Heat Transfer Analysis Collector P15483 Low Energy Fruit Drier 10/22/14 Background: Our proposed concept uses a solar collector to warm air before it is drawn into a separate drying chamber. In the chamber, air is passed over the fruit. This airflow is driven by a rooftop ventilation unit, ideal because it is inexpensive, and can generate a great deal of airflow at low wind speeds. This report detail an analytical model for such a system, in order to size the components involved and check feasibility. The model relies on heat transfer calculations done to the collector itself.
Model Features: Our model is based on the geometry of a common solar collector design. It is a wooden enclosure, with an inlet and an outlet at the bottom to allow for airflow. At a 45 degree angle on the front is panel made of glass or some other transparent material. This allows heat into the enclosure as solar radiation, but prevents losses due to convection and conduction. A black interior ensures as much radiation is absorbed as possible The design is pictured below. Fig. 1 To start with we sized a box that was nominally a one foot cube; this would allow simple scaling as we iterated. Figure 2 shows these nominal, initial dimensions. Fig. 2
The thickness of the plywood was taken to initially be ¾, because of its cost and availability, and the thickness of the window, assumed to be polycarbonate because of its durability, cost and transparency, was taken to be ½. Additionally, we assumed some other properties of the system. From our research, the ideal temperature for drying of fruit is between 100 to 150, with a target for our project of 125. For our model we used an output temperature of 150 to make sure we would overestimate how much heat was required, to be safe. For an ambient temperature, which is also the air temperature of the incoming air, we selected 70. Haiti very consistently has temperatures between 70 and 80 year round, so to underestimate the heat available, a value of 70 was used. The average worldwide usable solar flux is 240 W/m 2. We used this figure for our solar flux, as it will underestimate available flux on account of Haiti s proximity to the equator, and greater solar resources. The flow rate was sized based off available rooftop ventilation turbines. We initially selected a Air Vent Inc. 12 Turbine Vent 52606, based on it s low price and availability. The turbine, pictured below, is wind powered. Figure 4 lists the turbines airflow at various wind speeds. Fig. 3 Flow (CFM) Wind speed (MPH) 345 5 544 8 698 15 Fig. 4
Because average windspeed in Cap Haitien is 5.5 m/s, the 5 mph (2.2 m/s) flow rate is reasonable to use as a baseline. Various heat transfer coefficients also had to be estimated with varying degrees of accuracy throughout the system, in order to estimate heat losses through the walls. Using The Engineering Toolbox s table for thermal conductivities of various materials, the conductive coefficients for plywood and polycarbonate were found to be 0.13 and 0.19 W/m K, respectively. The convective coefficient for air varies with airspeed and other factors. Figure 5 shows a set of empirical data for the convective coefficient of air at different velocities. Fig. 5 At the selected airspeed, 2.2 m/s, the coefficient can be estimated conservatively at 20 W/m 2 K. Assumptions In any engineering model, assumptions must be made in order to apply the model to a real world system. To avoid complicated calculations involving how the incoming radiation interacted with the enclosure, it was assumed the inside of the box was a perfect black body. Thus, all the radiation that comes in through the window is transferred to the enclosure. It was further assumed that at steady state, the temperature of the walls of the enclosure was the same as the air in the enclosure. While the inlet temperature and desired outlet temperatures were known, the temperature of the air inside the box is more complicated to assess. Knowing the temperature while not necessary to analyzing the balance between the energy leaving the enclosure with the air, and the energy entering as solar flux is necessary to estimate losses through the walls of the enclosure. A typical practice is to use a temperature that is the average of the temperature at either end of the enclosure. This works out to 110.
Analysis: Below is a tabulated list of variables used in the calculation. Parameters Value/Formula Unit Description t w 0.0127 m Thickness of the window k w 0.19 W/m-K Thermal conductivity of the window A w 0.1316 m 2 Area of the window h t s k s A s 20 W/ m 2 -K Convective coefficient of air at sea level, 2.2 m/s 0.01905 m Thickness of the sides of the box 0.13 W/m-K Thermal conductivity of the sides 0.0929 m 2 Area of the sides of the box Q 0.0001628 m 3 /s Volumetric flowrate through the box ρ 1.2 kg/ m 3 Air density at sea level ṁ Mass flow rate through the box, calculated from (Q)( ρ) kg/s density and volumetric flowrate c 1.005 kj/kg-k The constant pressure heat capacity of air at 40 T Out T In 338.706 K The desired output temperature, converted to K 294.3 K The estimated input temperature, converted to K q solar 250 W/ m 2 The estimated solar flux (T Out+T In ) T Coll 2 T amb T In K K The estimated air/wall temperature inside the enclosure The ambient temperature of the surroundings Fig. 6
The calculations for the area of the different panels, mass flow rate, and interior temperature will not be covered in depth due to the trivial nature of the calculations. The model is primarily based on the concept of energy balance in a control volume. The heat transfer in and out of the collector can be summarized in three components: 1. The incoming heat due to solar flux, according to the equation: E solar = q solar A w 2. The outgoing heat due to mass flow out of the control volume. The energy, also taking into account the incoming air is: c(t ) E flow = ṁ Out T In 3. The heat loss through the walls of the enclosure E loss = [T Coll T amb] [ 1 + 1 ] tw kwaw + haw 1 1 ts ks2as + 1 h2as Together these terms form an energy balance that should, ideally, sum to zero: 0 = E Total = Esolar E flow E loss A program was written in Matlab to calculate the total energy difference. clc, clear all, clear, format compact % Energy Balance Collector Calculations % All units in SI tw = 0.0127 % m kw = 0.19 % W/m K Aw = 0.1316 % m^2 h = 20 % W/m^2 K, assumed from 5 mph outside wind ts = 0.01905 % m ks = 0.13 % W/m K As = 0.0929 % m^2 RNet = ((1/((tw/(kw*Aw))+(1/(h*Aw)))) + (1/(ts/(ks*2*As))+(1/(h*2*As))))^ 1 Q = 0.0001628 % m^3/s, from 345 cubic feet per minute from rooftop exhaust fan 0.1628 rho = 1.2 %kg/m^3 mdot = Q * rho c = 1.005 % kj/kg K, assumed 40 degrees celsius
Tout = 338.706 %K, converted from 150 F << what we want Tin = 294.3 %assume worse case, 70 degrees F Qsolar = 250 %W/m^2, wiki look up for average sunlight Tcoll = (Tin + Tout) / 2 Tamb = Tin DeltaE1 = 1000*( mdot * c * (Tout Tin)) DeltaE2 = (Qsolar * Aw) DeltaE3 = ((Tcoll Tamb)/RNet) DeltaEnergy = DeltaE1 + DeltaE2 DeltaE3 Using the initial values tabulated above, the code yields the following results: DeltaE1 = 8.7185e+03 DeltaE2 = 32.9000 DeltaE3 = 59.1341 DeltaEnergy = 8.7448e+03 It is clear the the energy is strongly imbalanced towards energy leaving the volume. In practical terms this means that the solar energy coming in to the system is not enough to heat the large volume of air passing through the system (by a huge margin.) Additionally, even with zero air flow, the heat losses through the walls are greater than the incoming solar heat. While the design is proven to be a failure, the model is successful, and has identified and quantified several important characteristics of the system. From these calculations we have learned the current design: 1. Has too much airflow for solar power to support. The solar heat rate is at least two orders of magnitude less than the outgoing heat by air flow. An area for incoming heat flow of more than 100 times the initial area (Aw) is obviously infeasible, so the airflow needs to be decreased. 2. Loses too much heat to the surroundings to maintain the required inside temperature, even at zero air flow. (32 watts in, 60 watts out) This means that a better ratio of windowed panels to solid panels is needed, or a material selection/design that increases in the insulation of the enclosure. Simply increasing the small windowed space (roughly 1.5 sq ft by a factor of 5 puts the energy balance back in favor of generating energy while maintaining T coll. Similarly, doubling the thickness of the materials, or halving their thermal conductivities will bring the balance to zero. Recommendations For Design Improvements: I. Reduce airflow. This can be done in a number of ways. One is to size a smaller fan. However the 12 vent turbine we sourced is already on the small end of the spectrum for these devices; alternatives would likely have to be electrical in nature, which impacts robustness and simplicity. Another way to reduce air flow is by increasing the pressure
II. III. losses acting on the turbine. An in depth fluid analysis of the drier is in order to better estimate these losses. It is possible that the air will lose enough pressure having to pass through a fully loaded tray of fruit. Or obstructions could be added to increase back pressure. A serpentine arrangement that frequently changes air direction could be designed to increase head loss, while at the same time ensuring more uniform air flow over the fruit. The turbine could also be throttled by separating its inlet such that it is also sucking air in from the surroundings, without drawing it through the machine. This effectively takes a fraction of the airflow the vent generates and uses it to pump air from the surroundings back into the surroundings, a simple but inefficient way to throttle airflow. The area open to sunlight needs to be greater. The main chamber (drying chamber) should also have transparent panels. The walls should be designed to hold more heat. Greater thickness adds cost, so a more elegant solution should be sought out. A common practice is an air gap laminated between two solid wall layers. A solution may be panels that are square wooden frames, wrapped with transparent plastic tarp, and stapled, such that the end product is a volume of air enclosed by plastic tarp. The panel would let sunlight in, while costing less than a polycarb panel, and weighing less than a plywood panel. It would also insulate better than either (air has a very low thermal conductivity). The panels would likely cost less as well. This analysis has generated useful design data, and more importantly a useful design tool. Changes in geometry, materials, and other characteristics and quickly be numerically evaluated to determine how they affect the system. Further design changes will not carry the slowing burden of complicated analysis. Further analysis should be done in both the fluid mechanics of the system as a whole, and heat transfer in the drying module itself.