HEAT TRANSFER EXPERIMENT NATURAL CONVECTION ON A FIN SURFACE

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1 HEAT TRANSFER EXPERIMENT NATURAL CONVECTION ON A FIN SURFACE INTRODUCTION The removal of heat from the surface of a body can be accomplished by conduction, convection, and radiation. Convective heat transfer refers to the removal of heat by either forcing a fluid over the surface (forced convection) or by the natural fluid motion due to density gradients near the surface (free convection). The efficiency of a body s ability to transfer heat by convection to the surrounding environment is defined by the convective heat transfer coefficient (h). In this experiment, a cylindrical fin, made of a metal, having a diameter d and a length L, is placed inside a water tank. The base of the fin is attached to metal block that houses the electrical heater and the heated base is well insulated from the surrounding air. As the result, the supplied electrical energy is conducted through the base into the fin stem and dissipates into the water from the fin skin surface area via natural convection. In this setup radiation heat transfer is negligible. The heat transfer coefficient, h, can be determined by measuring the fin temperature along its length (distance x). The heat transfer coefficient, h, can further be verified by measuring the supplied electrical power and comparing the measured value with the results from heat transfer analysis. TECHNICAL OBJECTIVE Study free convection heat transfer over a cylindrical fin and evaluate the convective heat transfer coefficient, h. To achieve this, measure the fin temperature along its length using type E thermocouples. Convert the thermoelectric potential produced by thermocouples to temperatures values using the appropriate National Bureau of Standards (NBS) polynomial. Compensate all temperature measurements for undesired thermoelectric potentials (e.g., ice junction). Obtain heat transfer coefficient from measured temperature gradient. Use the obtained heat transfer coefficient to determine the fin heat transfer rate and compare the result with the value found by measuring the input electric power. PRE- LAB ASSIGNMENT 1. Read section , pp of the text, Wheeler and Ganji, Introduction to Engineering Experimentation. 2. Review the appropriate heat transfer course material ( Conduction & Radiation) --heat transfer from fins and extended surfaces. 3. Given that the copper fin diameter is 6.35 mm, what condition(s) must be met to use an infinite length fin model? 1

2 4. Explain two ways of compensating for the thermoelectric potential that is generated by connecting thermocouples to dissimilar metallic junctions at the interface of a digital multi- meter, oscilloscope, or PC based digital data acquisition system. BACKGROUND The heat transfer characteristics of fins are known as conduction-convection systems. Consider a cylindrical fin with a heat source located at its base and its surface is exposed to a surrounding. The thermal energy is conducted away from the heat source into the base and along the cylinder length. This energy will then be taken away by the surrounding fluid if the environment is at lower temperature than the base temperature, (free convection). Convective heat transfer rate can be calculated by: Where: Q = heat transfer rate h = averaged heat transfer coefficient A s = surface area T w = local temperature of the cylinder surface T = temperature of the fluid surrounding the cylinder In case of fins, T w, varies along the fin length and therefore, Equation 1 is not useful. An energy balance on a differential element of thickness dx yields the following equation: Where: T x = temperature at position x P = perimeter of the cylinder (πd) K = thermal conductivity of the fin material A = cross sectional area of the cylinder (π d 2 /4) Applying the proper boundary conditions and assuming the fin can be modeled as an infinitely long fin, the solution to Equation 2 is: 2

3 Here, T o, is the base temperature (at x = 0) and the parameter m is the slope of the natural logarithm of the non-dimensional temperature ratio, θ x versus position x. Performing a regression analysis on the natural logarithm of the non-dimensional temperature ratio versus position and using the definition of parameter m can determine the heat transfer coefficient h. That is: For the case of long cylindrical fin, the fin heat transfer rate is evaluated from: Where, the value for h comes from the previous analysis, Equation 4. THE EXPERIMENTAL SETUP The experimental setup is shown in Figure 1. It is consisted of a cylindrical fin with a total of 15 type E thermocouples embedded along its length, 4 thermocouples before and 11 after exposure to water; (thermocouple number 5 is the fin base temperature, T o ). Other components are: an electrical heat source, a DC power supply, a digital multimeter, an ice bath, and a multi-channel thermocouple switch. The fin stem is placed inside a water tank holding about 3 gallons of water as shown in Figure 1. Figure 2 shows a schematic diagram of the fin and the locations of the thermocouples. The outputs of the four thermocouples before thread -- (these four are surrounded by 3

4 insulation) -- are used to estimate the amount of heat being conducted from the electric heater to the water exposed section, (after thread) Figure 2 - Schematic Diagrams of the Fin and the Locations of the Thermocouples 4

5 PROCEDURE The following experimental procedure is intended only as a guide. This procedure does not include all relevant information, which is required to successfully perform the experiment. 1. Measure and record the thermocouple resistances and make sure they are in good working condition and check the ice/water bath. 2. Record all pertinent atmospheric properties, initialize all instrumentation (record all initial outputs). 3. Turn on the power supply, set the power level to produce the desired input power given by the lab instructor and record the time. 4. Record all thermocouple output voltages, the power supply voltage and current, and water temperature every 10 minutes. When the system has reached steady state, perform the final recording of the data. 5. Notify the lab instructor when the thermal part of experiment has been completed. 6. Turn off the power supply and the multimeter. POST-LAB ANALYSIS 1. Correct all thermocouples (TCs) outputs for ice-junction compensation. 2. Convert the corrected TCs outputs to temperature values using the appropriate NBS polynomial and/or tables. 3. Determine whether or not the cylinder can be modeled as an infinite fin -- (use experimental observations to support conclusions made). 4. Find the temperature slope (ΔT/Δx) for the first 4 TCs and compute heat conduction through the fin stem [q = - k A (ΔT/Δx)]. 5. Compare the q result obtained in Step 4 with the heat supplied by the power supply. Is there a difference? Explain the reason. 6. Plot the natural logarithm of dimensionless temperature ratio θ versus position x. 7. Calculate the convective heat transfer coefficient h. 8. Based on the computed h value, evaluate the fin heat transfer rate from Equation Compare this value with the data obtained in Step 4 and that of the power supply; explain the differences. 10. How would you alter the design of the experiment to allow for the evaluation of the fin heat transfer using the expression given by: = dt qfin ka dx x= 0 5