Your task The initial design for the pin fin has been suggested. This states that the pin fin should be made of carbon steel (k = 55 w/mk), with a length of five centimetres and a diameter of one...

Extracted text: Your task The initial design for the pin fin has been suggested. This states that the pin fin should be made of carbon steel (k = 55 w/mk), with a length of five centimetres and a diameter of one millimetre. The fin is to be located in stagnant air at 22°C, with a convective heat transfer coefficient of 20 W/m²K. You are required to produce a report on your findings as to how effective the proposed design is at dissipating heat away from the electrical component, and suggestions you have for improvements. To undertake this study, you must develop a numerical model by applying both a third order Runge Kutta method, and an Euler method of your choice, to the differential equation in equation 1. This model must be written using Matlab. Any design improvements you make must be justified by use of your model. The appendix must include a copy of your code, which should be adequately annotated. Things to consider • How will you verify your model? • Look at which variables you can change in equation 1 to improve the design. Further information If you are intending to enhance the fin by changing the shape such that the cross-sectional area increases with the length of the fin, then equation 1 is no longer valid. You will need to modify equation 4 according to the shape you choose. 1 dA, dT 1 hdA. + (i)-G) (r – T.) = 0 da? A, dr Ack dr


Extracted text: The Brief Background An electrical component should not exceed a temperature of 55 C In order to maintain the temperature, a pin fin style heat sink (see figure 1) has been attached to the component to enhance the heat transfer to the surrounding air. There will be heat transfer through conduction along the length of the pin, and heat transfer through convection from the surface of the pin. T. Figure 1: Heat transfer through a Pin Fin This system can be described by the second order differential equation in 1, where h is the convective heat transfer coefficient, pis the perimeter (circumference) of the pin, kis the conductive heat transfer coefficient and A, is the cross-sectional area. hp (T – T.) = 0 da kA. Fourier's law (2) is an equation relating the heat dissipated by the fin (q), to the rate of change of temperature along the length of the fin. No heat transfer is assumed to take place at the tip of the fin. dT q = -kA. dx