientations.

Shape factor also known as geometry factor or view factor is considered when radiation is considered between two bodies when they are at two different orientations. A part of radiation will be absorbed by the other body and vice-versa.

Dear Pisipaty,

thanks for this valuable post.

I investigated the effect of the geometrical shape of the reflector of a solar concentrator. Now, a referee asked us why we don't use shape factors in our case. It seems that the shape factor is related to radiation, while our case is an optical investigation. In your opinion, Is my understanding of the shape factor correct? If yes, what is the best answer to this question?

Regards,

Ali

Ali Minaeian, Shape factor is related in your case to radiation. There are also conduction shape factor and are not much available in literature. But in order to evaluate, radiation heat transfer or absorption of radiant heat, radiation shape factor is used.

Dear Pisipaty,

Thanks for your reply.

Could you please tell me how to calculate the shape factor for the secondary reflector in this figure?

https://www.google.com/url?sa=i&source=imgres&cd=&cad=rja&uact=8&ved=2ahUKEwiz48S73-_oAhUMD2MBHTUPBxsQjRx6BAgBEAQ&url=https%3A%2F%2Fwww.semanticscholar.org%2Fpaper%2FDesign-and-Analysis-of-Rooftop-Linear-Fresnel-Solar-Gouthamraj-Rani%2F6771c01a265a0b2e975e29edfd0371057a308cf3&psig=AOvVaw3F4cNYonP00E_is7l0lUVX&ust=1587222700261133

Regards,

Ali

Ali Minaeian, refer to any heat and mass transfer text book, you will get an answer. But one thing is clear, when you are on optical investigation, shape factor is not needed. But once if you want to study actual radiant heat transfer, then multiplying radiant shape factor, which varies in between 0 to 1 depending on orientation to one to another can give you exact value.

This is my answer.

Thanks.

Thank you

Regards,

Ali