Lab Report 5

Lab 5: Forced Convection Mass Transfer - The Flat Plate Name: Michael Lollino Lab Div.: 31 Date: 04 /12/2023 Lab TA: Manohar Bongarala

Introduction The purpose of this experiment is to evaluate convective heat and mass transfer coefficients of a damp cloth that is exposed to three different air speeds: 4, 6, and 8 m/s. The experimental procedure consisted of first using a dropper to add water to the surface of the cloth while measuring the weight of the cloth before exposing the cloth to the blower. While the cloth is being exposed to the blower, a transient temperature response is recorded for the cloth. After around 10 minutes, the cloth is weighed again. The humidity of the air was measured before any experimental data was taken. This process is repeated for all three wind speeds. Once the data was collected, the temperature of the cloth at the end of the transient analysis was used to find the density of water at the surface of the cloth and in ambient air using humidity. Using these values and other measured values, many different dimensionless parameters were calculated. These dimensionless parameters were then used to find the heat and mass transfer coefficients along with the convective and evaporative heat transfer. The Sherwood number was found twice using correlations and using experimental data. We found that the energy balance of the experiment was not satisfied as the convective and evaporative heat transfer coefficients were not equal in magnitude. However, we did find that as the air speed was increased, the magnitudes of the convective mass and heat transfer coefficients and the heat transfer magnitudes also increased.

The following table shows many dimensionless parameters necessary to perform correlation calculations. These correlations are used to find convective heat and mass transfer coefficients and the convective and evaporation heat transfer magnitudes. The experimental Sherwood number was found using the experimental convective mass transfer coefficient. U air (m/s) Re L Pr Sc Nu L Sh corr h conv (W/m 2 K) h m (W/m 2 K) q evap (W) q conv (W) Sh exp 4 2907 1 0.707 0.588 100.9 94.85 23.38 0.013 4.95 -2.14 53.35 6 4360 6 0.707 0.588 123.5 116.2 28.64 0.015 5.72 -2.63 63.11 8 5814 2 0.707 0.588 142.6 134.1 33.07 0.022 8.53 -3.03 94.64 Table 2: Calculated Heat & Mass and Dimensionless Parameters Discussion According to Figure 1, it is appropriate to assume that the experiment was conducted under steady state conditions. This is because the transient temperature response begins to flatten at time is increased, meaning the temperature is reaching steady state. This assumption affects the results because in order to calculate almost all of the values in Table 2, it needs to be assumed that the last temperature recorded for each air speed is the steady state temperature of the surface of the cloth. Without this assumption, the calculated values in Table 2 would be completely different. Also, without the steady state assumption, the temperature would be changing with time, which then changes the energy balance equation as there is an additional dT/dt term. For each air speed, the respective experimental Sherwood number is consistently smaller than the theoretical Sherwood number. Since the experimental Sherwood number was calculated using measured values, it can be assumed that there theoretically should

have been more convective mass transfer occurring in the experiment. However, the smaller experimental Sherwood numbers means that this was not the case. This is because a larger Sherwood number is representative of a larger convective mass transfer coefficient and therefore more convective mass transfer. The differences in the sherwood number could have been caused by an inconsistent dampening of the cloth, the cloth not being perfectly positioned in front of the blower, and an air speed that was not exact or not uniform throughout the duration of the experiment. All of these errors could potentially affect the experimental and theoretical Sherwood numbers. The energy balance is not met as q conv and q evap are not equal in magnitude. Since it is assumed that the experiment is being conducted at steady state and there is no energy generated, the energy in must be equal to the energy out. However, there is a noticeable difference in the convective and evaporative heat transfer. According to Table 2, this difference ranges from around 3 to 5.5 Watts, depending on the air speed. One factor that could have affected the energy balance is that the insulation of the wet cloth may not have been perfect, resulting in some energy lost through the sides. Another factor could be that a small amount of energy is being lost to radiation effects. It was assumed that radiation effects are negligible, however, there still could have been a small amount of heat transfer caused by radiation. Lastly, errors and inaccuracies caused by measuring the weight of the cloth before and after each experiment could have caused inaccurate heat transfer values. Even a small change in the placement of the thermocouple resulted in a different weight being shown on the scale. This means that the scale was very sensitive and may not have provided perfectly accurate measurements. There are several sources of error in this lab that could have resulted in slightly inaccurate data. The first source being the extended time in between weighing the cloth and exposing it to the respective wind speed. Specifically, for 4 m/s, the cloth was weighed, then it was left to sit out while the labview program was starting up. A minute or two passed until the cloth was exposed to the air speed. During this minute, some water could have evaporated and the cloth may have lost mass. This means that the recorded initial mass for

Figure 2: Schematic of Experiment c. Terms Defined u air - Air velocity [m/sec] ɸ probe - Relative humidity m i - Initial mass of setup [g] m f - Final mass of the setup [g] Δ m - Change in mass of setup [g]. (Equivalent to mass evaporated) Δ t - Time for evaporation [sec] ⍴ A,s - Mass of water per unit volume at saturation near the surface [Kg/m -3 ] ⍴ A,sat,inf - Density of water at saturation temperature of infinity [Kg/m -3 ] ⍴ A,∞ - Mass of water in ambient air, per unit volume [Kg/m -3 ] L - Characteristic length for reynolds number [m] T s - Saturation temperature [K] T inf - Free stream temperature [K] T film - Air temperature in the boundary layer/film [K] - Kinetic viscosity of air at film temperature [m ? 2 /sec] - Thermal diffusivity of air at film temperature [m ɑ 2 /sec] k - Thermal conductivity of air at film temperature [W/ (m-K)] D AB - Binary diffusion coefficient of water in air at 1 atm [m 2 /sec] h fg - Heat of vaporization at surface temperature [J/kg] Re L -Reynolds number Pr - Prandlt number Sc - Schmidt number Nu L - Nusselt number (averaged over the surface) Sh corr - Sherwood number calculated using correlation ( averaged over the surface) Sh corr - Sherwood number calculated using experimental values ( averaged over the surface) h conv - Heat transfer coefficient [W/(m-K)] (averaged over the surface)

h m - Mass transfer coefficient [m/s] (averaged over the surface) q evap - Rate of heat lost due to evaporation [W] (over the entire surface) q conv - Rate of heat lost due to convection [W] (over the entire surface) d. Symbolic Analysis The following calculations are used to obtain the dimensionless parameters Re L , Pr, and Sc. These are necessary in order to perform correlation calculations. Re L = u air * L / ? (1) Pr = / ? ɑ (2) Sc = / D ? AB (3) Once these dimensionless parameters are found, we can use correlation calculations to find Nu L and Sh corr . Nu L = 0.664 * (Re L 1/2 ) * (Pr 1/3 ) (4) Sh corr = Nu L * (Sc / Pr ) ⅓ (5) Now we can use heat and mass transfer equations and these dimensionless parameters to find h conv and h m . The Δ m term is divided by 1000 in Equation 7 in order to convert g to kg. h conv = Nu L * k / L (6) h m = (Δ m /1000) / Δ t / A / (⍴ A,s -⍴ A,∞ ) (7) The q evap and q conv can now be found using previously calculated values. q conv = h conv * A * (T s - T inf ) (8) q evap = h m * A * (⍴ A,s -⍴ A,∞ ) * h fg (9) Finally, the experimental Sherwood number can be calculated using the following