Design of a Heat Sink - Case Study Example

Your Full Name: ------ Professor’s Name: ---- Subject: Hydraulic parking system Date: 8th February, 2013 Design of a Heat Sink Summary The increases of temperatures beyond the recommended level of 380oK leads to failure of the equipment thus required a heat sink. The design ascertains how heat sink could be coordinated under various variations of its heating parameters to give a more reliable and controllable functioning of equipment. It is from this understanding that this report is based in an attempt of communicating these findings. Various methods of heat reduction were available to the company including thermal radiation and convection by cold air in heat sink. The designed heat sink showed that use of flat plate fins of thickness 2.0mm and a gap between them 12mm. Aluminium was used because of its thermal conductivity of kAL = 202 – 249 W/mK and its relatively low density ρAL = 2700 kg/m3 that is a desirable for a low weight solution. The increase of the thickness or diameter will increase the surface area leading to improvement of heat sink. Thermal radiation is another way there is heat transfer which depends on the on the emission coefficient of the aluminium that is low emission coefficient as compared to others. Therefore, a slight change in parameters like cold airflow rates could bring an effect on the entire processing unit. How these changes could be coordinated to give a more desired aftermath was integral in this design. Of these, three types of heat exchangers were used for the entire experimental design; these were shell and tube, concentric tube, and the plate systems of exchangers. This kind of design was important to help compare overall efficiency of these systems at different flow rates when both cold and hot flow rates are varied at different inlet and outlet temperatures. Based on results obtained each from the three systems, calculation of efficiency from these various variations were important in deducing the most effective rate at which the exchanger would give the desired efficiency and thus function at the optimum. Energy balance across the heat exchanger was examined. Obtained results show that the efficiency of the machines was varied with an effect of changing both flow rates. Various temperatures were indicated alongside these variations; however, some setting did not indicate consistent variations when the flow rates were varied. The first experiment showed a more close prediction to what was expected, since efficiency remained within a given range. The problem A company that produces a wide range of electrical and mechanical equipment and one particular piece of equipment has caused the company extensive problems as it continually fails due to excess heat causing the electrical circuitry/components to fail. They realised that there is a heavy duty piece of electrical switching equipment generates a tremendous amount of heat. Thus to prevent the equipment failing it became essential that a heat sink is designed to remove this heat. This is done by using the windage of the electrical equipment to blow air over the heat sink so that the forced convection may increase the effectiveness of the heat sink. Assumptions In our design radiation of heat important but it is difficult to quantify its effects thus we choose a polished aluminum of emissivity of 0.05. It is known that hot air moves upwards as compared to cold air thus the materials used will affect the airflow in the heat sink. The number of fins used in our design can be noted to be nine of aluminum that had thickness of 20mm and gap between them of 10mm. From the diagram below fins is shown to be horizontal and parallel to the airflow which helps to increase efficiency of the heat sink. These materials that were used are good for heat dissipation especial when forced convection is necessary. In this case Plate-fins are helpful in ensuring that airflow is over the plates. It should be noted that Pin fins are essential when the turbulence of airflow is not known. This is the reason why pin fins have been chosen to avoid airflow diversion from the heat sink by using plate-fins. The measurement of pin fins was cut from the aluminium sheet that was available and was arranged on the top and right sides as shown in the diagram below. It shows that the arrangement is parallel to the base attached with screws Assumption table Item Measurement Unit 1. Fin Depth 20 [mm] 2. Fin Height 20 [mm] 3. No. Fins 17 4. Length of heat sink 200 [m] 5. Heat sink temperature 380 K 6. Ambient temperature 300 [K] 7. Emissivity 0.05 8. Fin thickness (m) 20 [mm] 9. Fin width (m) 20 [mm] Design steps and the logic sequences Step 1; identify the measurement of heat sink footprint Step 2: identify onset air velocity as 1.0m/s velocity Step 3: ambient air and constant base temperature as 300oK and 380oK Step 4: determine the absolute pressure as 1.0bar Step 5: determine the transfer characteristics of in-line tube banks using Where subscript f is the film temperature, C and n are constants C and n, is Reynolds number based on the maximum velocity occurring in the tube bank, i.e., the velocity through the minimum-flow area and depend on Step 6: determine the flow over a bank of tubes (or fins) is the pressure drop by employing the following formulae to Where Gmax = mass velocity at minimum flow area, kg/m2s ρ = density evaluated at free-stream conditions, kg/m3 N = number of transverse rows μw = viscosity evaluated at surface temperature, Pa.s μb = average free-stream viscosity, Pa.s The empirical friction factor f’ is given by: Results From the results of designing in excel radiation and convection coefficients are 0.001088W/cm2 and 0.000262W/cm2 respectively. It implies that more heat lost through radiation than convection in heat sink is radiation coefficient is higher than convection coefficient. This regression coefficient indicates towards a close association between the two variables. This finding is further reinforced by the value of R squared. Very high value of r squared, 0.998, suggests that variation in the given data of M* is capable of explaining 99.8 percent of total variation in other variable around its average value. It implies that the regression model is a good fit in the given data Heat Transfer Rate from Rectangular Fin to Surrounding Air h k h h extrusion length width (m) 0.2 0.2 0.2 0.2 0.2 0.2 thickness thickness (m) 0.002 0.002 0.002 0.002 0.002 0.002 protrusion out length (m) 0.05 0.075 0.1 0.125 0.175 0.2 # fins 17 17 17 17 17 17 k (W/m/K) 202 212 222 232 242 249 h (W/m2/K) 0.004 0.004 0.004 0.004 0.004 0.004 ambient air T_infinity (deg K) 300 300 300 300 300 300 width (m) T_base (deg K) 380 380 380 380 380 380 Computed Values theta_b 80 80 80 80 80 80 perimeter (P) 0.404 0.404 0.404 0.404 0.404 0.404 area (Ac) 0.000 0.000 0.000 0.000 0.000 0.000 M 0.914 0.937 0.958 0.980 1.001 1.015 m^2 0.020 0.019 0.018 0.017 0.017 0.016 m 0.141 0.138 0.135 0.132 0.129 0.127 Results             Heat Transfer Rate per Fin (mW) 7 10 13 23 26 26 target rate 200mW Heat Transfer Rate for All Fins (mW) 112 167 222 387 442 442 Selected                 Heatsink Details           Fin Depth 20.00 mm Heatsink Calculator       Fin Height 20.00 mm No. Fins 17   Length 200.00 mm Width 10.00 Mm       Thermal Ratings       Temperature (maximum) Per Fin 15.7433 deg K / Watt   Heatsink 380.00 deg K H/S Body 138.1487 deg K / W     Ambient 300.00 deg K Total 5.2611 deg K / Watt   Emissivity 0.05                         Surface Treatment Emissivity (typical) Coefficients:             Min Convection 0.001088W/sq cm 0.0070 W/sq in Polished aluminium 0.05 Radiation 0.000262W/sq cm 0.0017 W/sq in           Determine the transfer characteristics of in-line tube banks using =13.297 Where subscript f is the film temperature, C and n are constants C and n, is Reynolds number based on the maximum velocity occurring in the tube bank, i.e., the velocity through the minimum-flow area and depend on = 5 The empirical friction factor f’ is given by: = 0.55635x(749.15)-0.15 = 0.9269 The graph below shows that when the fin length increases, the heat transfer rate increases but which means long fins will have low thermal resistance due to conduction. The same case applies to short fins where thermal resistance increases and has reduced the convection heat transfer. The pattern of the plotted points on the graph slopes from right to left of the scatter plot suggesting a positive relationship between the variables. This kind of association simply implies that as the length increases heat transfer rate changes slightly. This kind of findings simply goes with the general expectation. The finding through the scatter diagram is further reinforced by the value of the correlation coefficient between the variables under consideration. The positive sign of the coefficient indicates a positive relationship while the very low absolute value of the coefficient, simply implies minimum relationship in the figure below. The velocity profile is thus constrained to a no-growth condition and fully develops only after traversing airstream. Theoretically the airstream heat increase recorded would be linear. The transverse velocity profile, mentioned above, also helps in understanding the development of the boundary layer. The fully developed air flow would either be laminar or turbulent and would be validated by the Reynolds number calculated for the velocity at a particular cross section under review. From the figure below it is shown that the optimal fins are nine and have resistances that sum up to the overall thermal resistance heat sink fin which consist of conduction and convection resistances of fin. Heat Sink Dimentions Set the values in the green cells and find your results Height 0.02 Calculated Properties Results Width 0.2 Ab 0.002 Rbase 0.040161 Depth 0.01 Ac 0.0002 Rconvection with fins 2.905217 At 0.0088 Rconvection no fins 12.5736 Fin Dimentions Af 0.0006 q no fins 6.342278 Height 0.02 Ab,0 -0.0014 q with fins 27.1612 Width 0.02 Ap 0.0004 Fin Array Effectivness 4.282562 Depth 0.01 Lc 0.03 P 0.06 Number of fins 17 nf 0.98587 no 0.983623 Properties m 6.921753 q goal 200 k 249 Tb 380 Tair 300 hair 39.76585 The convection coefficient for the front rectangular-fins was found at the middle position of the fins, where as the rear fins’ convection coefficient was found at the rear point of the base plate. Presents the results: h front plate-fins h back plate-fins 20.673 9.52 q fat fins(W) q thin fins(W) q front-plate fins (W) q back plate-fins (W) q total (W) 13.4 10.16 3.5 1.61 28.67 Rtotal K/W) 0.87 Discussion of Results There was heat transfer rate of 15.7433oK/W and at 2.5m/s, while its corresponding cold having an efficiency of 105%. Calculated power conducted in this case is 10.8835 watts while power through convectional was 2.229watts. The variation of fin length gave different heat Transfer Rate values which calculation of the overall efficiency could be done together with performance of energy balance across the heat sink. In this case it is clear that there was absorption of heat energy from the environment. One major observation from these data findings is that as the flow rate for cold air was maintained constant, variation of lengths rate from a lower value to a more significant value gave an increased thermal efficiency. The other observation is that some extra heat could be conducted materials, thus variation of these gave different values which determinations of the overall efficiency is possible. Whereby the airflows to the system from different sides of the system and then meets each goes down and hot air goes up. This is opposed to parallel heat exchanger systems in which the air would enter the system on one end and then flow parallel to each other for exchange to take place. As these exchanges positions because of cases in weight, heat would be transferred from one lower side where there are higher temperatures to the one with lower temperatures. The eventual temperature at the outlet would be different from that recorded from the initial setting. It is from these temperature differences that their mean and differences calculates efficiency of the system at various variations of flow rates. Once the system is on, temperature changes were recorded alongside their flow rates. In a heat sink having a fluid flow, the portion near the boundary surface, is affected since all air are practically not in viscid and hence the solid surface imparts a no-slip condition which in turn retards the smooth air flow giving rise to a slower moving boundary layer. When a flow enters a heat sink, a boundary layer is almost immediately formed circumferentially around the inner side of the heat sink. The core of the flow which is in viscid in relation to the walls is restricted from freely moving due to the growth of a viscous boundary layer. The velocity profile is thus constrained to a no-growth condition and fully develops only after traversing downstream. Theoretically the downstream pressure drop recorded would be linear. The transverse velocity profile, mentioned above, also helps in understanding the development of the boundary layer. It is with these values that the Coefficient of Discharge corresponding to each pressure head difference was also calculated. The coefficient of discharge varies according to the change in the pressure head. It was then compared with the Reynold's number at each of the top that were being observed. The flow of a fluid through a closed conduit can either be laminar or turbulent. This difference of flow characteristics is dependent on the flow velocity, density and viscosity of the fluid and the conduit diameter. These values have then been compared with the coefficient of discharge to show how they are interdependent. Flow up to a Reynold's number of around 2100 is considered laminar flow and that above 4000 is considered turbulent flow. When the Reynolds number falls between these two extremes, it corresponds to a transition phase where, the flow can exhibit laminar, turbulent, or intermittent flow characteristics. The wide fluctuations and waviness of the graph could allude to the turbulence, or a phase of transition to turbulence flow property inside the pipe. Further to that, the fact that the friction factor of the pipe causes a marginal energy loss and thus a reduced pressure head difference could I turn be a limiting factor to properly evaluate the data and understand the flow process. Conclusion The designed sink was a simple model that used flat pin fins to allow convection from a flat plate to the air flow. The convection coefficient was calculated and it was discovered that was rear fins’ convection coefficient was at the base while middle fins had in the middle. The design was done successfully to understand the methods of flow measurement and the concepts of flow process that happens inside a sink. Determining the velocities along a particular cross section by the measurement of heat transfer and the application of the Bernoulli’s principle in determining the velocities were done successfully. The graphical representation of the velocities at various positions over the length helped understand the basis of how a boundary layer is formed and how it affects the flow process. The coefficient of discharge of the flow regime over different sections of the pipe was also successfully calculated. The graphical comparison of these values with Reynold's number was also done successfully. The multi tube manometer was used to measure the heat on both sides of the sink. This recording was tabulated and studied with reference to the air discharge that was independently determined. As a result of that, it was understood that the pressure differences between the two sides was related to the jet velocity and therefore the discharge. Summary of engineering The designed heat sink uses a self contained process of heating simulation with an inbuilt controller function. In this engineering set up, the method that was utilised involved altering parameters under investigations and measuring their corresponding effects on the temperature changes, these were then compared with the set values so at to generate a control signal that could enable regulation of the electrical power supply to heaters. The justifications for this engineering control process is based on the fact that most if not all industrial processes require energy utilization, but of late these have become so expensive that maximum utilization has become a key consideration. There is a need to therefore formulate ways and methods of ensuring such processes attain maximum utilization of the available resources at a controlled approach. Heating applications is the generation and transfer of heat as well as its regulation within set limits to avoid loss of this precious energy. Such settings would more often give a better combination of various parameters under investigations that could be unified to give the best result in any controlled engineering process. CFD theory Computational Fluid Dynamics is mathematical modelling tool in a computer software which uses theory and some input of heat transfer and fluid flow dynamics. It gives primary technique for large tabulation of data that carries the fluid flow system and require direct resolutions so as to represent a flow process that has the desired accuracy. It uses two-fluid model, it is performed to get a flow pattern and the gas flow. The modelling has the ability to reduce computational demand with the overall speed of simulation process being improved. It modelling does not require the use of the averaged parameters and this makes it possible for a transient solution being obtained easily. With the availability of an inaccurate prediction of an incomplete burning levels thud impacts the calculations derived from radioactive heat transfer and burning rates which are estimated by human tenability’s. High quality which comes in with quantified uncertainty and relatively low temperatures provides measurements of heat flow from the interior of the under ventilated environment that are needed for guiding the development and also for validation of improved fire fields models. Works Cited Goodson, Kevin. Background Reading Material for Heat Sink Thermal Design Competition. Mechanical Engineering Department, Stanford University, 1999 Kraus, Allan & Avram Bar-Cohen. Design and Analysis of Heat Sinks. New York: John Wiley and Sons, 1995. Print White, Frank. Fluid Mechanics. Boston: McGraw-Hill, 1999. Print Read More