The temperature at the base of fin is 75° C, the surrounding air temperature is 20☌ and the heat transfer coefficient between the fin as well as the tube surface and the surrounding air is 9.5 W/m 2K. The tube is fitted with 20 steel fins of rectangular section with height 40 mm and thickness 2.5 mm. The length of the fin is represented by projection perpendicular to the plane of the pipe.Įxample 5.8 A heating unit is made in the form of a vertical tube of 50 mm outside diameter and 1.2 m height. Determine the power dissipated by the fin array. Each fin measures 3 mm wide 0.4 mm thick 5 cm length and has its base at 60☌. Solution The heat loss from n-fins is given byĮxample 5.7 An array of 10 fins of anodized aluminium (k=180 W/m-deg) is used to cool a transistor operating at a location where the ambient conditions correspond to temperature 35☌ and convective coefficient 12 W/m 2-deg. Neglect the heat loss from the tip of fin. Each fin has cross-sectional area 2.5 cm 2, perimeter 5 cm and is made of a material having thermal conductivity 250 W/m-deg. The base temperature of the fin is maintained at 200☌ and the fin is exposed to a convection environment at 15☌ with convection coefficient 25 W/m 2-deg. Accordingly it is uneconomical to extend the fin beyond a certain value.Įxample 5.6 Which of the following arrangement of pin fins will give higher heat transfer rate from a hot surface? Heat conducted upto any length is worked out by taking the difference of total heat and heat conducted at that section.Ĭomments: Most of heat is dissipated in a short length of the fin. Solution Heat dissipation for an infinity long fin is Adopt a long fin model for the arrangement. Of 195☌ in an environment at 24☌ with the given value of surface coefficient.Įxample 5.4 A rod of 10mm square section and 160mm length with thermal conductivity of 50 W/m-deg protrudes from a furnace wall at 200☌, and is exposed to air at 30☌ with convection coefficient comment on the result. Solution The physical situation approximates as two infinite fins with a base temperature For the wire alloy, take the thermal conductivity 340 W/m-deg. the wires are positioned vertically in air at 24☌ and the heat transfer coefficient on the wire surface is 17 W/m 2-deg. Estimate the energy input required to solder together two very long pieces of bare copper wire 0.1625 cm in diameter with a solder that melts at 195☌. Substituting the value of m from equation (13) in equation (12), we getĮfficiency of most of the fins generally used is above 90 percent.Ħ. If fin tip is insulated, efficiency is expressed asįor a straight rectangular fin, A c = w x 2δ and P= 2(w+2δ) as 2δ<< w, P=2w. To account for this decrease in heat transfer, fin efficiency is defined as However, due to conductive resistance of fin material, temperature decreases along length of fin, hence, heat transfer rate decreases due to decrease in temperature difference. Q max = hA fin (T o – T a) = h PL (T o – T a) (10) Heat transfer from the base of fin to surrounding fluid will be maximum as temperature difference is maximum at the base of fin and is expressed as Therefore, temperature at the base of the fin is maximum and equal to the surface temperature. It is generally assumed that bond between a fin and surface, to which fin has been attached, is perfect and it does not offer any thermal resistance. If, then this is desirable because heat transfer rate increases with the use of a fin. If, heat transfer rate decreases with the addition of fin as it acts as an insulator. If, there is no use of putting the fin as heat transfer rate will remain the same. Its effectiveness is given expressed asĮquation (9) gives the expression of effectiveness of a fin in terms of Biot Number. Performance of a fin is characterized by fin effectiveness, ε f and is defined as ratio of heat transfer from a finned surface to that of without a fin.Ĭonsider the case of a rectangular fin that is losing heat at the tip only. The purpose of use of fins is to enhance heat transfer from a surface. In order to determine the proper length of the fin, heat transfer from a fin of finite length is compared with that of infinite length.
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