Heat transfer in a fin

The heat transfer problem solved in example 3.1 can be solved using Maple s dsolve command as follows  

The solution can be converted to trigonometric form and simplified further as ya =convert(ya,trig)  

We observe that dsolve gives a long solution compared to the matrix exponential 

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The ratio of heat transferred in a finned-tube unit to that in a plain-tube exchanger working within the same temperature limits is ... 

The heat transfer in a finned tube bundle is calculated using similar equations. For this we suggest [3.23] in the literature. 

One can also use dsolve to solve boundary value problems. Consider heat transfer in a fin [3]... 

Consider heat transfer in a fin with variable conductivity and nonlinear heat transfer coefficient. [25] The governing equations and boundary conditions are ... 

Exercise 6.1 Consider the problem of heat transfer in a fin with variable thermal conductivity. For a rectangular fin of thickness 2B and length L, it can be shown (with suitable assumptions) that the governing ODE is... 

The fin surface area will not be as effective as the bare tube surface, as the heat has to be conducted along the fin. This is allowed for in design by the use of a fin effectiveness, or fin efficiency, factor. The basic equations describing heat transfer from a fin are derived in Volume 1, Chapter 9 see also Kern (1950). The fin effectiveness is a function of the fin dimensions and the thermal conductivity of the fin material. Fins are therefore usually made from metals with a high thermal conductivity for copper and aluminium the effectiveness will typically be between 0.9 to 0.95. 

Nag, P. K., and Mukhtar, Sallam Ali. An Experimental Study of the Effect of Fins on Heat Transfer in a High Temperature Circulating Fluidized Bed, in Circulating Fluidized Bed Technology IV (Amos A. Avidan, ed.), pp. 362-367. Somerset, Pennsylvania (1993). 

Find the increase in the heat transferred for a finned-tube exchanger over a plain-tube exchanger, if c AfJc Ai =1.5 and Af/Ap - 2.0. From the figure, Qf/Qp = 1.25, i.e. an increase of 25%. 

Using a hand calculator, (he values of tanh niL are evaluated for some values of mL and the results are given in Table 3-5. We observe from the table that heat transfer from a fin increases with inL almost linearly at first, but the curve reaches a plateau later and reaches a value for the infinitely long fin at about mL = 5. Therefore, a fm whose length is = jm can be considered to be an infinitely long fin. We also observe that reducing the fin length by half in that case (from mL = 5 to mL = 2.5) causes a drop of just 1 percent in heat trans-... 

Consider heat transfer in a thin metallic circular fin.[18] The dimensionless temperature is governed by ... 

FIGURE 6.8 (a) Schematic for heat transfer in a constant cross-sectional fin, (b) typical temperatnre profile, for the longitudinal fin, and... 

C. C. Chen, J. V. Loh, and J. W. Westwater, Prediction of Boiling Heat Transfer in a Compact Plate-Fin Heat Exchanger Using the Improved Local Technique, Int. J. Heat Mass Transfer (24) 1907-1912,1981. 

Fins are used to enhance heat transfer. Consider a fin (length L, width W, thickness 2B) attached to a large vertical surface. Assume no heat is lost from the end or edges of the fin. Use a coordinate system such that x is 0 at midthickness (i.e., B and —B for edges), Z is 0 at the wall, and L is at the end of the fin y ranges from 0 at one edge to L at the other edge. Find the temperature profile in the fin. Indicate all assumptions. 

Heat-transfer coefficients for finned tubes of various types are given in a series of papers [Tran.s. Am. Soc. Mech. Eng., 67, 601 (1945)]. 

The usual applications for finned tubes are in heat transfer involving gases on the outside of the tube. Other applications also exist, such as condensers, and in fouling service where the finned tube has been shown to be beneficial. The total gross external surface in a finned exchanger is many times that of the same number of plain or bare tubes. 

The heat transfer area, A ft, in an exchanger is usually estahlished as the outside surface of all the plain or hare tubes or the total finned surface on the outside of all the finned tubes in the tube bundle. As will be illustrated later, factors that inherendy are a part of the inside of the tube (such as the inside scale, transfer film coefficient, etc.) are often corrected for convenience to equivalent outside conditions to be consistent. When not stated, transfer area in conventional shell and tube heat exchangers is considered as outside tube area. 

The heat transfer area. A, can be greatly increased by using finned tubes, but care must be taken to ensure good conduction of heat away from the fin into the tube and subsequently into the water. Some common fin types are shown in Figure 25.3 while Figure 25.4 shows some of the attachment methods employed to ensure satisfactory fin to tube heat transfer. 

Another approach is to improve the heat transfer conditions from the product. This can be accomplished in several ways. One way is to operate in a coolant medium that would also act as the lubricant for the system. The heat transfer to a liquid is usually much better than to air, and the liquid can be cooled by passing it through a heat exchanger device. A second approach is to improve the heat transfer to air. This can be done by increasing the surface area of the product by means of fins or other surface projections. The larger area will increase the heat flow... 

The simulations of fluid flow and heat transfer in such microstructured geometries were carried out with an FVM solver. Air with an inlet temperature of 100 °C was considered as a fluid, and the channel walls were modeled as isothermal with a temperature of 0 °C. The streamline pattern is characterized by recirculation zones which develop behind the fins at comparatively high Reynolds numbers. The results of the heat transfer simulations are summarized in Figure 2.34, which shows the Nusselt number as a fimction of Reynolds number. For... 

Finned tubes are used when the heat-transfer coefficient on the outside of the tube is appreciably lower than that on the inside as in heat transfer from a liquid to a gas, such as in air-cooled heat exchangers. 

The essential features of the earlier commercial models were that the two piston engines were vertically arranged inside the large finned heat exchanger in a static atmosphere of helium with LHe from the Joule-Thomson expansion collecting in the bottom of the dewar. This liquid could be either used in situ or transferred to all external storage dewar. The energy of expansion was absorbed in a crosshead on top of the dewar assembly. 

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