Fins are extended surfaces put to remove the heat from a surface. Non uniform cross section fins are not of equal cross section throughout, but reduces its cross section to the end. This type of fins are used, in order to reduce the material, thereby reducing the cost. This non uniform cross section unlike regular fins, utilizes the material effectively for heat removal.

In fins there is two dimensional heat transfer takes place.

The convection at the tip side increases heat conduction rate along the fin length and across the fin cross section.

The increase in difference of heat transfer will increase the heat transfer rate.

Also the increased surface area due to non uniform cross section, would increased the cooling by increased heat rediation...

I've never heard of anyone associating non-uniform cross-section with increased heat transfer in fins. The non-uniform cross-section is a consequence of casting or machining or material reduction (conservation), that is, for fabrication reasons, not for heat transfer augmentation. You add larger/longer or more fins until you get adequate heat transfer. Radiation is proportional to the net projected area, rather than the total surface area, (i.e., the "view factor" or "configuration factor"), which doesn't matter if the fin is of constant or diminishing thickness. There is some slight impact of surface conditions (i.e., rough or smooth), but this doesn't depend on cross-section. I'm not sure what your motivation is in pursuing this particular connection.

Fin as extended surface helps for increasing heat transfer whether it may be uniform or non uniform cross-section which is proven. Non uniform cross-section especially triangular fins are found rare in literature put around the surface of cylinder and cylinder head and also used in micro heat sinks. Wavy fins used in automobile radiators. These has definitely an application as found in literature. In this direction other non uniform cross-sections (eg. parabolic etc.) can be used. This is the motivation behind the question.

This is an excellent point and good examples. The fins in an automobile radiator are designed to promote and take advantage of turbulent forced convection, as the vehicle is always moving or a fan is running. The radiator is also protected inside some sort of shroud. The fins on a head or cylinder of a motorcycle engine must provide natural convection when not moving and also work with forced convection when moving, plus they are not protected, so they must be much sturdier. Again, the shape (thin wavy ribbon or tapered flat) and material (rolled copper or cast aluminum) are determined by fabrication considerations more so than thermal effectiveness, although that must also be achieved.

See

https://www.researchgate.net/publication/223885335

Performance of annular fins with different profiles subject to variable heat transfer coefficient.

I think that an uneven cross section can lead to an uneven

distribution of coolant flow over the cross section, which will

affect the velocity field, the pressure change over the cross

section. Winning in my opinion will not be - it is leveled.

Sorry for my "bad" English.

The temperature difference between the fin and the surroundings decreases exponentially from the base/root to the tip. Using greater surface area close to the base helps in exploiting this greater temperature difference to achieve enhanced heat transfer, as a large fraction of the overall heat transfer takes place close to the base. For the same quantity of fin material, this non-uniformity of cross sectional area maximises the heat exchange. As pointed out above, strength considerations also play a role in increasing the thickness at the base - both mechanical stresses (like in a cantilever) and thermal stresses (on account of greater temperature gradient) will be dominant close to the base.

Thank you all for providing me with answers.

Thank you Supriya Sagar More , Bhupendra Desai , Dudley J Benton , Mladen Bošnjaković , Terekh Alexandr M. , Horimek Abderrahmane and Saleel Ismail for your useful answers.

the fins form and orientation or direction also increases the heat transfer rate

Thanks Abbas J Jubear for providing answer.

Extended surfaces are used for enhancing heat transfer. Non uniform cross section, wavy fins have application in automobile radiators and triangular fins have found application on the cylinder of internal combustion engine.

Fins are extended surfaces to remove heat. Irregular cross section find use in automobile radiators and on internal combustion engine cylinders to remove heat.

Non uniform cross section fins are useful to reduce the fin material and conduct heat through fin in an effective way which is more desirable.

Non uniform cross section are now coming in application in micro heat sinks, on internal combustion cylinder heads and in computer processing units

Non uniform cross section fins are coming now in applications in micro heat sinks and computer processing units. The wide spread and use is to see that effective material has to be put into utilization for a good amount of heat transfer. Since high thermal conductivity materials are used, this ultimately saves the cost.

Non uniform cross section fins are used to remove heat from the surface which are at high temperature. As the base temperature is more, more base is required to remove heat and as it goes along a length, the temperature also decreases and requires less cross section area, cost also reduces when used a gradually reduced cross section towards end length.

Non uniform cross section fins are used same as regular cross section fins connected to the surface from which heat has to be removed. These come into picture when the material becomes costly and weight has to reduced. This fin reduces its cross section from starting as it goes to the end.

Fins as high thermal conductivity material is used for removal of heat from the base which is at high temperature. Non uniform cross section fins are triangular, trapezoidal and parabolic. They have a reduced cross section at the end. These are normally used to save the cost without hampering the heat transfer.

Fins are extended surfaces put to remove the heat from a surface. Non uniform cross section fins are not of equal cross section throughout, but reduces its cross section to the end. This type of fins are used, in order to reduce the material, thereby reducing the cost. This non uniform cross section unlike regular fins, utilizes the material effectively for heat removal.

Non uniform cross section fins are finding application in micro heat sinks, in control processing units and on the cylinder heads for effective heat removal.

As fins are considered to remove heat from the surface, Non uniform cross section fins also has the same but in addition, the material utilized is effective and cost of material to prepare is reduced.

Fins of gradually reduced cross section fins are called as non uniform cross section fins. The fins can be triangular, trapezoidal and parabolic. Now a days, triangular and trapezoidal fins are finding its applications.

Following..

Thank you Abdul Kuddus for following.

Basic purpose of find is to increase surface area

In non uniform fin design you can try perforations at slanting Angeles

Spacing between fins may be optimally increased to facilitate flow of cooling air

Thank you Satish Narula for your answer.

Fins are of high thermal conductivity materials to remove heat from the base or surface when connected. Non uniform cross section fins like triangular, parabolic and trapezoidal fins are used to take same heat effectively throughout by gradually reducing cross section to till end.

As regular cross section fins, non uniform cross section fins serve the same purpose as to extract heat from hot surface when attached. Heat at the base or hot surface will be at higher temperature and extraction will be more at the base, hence cross section be more and as and when it is going to a certain length, heat exposure will be less and hence require less cross section. Hence by using non uniform cross section fins, material is saved and also the cost.

Non uniform cross section fins which serve the same purpose as uniform cross section fins has an advantage that it saves material as well as cost. Since the material is of high thermal conductivity, hence costlier.

Fins are used to take away the heat from the surface which is at high temperature. This can be uniform fins or non uniform fins. Uniform fins has found application in internal combustion engines and in several heat transfer devices. Non uniform cross section fins are paving a way in micro heat sinks and in control processing units since material and its cost can be reduced

In applications involving small devices such as MEMS non-uniform fins may be employed to fit the fine geometries. Especially when space considerations are prominent in applications such as ever shrinking electronic devices nonuniform fin design are most applicable.

Thank you Srini Vasan for your answer.

Non uniform cross section fins are triangular, trapezoidal and parabolic fins. These are also used to take away heat from the wall which is at high temperature. The advantage being, material, weight and cost are reduced.

Fins serve the purpose of removing heat from the surface which is at high temperature whether it may be regular cross section or non uniform cross section fins. Non uniform cross section fins save the material thereby reducing cost for the same heat flow into fin. These find applications on the internal combustion engine cylinder, micro heat sinks etc.