Surface area of rectangle number of fins9/23/2023 Is the expansion coefficient with the temperature units in Kelvin A detailed explanation of this derivation can be found in. Equation 5 was derived by calculating the fin spacing at which the product of the internal surface area of the fins and the convection heat transfer coefficient is maximized. The optimum spacing between the fins, s opt that produces the maximum heat transfer due to natural convection is given by equation 5. The next step in the calculation is to determine the heat dissipation, Q c2 due to natural convection from surface area, A 2 of the fins as shown in figure 2. As such utilization of equation 3 for this entire area will not introduce significant error and will simplify the calculation. The difference in magnitude of the natural convection coefficient for horizontal and vertical surfaces is not significant and the horizontal areas are small relative to the vertical surfaces. The area A 1 includes small areas of horizontal surfaces. See reference for details regarding the development of this formula. This formula is for natural convection from a vertical surface. The convection coefficient, h 1 for the area A 1 is calculated using equation 3. The convection heat dissipation, Q c1 from area A 1 the external side surfaces of the heat sink shown figure 2 is first calculated. The width, W of the heat sink, spacing between the fins, s and number of fins, N will then be calculated for the selected values of L and H. Values for L and H are first chosen based on your heat sink design constraints. This analysis is for a heat sink whose base is oriented vertically utilizing via natural convection and radiation only as shown in figure 1. More sophisticated calculation methods, software or testing can then be used to refine the design. However, the purpose of conducting this calculation is to get a rough estimate of the size of the required heat sink. The above assumptions will introduce some errors in your calculations. The heat source is in perfect contact with the base of the heat sink.The heat source has the same length and width of the heat sink and is centered on the base of the heat sink.The thermal conductivity of the heat sink is high enough so that the temperature of the surface of heat sink is uniform and approximately equal to the temperature of the heat source.The surface area due to the thickness of the fins t, and thickness of the base b are much much smaller than the total surface area of the heat sink.In order to reduce the complexity of the calculations the following assumptions will be made: There are six dimensions that would need to be determined to design an appropriate heat sink for your needs. The output of these calculations will be the dimensions of the heat sink required to maintain the required source temperature.įigure 1 shows a typical plate fin heat sink used to cool common electrical / electronic components such as LEDs used in lighting applications and MOSFET used in digital circuits and microprocessors. Heat sink design assumptionsīy making a few simplifying assumptions you can conduct the heat sink analysis by hand or using a spreadsheet. If that type of software is not available to you some quick calculations using a spreadsheet or mathematical software can be done to get an estimate of the heat sink size required to maintain the desired temperature of your components. There are commercially available heat sink design software that would allow you to design and analyze a heat sink to meet the thermal requirements of the device(s) to be cooled. For example, if you are starting with mm and you know r and h in mm, your calculations will result with V in mm 3 and S in mm 2.īelow are the standard formulas for surface area.Heat sink size calculations can be daunting tasks for any one who does not have much experience in thermal analysis. The units are in place to give an indication of the order of the results such as ft, ft 2 or ft 3. Units: Note that units are shown for convenience but do not affect the calculations. Online calculator to calculate the surface area of geometric solids including a capsule, cone, frustum, cube, cylinder, hemisphere, pyramid, rectangular prism, sphere, spherical cap, and triangular prism
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