ME 331 Radiation Experiment 2017 The experimental apparatus consists of a radiant heat source mounted on a vertical stage, and a target suspended above the source. A cone shaped shield focuses the radiation emanating from the heater surface onto the target above. The target is a Pyrex beaker. The bottom surface of the beaker facing the source has been treated with a foil or coating to obtain a desired emissivity. The beaker is filled with water at the start of the experiment, and the depth is measured and recorded over time as the system is heated. Thermocouples are mounted throughout the system to monitor and record temperatures using a PC based data acquisition (DAQ) device. A diagram of the experimental setup, without the vertical stage, is shown below (Fig. 1). Target Heater Shield Figure 1. Experimental apparatus Experimental Procedure A. Preliminary steps that will be done before you take your measurements 1) The beakers are filled with water 2) The beakers are positioned a prescribed distance above the heaters 3) The heaters are turned and left on until the water reaches close to boiling
B. Taking Data 1) Select a time from the TA s doodle poll. The experiment takes about 2-3 hours so each group will need to arrange it so that someone is present throughout the experiment. 2) Using the DAQ measure the temperatures every 10 seconds 3) Measure the depth of water every 10 minutes Figure 2: The Setup C. Results The aim of the experiment and analysis is to compare the measured temperatures and heat fluxes with those predicted by TNSolver. Temperatures are measured on the bottom of the beaker, the surface of the heater and the cone and in the water. The heat fluxes must be computed as described below. The analysis consists of: 1) From the data for the amount of water evaporated, determine the heat flow rate, Qw, to the bottom of the beaker. Qw is approximately equal to the sum of the free convection from the surface of the water to room air, from the side of the beaker to the air (treat the beaker as a
vertical plate with an area equal to the surface area) and the heat necessary to evaporate the water. 2) From Qw, determine the flux and from Figure 10.4 find Ts-Tsat where Tsat is the temperature of the water and Ts is the temperature of the glass surface of the beaker in contact with the water. Now what we want to know is the temperature of the bottom of the beaker that is heated by the radiation. 3) The bottom of the beaker is 2 mm thick pyrex glass. The thermal circuit from the bottom of the target to the water will involve hw, conduction resistance of the pyrex and a contact resistance. Adjust the contact resistance value such that when using the computed Ts and the measured Tt (two values of target temperature are reported so use their average value) the heat transfer equals Qw. 4) Now the value of hw from Fig 10.4 may not be applicable to our experiment, so using the estimated value of Ts, compute the free convective heat transfer coefficient, hwfc using one of the correlations given below in Table 1. If the values of hw and hwfc are very different, explain why you think they are different. 5) Free Convection correlations that you can use are Table 1 Correlations for a round disk are: Eq facing C n Ra L 9.30 up 0.54 1/4 laminar Area/Perimeter 9.31 up 0.15 1/3 turbulent 9.32 down 0.52 1/5 laminar Duncan (1) up 0.31 0.3 all D Yovanovich (2) up 0.71 1/4 laminar sqrt(a) up 0.17 1/3 turbulent down 0.35 1/4 laminar down 0.08 1/3 turbulent Kobus (3) up 1.759 0.15 < 10^4 D up 0.972 0.206 <10^7 The Nu for free convection for the cone is found by treating the cone either as a vertical plate or a horizontal plate, (depending on the angle) and using g cos(angle) as described on page 577 of the text.
6) Running TNSolver This will require using nodes to represent: heater (h), target (t), radiation shield (si is the inner surface and so is the outer surface), and the environment (env). You will need to enter an enclosure radiation block for radiation between the nodes, a conductor between the target and the water (computed in 3), and convection from the bottom of the target to the air and from the shield to the air. The thermal network used in TNSolver is shown in Figure 3. Figure 3. TNSolver Thermal Network Free convection from a horizontal surface in TNSolver is based on the correlations 9.30-9.32 in the textbook: The horizontal plate up (ENChplateup conductor type, Section 4.2.11 in the TNSolver User Manual) requires that the surface node come first (nd_i), followed by the fluid node (nd_j). The correlation is then chosen based on Ts < Tfluid or Ts > Tfluid. Same goes for the horizontal plate down (ENChplatedown conductor type, Section 4.2.10 in the TNSolver User Manual):! surface fluid! label type nd_i nd_j material A/P A t-w ENChplateup target water water (R) (R) t-a ENChplatedown target env air (R) (R) You need to enter A/P as suggested in your text. Note that (R) means a single real number is to be provided by you.
For the shield, the external natural convection inclined plate up conductor is used (ENCiplateup, Section 4.2.13 in the TNSolver User Manual):! label type 4 nd_i nd_j material H L angle A so-a ENCiplateup so env air (R) (R) (R) (R) 7) Compute the viewfactors using the programs on the web entitled Heater2Target and Target2Cone. Then use viewfactor algebra to compute all needed values. For calculating the viewfactors we have The viewfactors are found by the calls [Fhop,Fht]=Heater2Target(Rh,Rc,Rt,Zc,Zt,10,36) [Ftco,Ftci]=Target2Cone(Rt,Zt,Rc,Rh,Zc,10,36) Table 2 The viewfactor table is then h t si so env h 0 H2T S 0 S t R 0 T2C T2C S si R R A 0 S so 0 R 0 0 S env R R R R S Where H2T and T2C indicate that the values come from Heater2Target and Target2Cone, R refers to reciprocity, A to viewfactor algebra, S to the sum rule.
env refers to radiation that escapes to the environment. The area of the environment is that of a frustrum of a cone whose top is the target and whose bottom has a radius equal to Rh. The radiation enclosure is specified in TNSolver using the Radiation Enclosure block and the view factors from Table 2: Begin Radiation Enclosure! label emiss area view factor matrix entries h (R) (R) (R) (R) (R) (R) (R) t (R) (R) (R) (R) (R) (R) (R) si (R) (R) (R) (R) (R) (R) (R) so (R) (R) (R) (R) (R) (R) (R) env (R) (R) (R) (R) (R) (R) (R) End Radiation Enclosure The resulting script-f conductors are reported in the output file when TNSolver is used to solve the model. See Chapter 9 in the TNSolver User Manual. D. Results and Report 1) Enter the information into TNSolver and compare the predicted temperatures and heat fluxes with the measured values 2) Comment on the agreement or disagreement between the measured and predicted heat flows and temperatures. 3) Compare the rate of water loss with that computed using the equations given in class. E. References 1) Duncan, D.S., Natural Convection Heat Transfer from a Horizontal Disk in a Cylindrical Enclosure, M.S. Thesis, Naval Postgraduate School, Monterey, CA 1971 2) Yovanovich, M. M.and Jafarpur, K., Bounds on Laminar Natural Convection from Isothermal Disks and Finite Plates of Arbitrary Shape for All Orientations and Prandtl Numbers, ASME Winter Annual Mtg, HTD-264, pg 93, 1993 3) Kobus, C. J. and Wedekind, G. L., An Empirical Correlation for Natural Convection Heat Transfer from Thin Isothermal Circular Disks at Arbitrary Angles of Inclination, Int. J. Heat and Mass Transfer, 45, (2002) 1159-1163