Analysis of different fin profiles with temperature-dependent thermal conduction with analytical methods

Master's thesis in the field of mechanical engineering with energy conversion orientation

Abstract:

Given that heat transfer is widely used in various fields of science, it is necessary due to spatial and physical limitations in electrical systems, from Wide recessed or raised surfaces can be used. The main purpose of using these surfaces is to increase heat transfer by increasing the surface. As a result, the best wide surface (fin) is the one that provides the greatest heat transfer, or in other words, the greatest temperature difference. A very important point is that in practice, the right fin should have the lowest amount of consumables at the same time as high heat transfer capability, which depends on its material and shape, so that its construction and, as a result, its use has the lowest possible cost. These two points about a fin cannot be investigated simply, but the most optimal mode must be found in which these conditions are taken into account simultaneously.

In this thesis, fins of different shapes with fixed base surface and length, as well as wet fins, have been investigated. The equation of the lateral surface and the cross-sectional area of ??the fin are defined as functions that include different fins. On the other hand, the conductive heat transfer coefficient is considered dependent on temperature and changes along the length of the fin with temperature. After dimensionlessization, the one-dimensional general differential equation, which has a high degree of nonlinearity, has been solved and analyzed by Galerkin [1], least squares [2], collocation [3], and differential transformation [4] (DTM) and Adomian [5] methods. To investigate the correctness and accuracy of this solution, the answers have been compared with the answer obtained from the numerical solution in several special cases.  After obtaining the temperature differential equation and its analytical-parametric solution, the general temperature equation was obtained. This equation is parametrically expressed in terms of the independent variable of length, conductive heat transfer coefficient, displacement heat transfer coefficient from the fin surface and most importantly, the parameter representing the fin profile. From the findings of this thesis, we can point out the effect of the slope of the conductive heat transfer coefficient on temperature, which increases with its increase, and also decreases with the increase of relative humidity in the wet fin. style="direction: rtl;"> 

1-1 Application of fins

Fins are widely used in the industry, including cooling fins on the engine body in motorcycles and lawn mowers, cooling fins in electric transformers, finned tubes that enhance heat exchange between air and working fluid. Air conditioners are used, as well as cooling fins for various computer parts, etc. These expanded surfaces are also used in heat exchangers for maximum heat exchange. Nature has also benefited from the Finn phenomenon; The ears of rats and desert foxes act as fins to transfer the heat of the blood flowing through them to the air.

Although the use of needle fins in some types of heat exchangers (in automobiles, air conditioners and aerospace industries) has not been common, these types of expanded surfaces have been widely used in the electronics industry. In the electronics industry, due to the increase in speed and efficiency of parts and the resulting increase in heat, as well as the limitation of space (in computers and notebooks), the use of fins is very important. Another use of fins is to increase the contact surface in pipes. Depending on the application, the fins used may be installed inside or outside the tube.

Also, fins or developed surfaces are often used to increase the air heat transfer rate in various heat exchange applications.

Fined heat exchangers are usually used in air conditioning, refrigeration, and heat transfer processes where the temperature is lower than the dew point of the surrounding moist air as a result of moisture in the air. It condenses on the surface and finally, mass transfer occurs simultaneously with heat transfer.

Depending on the temperature of the surface and the dew point of the surrounding air, the heat transfer between the final surface and its surroundings in any part of the uncovered surface takes place in both forms, sensible or latent heat.  The difference between the temperature of the air and the surface of the fin is the driving force for sensible heat transfer, and the difference in the humidity ratio between the air and the adjacent air on the surface of the fin is the driving force for mass transfer. Therefore, a dense surface with a thin layer of liquid in the form of condensation is continuously covered on the final surface, and the condensed liquid is transported on the surface by the movement caused by gravity.

For each application, the selection of the type of fin depends on factors such as dimensions, weight, manufacturing process, production costs, the reduction of the conduction coefficient and the increase of the flow pressure drop on the fins.

1-2 Background of the subject

Numerical and analytical investigation of heat transfer in fins with different sections and as a result different side surfaces is of great importance and has been studied by physics, mathematics and especially engineering scientists.

Investigation of heat transfer in wide surfaces for various situations has been investigated in one-dimensional or two-dimensional way.

In these studies, different sections, variable thermal conductivity coefficient, fin length and fin base radius, as well as porous and wet conditions have been investigated. Different sections represent different fin shapes and are used for different applications as well as increasing heat transfer. Considering the variable heat conduction is for situations where the temperature difference between the fluid and the desired object is such that it causes the conduction heat to be transferred with different rhythms along the fin. The length and radius of the fin base can also be changed in a certain range according to its applications, which results in different heat transfer rates and volume of the fin (consumable material).  And the state where the fin is at a lower temperature than the dew point of the surrounding air, in which case, in addition to convective heat transfer, heat transfer is also done by mass transfer. One of the important issues in the design of fins is to consider these two issues at the same time; This means that between the two parameters of heat transfer and volume (weight), an optimal state should be found in which heat transfer is maximum and volume is minimum. Of course, the optimal fin that is obtained in this way is parabolic, and as a result, it is expensive to manufacture, and as a result, in many applications, the use of a rectangular fin is still preferred.

However, due to the very limited space in advanced electronic tools and circuits and the necessity of relatively high heat transfer, in some cases forms of fins that have high manufacturing costs are forced to be used.

For these cases Many articles have also been published. Among others, we can refer to the study conducted by Aziz[1] and Green[2][2], which analyzed the performance and optimal design of a convective-radiative rectangular fin with convective base heating, resistant to wall transfer and between the wall and the contact-resistant fin base, and also an approximate analytical solution for convective-radiative heat transfer from a continuously moving fin with temperature-dependent thermal conductivity was developed by Aziz and Khani[3].

ABSTRACT

Extended surfaces such as fins are one of the basic methods used to enhance the rate of heat transfer. They possess a wide range of applications pertaining to various industrial processes such as air conditioning systems, electronic systems, etc.  The goal of fin optimization is to find the shape of the fin which would minimize the fin volume for a given amount of heat dissipation. In this thesis, different shaped fins with a base level of fixed length have been investigated. The equation of area is defined as a function of the cross-Fin various cover. On the other hand, the heat transfer coefficient depends on the temperature considered and the fin with temperature changes.  After using non-dimensional parameters, the obtained nonlinear equations are solved via Galerkin method (GM), least square method (LSM), collocation method (CM) and differential transformation method (DTM) and Adomian decomposition method (ADM).