Applications Of Forced Convection Engineering Essay

Applications Of Forced Convection Engineering Essay The experiment was carried out to verify the relationship between Nusselt number , Reynolds number and Prandtl Number using the different concepts of convection. Relative discussions and conclusions were drawn including the various factors affecting the accuracy of the calculated results. The main objective of this experiment was to verify the following heat transfer relationship: Therefore, the experiment is conducted by an apparatus where hot ait from heater is generated and flow through copper tube. Different values of temperatures and pressure were taken and recorded in order to calculate. Besides, graphs plotted and analysed to have a better understanding of convection heat transfer. Thus a Laboratory experiment was conducted where hot air from a heater was introduced through a copper tube with the help of a blower. Thermocouples were fixed in placed at various locations along the length of the copper tube. The different values of temperature and pressure were measured along with the various sections of the tube and other required values were recorded and calculated. Graphs were also plotted with the data obtained and then analysed. INTRODUCTION Heat transfer science deals with the time rate of energy transfer and the temperature distribution through the thermal system. It may be take place in three modes which is conduction, convection and radiation. Theory of convection is presented since this experiment is concerned about convective heat transfer. Convective is the mode of energy transfer between a solid surface and the adjacent liquid or gas that is in motion due to a temperature difference. It involves the combined effects of conduction and fluid motion. There are two major type of convective Forced convection is known as fluid motion generated by blowing air over the solid by using external devices such as fans and pumps. The other type is natural convection which meant by a phenomenon that occurs in fluid segments and facilitated by the buoyancy effect. It is less efficient than forced convection, due to the absence of fluid motion. Hence, it depends entirely on the strength of the buoyancy effect and the fluid viscosity. Besides, there is no control on the rate of heat transfer. Forced Convection Force convection is a mechanism of heat transfer in which fluid motion is generated by an external source like a pump, fan, suction device, etc. Forced convection is often encountered by engineers designing or analyzing pipe flow, flow over a plate, heat exchanger and so on. Convection heat transfer depends on fluids properties such as: Dynamic viscosity ( µ) Thermal conductivity (k) Density (à Ã‚ ) Specific heat (Cp) Velocity (V) Type of fluid flow (Laminar/Turbulent) Newtons law of cooling Where h = Convection heat transfer (W/(m2. °C) A = Heat transfer area = Temperature of solid surface ( °C) = Temperature of the fluid ( °C) The convective heat transfer coefficient (h) is dependent upon the physical properties of the fluid and the physical situation. Applications of Forced Convection In a heat transfer analysis, engineers get the velocity result by performing a fluid flow analysis. The heat transfer results specify temperature distribution for both the fluid and solid components in systems such as fan or heat exchanger. Other applications for forced convection include systems that operate at extremely high temperatures for functions for example transporting molten metal or liquefied plastic. Thus, engineers can determine what fluid flow velocity is necessary to produce the desired temperature distribution and prevent parts of the system from failing. Engineers performing heat transfer analysis can simply click an option to include fluid convection effects and specify the location of the fluid velocity results during setup to yield forced convection heat transfer results. TYPICAL APPLICATIONS Computer case cooling Cooling/heating system design Electric fan simulation Fan- or water-cooled central processing unit (CPU) design Heat exchanger simulation Heat removal Heat sensitivity studies Heat sink simulation Printed Circuit Board (PCB) simulation Thermal optimization Forced Convection through Pipe/Tubes In a flow in tupe, the growth of the boundary layer is limited by the boundary of the tube. The velocity profile in the tube is characterized by a maximum value at the centerline and zero at the boundary. For a condition where the tube surface temperature is constant, the heat transfer rate can be calculated from Newtons cooling law. Reynolds Number Reynolds number can be used to determine type of flow in fluid such as laminar or turbulent flow. Laminar flow occurs at low Reynolds numbers, where viscous forces are dominant. The condition of flow is smooth and constant fluid motion. Meanwhile, turbulent flow occurs at high Reynolds number and is dominated by inertial forces and it produce random eddies, vortices and other flow fluctuations. Reynolds number is a dimensionless number. It is the ratio of the inertia forces to the viscous forces in the fluids. Equation for Reynolds Number in pipe or tube is as below: Where à Ã‚  = Fluid density (kg/m3) V = Fluid velocity (m/s) D = Diameter of pipe ÃŽÂ ¼ = The dynamic viscosity of the fluid (Pa ·s or N ·s/m ²) ÃŽÂ ½ = Kinematic viscosity (ÃŽÂ ½ = ÃŽÂ ¼ / à Ã‚ ) (m ²/s) Q = Volumetric flow rate (m ³/s) A = Pipe cross-sectional area (m2) EXPERIMENT OVERVIEW Apparatus Figure 1 : Apparatus being used The experimental apparatus comprises of a copper pipe, which is supplied with air by a centrifugal blower and heater as figure 1. The test section of the pipe is wound with a heating tape, which is covered with lagging. Six copper constantan thermocouples are brazed into the wall of the test section. Another six thermocouples extend into the pipe to measure the flowing air temperature. In addition five static pressure tapping are positioned in the tube wall. A BS 1042 standard orifice and differential manometer measure the air mass flow rate though the pipe. Experimental Procedure Fully close the valve which controlling the air flow rate. Measure the everage intermal diameter (D) of the test section pipe by using a vernier calliper. Adjust the inclination angle of the manometer bundle ÃŽÂ ± to 30 °. Start the blower and turn the valve to the fully open position gradually, Adjust the power input to the heating tape to its maximum valve and allow the apparatus to attain thermal equilibrium. Take down the data and record Pressure drop through the metering orifice Pressure and temperature downstream of the orifice Ammeter and voltmeter readings Tube wall temperature along the testing section Air temperature along the test section Air pressure along the test section Ambient temperature and pressure. Repeat the foregoing procedure for another four different flow rate and adjust the heater input to give approximately the same wall temperature at each flow rate. DATA AND MEASUREMENT TABLE Property Symbol Units Value Barometric Pressure Pb mm Hg 741.60 Diameter of the test section pipe Dp m 0.038 Density of water (Manometers fluid) à Ã‚  Kg/m3 1000 Angle of the manometers bundle ÃŽÂ ± degree 30 Property Symbol Units Test 1 2 3 4 5 Pressure drop across orifice ΆH mm H2O 685 565 460 360 260 Pressure drop d/s orifice to atmosphere ΆP mm H2O 178 152 120 93 68 Air temperature downstream orifice t  °C 35 38 38 38 39 EMF (Voltage) across tape V Volts 230 200 165 142 129 Current through tape heater I Amps 7.3 6.3 5.5 5.0 4.0 Flowing air temperature t1  °C 35.0 36.9 38.2 40.0 41.4 Flowing air temperature t2  °C 36.1 37.7 38.9 40.6 41.9 Flowing air temperature t3  °C 43.1 43.6 43.4 44.4 45.6 Flowing air temperature t4  °C 42.2 42.4 42.4 43.5 44.6 Flowing air temperature t5  °C 49.6 48.6 47.0 47.3 48.1 Flowing air temperature t6  °C 63.2 59.6 55.7 54.3 54.6 Tube wall temperature t7  °C 38.9 40.0 40.6 41.9 43.0 Tube wall temperature t8  °C 81.20 73.6 65.9 62.2 61.2 Tube wall temperature t9  °C 99.8 89.1 77.5 71.5 69.5 Tube wall temperature t10  °C 105.9 93.9 81.3 74.6 72.4 Tube wall temperature t11  °C 106.5 94.5 81.8 75.1 73.1 Tube wall temperature t12  °C 108.1 95.5 82.3 75.0 72.5 Air static gauge pressure (Άl.sin ÃŽÂ ±) P1 mm H2O 385 324 255 195 145 Air static gauge pressure (Άl.sin ÃŽÂ ±) P2 mm H2O 264 223 175 132 99 Air static gauge pressure (Άl.sin ÃŽÂ ±) P3 mm H2O 210 181 141 108 79 Air static gauge pressure (Άl.sin ÃŽÂ ±) P4 mm H2O 108 97 81 57 42 Air static gauge pressure (Άl.sin ÃŽÂ ±) P5 mm H2O 23 31 20 16 14 Air static gauge pressure (Άl.sin ÃŽÂ ±) P6 mm H2O à ¢Ã¢â‚¬ °Ã‹â€ 0 à ¢Ã¢â‚¬ °Ã‹â€ 0 à ¢Ã¢â‚¬ °Ã‹â€ 0 à ¢Ã¢â‚¬ °Ã‹â€ 0 à ¢Ã¢â‚¬ °Ã‹â€ 0 Sample Calculations Based on 1st set data, Power Input to the tape heater: Power = = (230 x 7.3)/1000 = 1.679 Absolute Pressure downstream of the orifice: 741.60 + (178/13.6)=754.69 mmHg Absolute Temperature downstream of the orifice: T = t + 273 = 365+ 273 = 308 K The Air Mass Flow Rate: air =5.66x = = 231.88 231.88 Kg/hr = 0.06441 Kg/sec, Since 1 Kg/hr = Kg/sec Average Wall Temperature: = (38.9+81.2+99.8+105.9+106.5+108.1)/6 =90.07 Average Air Temperature: = (35+36.1+43.1+42.2+49.6+63.2)/6 = 44.87 The Bulk Mean Air (arithmetic average of mean air) Temperature: = (35+63.2)/6 =49.1 The Absolute Bulk Mean Air (arithmetic average of mean air) Temperature: 49.1+273 =322.10 K The Properties of Air at Tb: Using the tables provided in Fundamentals of Thermal-Fluid Sciences by Yunus A.Cengel From the table A-18 (Page958), Properties of Air at 1atm pressure at K Density, à Ã‚  = 1.1029 kg/m3 Specific Heat Capacity, Cp = 1.006 kJ/(kg.K) Thermal Conductivity, k = 0.0277 kW/(m.K) Dynamic Viscosity,  µ = 1.95 x 10-5 kg/(m.s) Prandtl Number, Pr = 0.7096 The Increase in Air Temperature: 63.2-35 = 28.2 The Heat Transfer to Air: (231.88/3600) x 1.006 x 28.2 =1.827 Where: = Heat Transfer to air = Mass flow rate = Specific heat capacity = Increase in air temperature The Heat Losses: 1.679-1.827 = -0.148 Where: = Heat losses = Heat Transfer to air The Wall/Air Temperature Difference: 90.07-44.87 = 45.2 Where: = Wall/Air temperature difference = Average air temperature The Heat Transfer Coefficient: = ((231.88/3600) x 1.006 x 28.2) / (3.14 x .0382 x 1.69 x 45.2) = 0.199 kW/ (m^2 .k) Where: = Mass flow rate = Specific heat capacity = Increase in air temperature = Average Diameter of the Copper pipe. = Length of the tube = Wall/Air temperature difference The Mean Air Velocity: = (4 x (231.88/3600))/ (1.1029 x 3.14 x (0.0382 ^2) = 50.9575 m/s Where: = Mean air velocity = Mass flow rate = Density = Average Diameter of the Copper pipe. The Reynolds Number: The Nusselt Number: = Nusselt Number = Average Diameter of the Copper pipe. = Thermal conductivity The Stanton Number: Where: St = Stanton Number = Nusselt Number = Prandtl number Re = Reynolds number The Pressure Drop across the testing section: at Tb = 320.1 K = Pressure drop across the testing section = Absolute pressure downstream of orifice. = Barometric Pressure The Friction Factor: RESULT Power Power kW 1.679 1.260 0.908 0.710 0.516 Absolute Pressure downstream of the orifice P mm Hg 754.69 752.78 750.42 748.44 746.60 Absolute temperature downstream of the orifice T K 308 311 311 311 312 Pressure drop across the orifice à ¢Ã‹â€ Ã¢â‚¬  H mm H20 685 565 460 360 260 Air mass flow Rate air 231.88 209.31 188.57 166.60 141.18 Average wall Temperature tw 90.07 81.1 71.57 66.72 65.28 Average air temperature tair av 44.87 44.80 44.27 45.02 46.03 Bulk Mean air temperature tb 49.1 48.25 46.95 47.15 48.0 Absolute bulk mean air temperature Tb K 322.1 321.25 319.95 320.15 321.0 Density at Tb à Ã‚  1.1029 1.1058 1.1102 1.1095 1.1066 Specific Heat Capacity at Tb Cp 1.0060 1.0060 1.0060 1.0060 1.0060 Thermal Conductivity at Tb K 2.77 2.76 2.75 2.75 2.76 Dynamic Viscosity at Tb ÃŽÂ ¼ 1.95 1.95 1.94 1.94 1.95 Prandtl Number at Tb Pr 0.7096 0.7096 0.7100 0.7100 0.7098 Increase in air temperature from t1 to t6 à ¢Ã‹â€ Ã¢â‚¬  t a 28.2 22.7 17.5 14.3 13.2 Heat transfer to air air W 1.827 1.328 0.922 0.666 0.521 Heat losses losses W -0.148 -0.068 -0.015 -0.044 -0.005 Wall/Air temperature difference à ¢Ã‹â€ Ã¢â‚¬  t m 45.2 36.3 27.3 21.7 19.25 Heat transfer Coefficient h 0.199 0.180 0.167 0.151 0.133 Mean air velocity Cm 50.9575 45.877 41.167 36.394 30.922 Reynoldss Number Re 110096.353 99380. 144 89994. 330 79509. 225 67204. 418 Nusselt Number Nu 274.4 249 232 209.8 184.1 Stanton Number St 0.00351 0.00353 0.00363 0.0037 0.0039 Pressure Drop across the testing section à ¢Ã‹â€ Ã¢â‚¬  P 1746.42 1491.59 1176.73 912.57 667.08 Friction Factor f 0.01378 0.0145 0.0141 0.0141 0.0143 Results Plot A Experiment 1 2 3 4 5 Y=ln(Nu x Pr-0.4) 5.75 5.65 5.58 5.48 5.35 X=ln(Re0.8) 9.29 9.21 9.13 9.03 8.89 Y-X -3.54 -3.56 -3.55 -3.55 -3.54 Plot B Experiment 1 2 3 4 5 Y=Nu 274.4 249 232 209.8 184.1 X=Re x Pr 78124.37 70520.15 63895.97 56451.55 47701.69 Stanton number: Reynolds Analogy: Experiment 1 2 3 4 5 Friction factor 0.01378 0.0145 0.0141 0.014 0.0143 Reynolds Analogy 0.00689 0.00725 0.00705 0.007 0.00715 Stanton number 0.00351 0.00353 0.00363 0.0372 0.0386 DISCUSSION In order to get more accurate results, there are some suggestions like cleaning the manometer, checking the insulation on the pipe and making sure the valve is closed tightly. An additional way to prove the heat transfer equation is by re-arranging it. Nu = 0.023 x (Re0.8 x Pr 0.4) Substituting in the experimental values into the above equation from section 5.0 returns the following results below: Experiment 1 2 3 4 5 Y=Nu 274.4 249 232 209.8 184.1 X=Re0.8 x Pr0.4 9415.08 8674.51 8014.48 7258.34 6344.14 Y/X 0.029 0.0287 0.0289 0.0289 0.029 Comparing this to the heat transfer constant, it shows that there is a little difference only which can be negligible. It can also be done by taking the gradient of the line from the plot Nu against (Re0.8 x Pr0.4) as shown below: CONCLUSION A better understanding of the heat transfer was achieved through conducting the experiment. Theoretical sums and experimental values were found to be approximately similar and the different sources of error have been identified. The main objective of this experiment was to verify the following heat transfer relationship: Nu = 0.023 x (Re0.8 x Pr 0.4) Therefore, relation of forced convective heat transfer in pipe is cleared and the objectives were completed.