The Heat Retention Solar Oven
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The Solar Oven Spreadsheet Explainedopen the Solar Oven Spreadsheet To understand the spreadsheet, you must first understand that a Heat Retention Solar Oven works by retaining heat from one day to the next. This increases the cooking temperature on successive days because energy in the form of heat is carried over from one day to the next. It also allows one to cook with the solar oven anytime, day or night, once enough energy has built up in the oven. Line 1 and line 2: give the size of the oven. Solar ovens should have well-insulated walls, which often means thick walls. The measurements are for the interior side of the walls. Length times width times height gives volume. When the length and width are the same (as in a square) the surface area of the walls, through which heat can be lost, is at a minimum for any given window area (the transparent top of the oven). However, the effect of reflector size is another matter. As for the height, a smaller value for height means less surface area through which heat can be lost. The ideal shape for a solar oven is often and correctly described as a pizza box: square and not very high.
Line 3 and line 4: give the size of the window, which is assumed to cover the entire top of the oven (not counting the thickness of the walls). In other words, the window is assumed to be the same width and length as the interior of the oven. Values in blue are calculated from other fields, but these can nevertheless be changed by backspacing over the calculation formula and entering a new number. Refreshing the page restores the default values and formulae.
Line 5: is the transmittance, the amount of light transmitted through the window. Each pane of glass reduces the transmittance by about 8% (4% for each surface times 2 surfaces). To reduce heat loss through the window (heat rises to the top of the oven), the window should have multiple panes of glass (high temperature glass). To increase the amount of energy entering the oven, the transmittance should be as low as possible. The problem is that more panes of glass decrease heat loss but also decrease transmittance.
Line 6 and line 7: give the area in square meters of the interior surfaces of the oven. These values are calculated from the length, width, and height, and are used in subsequent calculations, especially the total surface area of the oven (through which heat is lost). An ideal oven has a proportionately lower total surface area and higher window area.
Lines 8, 9, and 10: give the insulation values for the walls and floor and window of the solar oven. The R-value is a common measure (used in the U.S.) of the effectiveness of insulation. The U-value is the inverse of the R-value (1/R = U). Both R and U values are in British units (BTUs, sq. ft, etc.). Multiplying the U-value by the conversion factor of 5.674467 gives us the K-value. Lower K-values are better insulators.
Lines 12 and 13: factor in the extra light coming from the reflectors. Since the reflectors can be of virtually any size, one could erase the given value and enter the actual value. But, as a starting point, the reflector's surface area is assumed to be equal to the length of each of the 4 sides of the solar oven times 1/2 meter. In other words, a reflector is attached to each of the 4 sides of the oven, each reflector is the same length as that side by 1/2 meter. This is a conservative estimate of the reflector's size. A large solar oven could easily have larger reflectors than this estimate assumes.
The percent effectiveness of the reflector accounts for the fact that reflectors lose some percentage of sunlight. They do not reflect 100% of the light that strikes them. They have to be placed at an angle so that the reflected light will enter the oven. Therefore, the effectiveness of the area of the reflectors is reduced by a certain percentage, conservatively estimated at 50%. This gives us the effective area of the reflector, which, when added to the actual area of the window, gives us the total effective area (the plus window field). In other words, the solar oven behaves as if it had a larger window than it does have, because the reflectors add sunlight to the oven. * * Most solar oven designs will fail without an effective large reflector. Lines 14 and 15: give the temperatures inside and outside the oven, in degrees fahrenheight and centigrade. The centigrade numbers are are used in the subsequent calculations. The fahrenheight numbers can be changed to effect the calculations. * * Important: the temperature inside the oven has a profound effect on the subsequent calculations. The amount of heat loss depends greatly on the temperature difference (f14, f15) between the interior and exterior. The greater the difference in temperature, the greater the heat loss. A solar oven which succeeds at a temperature of 300 degrees F may easily fail at 400 degrees. Also, at lower internal temperatures, the solar oven will initially have a large excess of energy, but as it heats up it will lose more and more energy to the exterior, greatly reducing excess energy used for cooking or for storage in heat retention material.
Lines 17 thru 21: give the heat flow out of the solar oven through the floor, walls, and top. This heat loss greatly affects the maximum temperature of the oven. In order to decrease heat loss during the night and the least sunny hours of the day, the heat retention solar oven is covered with a well-insulated cover. Field c17 gives the heat loss from the whole oven whenever it is covered. The units used are watts (joules/second), but we can think of this as "watt-hours per hour" because we will be multiplying by the number of hours the oven is covered, giving us just "watt-hours." Field f18 gives us the heat loss from the whole oven whenever the oven is uncovered. Notice that the heat loss is much greater when the oven is uncovered. The oven can only be uncovered when there is enough sunlight to more than make up for the increased heat loss.
Line 19: gives the number of hours that the oven is covered and uncovered. * * For solar ovens that only operate during sunny hours, change the covered hours to zero and the uncovered hours to 8 or less hous. For a heat retention solar oven, the number of hours per day with enough sunlight will probably range from 7 to 9 hours. In general, uncovered hours plus covered hours should equal 24 hours. Line 20 gives the heat loss covered and uncovered, each multiplied by their respective number of hours. Line 21 give the total heat loss, covered and uncovered combined, per day.
Lines 22 thru 25: give the amount of energy from sunlight entering the oven, which determines the amont of heat input. Line 23 is the daily amount of solar irradiation (energy from the sun), in watt-hours per square meter. Note that the solar oven window will have an effective total area of greater than one square meter. Since we do not leave the heat retention solar oven uncovered for every daylight hour, not all of that energy affects the oven. With 8 hours of uncovered time during the middle of the day, the amount of sunlight not used should be less than 20%. That is why the daily amount (b23) is multiplies times 80% to find the actual amount of solar energy affecting the oven (d23). This amount is only for reference and does not affect the subsequent calculations of the spreadsheet.
Lines 24 thru 25: calculate much the same value as lines 22 and 23, but this time the result affects subsequent calculations. Field b25 gives the average number of watt-hours per square meter per hour; field c25 gives the number of hours; field d25 gives the total watt-hours per square meter for that time period (usually the daylight hours of one day). Field e25 multiplies that total by the number of square meters in the window plus the effective area of the reflectors (from field e13). And field f25 reduces that amount of energy by multiplying by the transmittance. If the window only transmits 73% of the energy that strikes the outside of the window, then the field f25 gives us the energy that actually enters the oven (i.e. 27% was lost in transmitting the sulight through the window.
Line 27: then sums up the heat flow as energy input (from f25) minus energy lost (from b21) to arrive at the net energy that can be used to heat the oven and the food. The heat flow numbers on this line are in watt-hours per day.
Line 28: gives a typical value for the amount of cooking heat used to cook for a 4-person family per day, 1500 watt-hours. This number can be increased or decreased and will affect subsequent calculations.
Fields e29 and f29: give the excess energy that the oven generates after deducting for heat loss through the insulation (d27) and heat loss through cooking (f28). This excess energy can be stored in the heat retention material.
Fields e30 and f30: give the number of days that the solar oven has been in continuous operation. This number is important because the oven continually stores heat and adds further heat as each day passes. After a certain number of days, depending on the oven design, the heat storage will be sufficient to cook for several days, even if the oven is covered all day due to cloudy weather. * * When adjusting the values for mass in fields b31, c31, and d31, the value for days must sometimes be re-adjusted so that the spreadsheet recalculates the subsequent values.
Fields e31 and f31: is simply the excess energy per day times the number of days. This amount of energy is assumed to be stored in the heat retention material * until * the heat retention material reaches the maximum oven temperature. The higher the oven temperature, the greater the heat loss.
Fields e32 thru f36: give the minimum cooking temperature (MCT). This is necessary because much of the excess energy stored in the heat retention material is used to heat that material from ambient temperature (e14, e15) to the minimum cooking temperature. Once MCT is reached, only the amount of energy above the MCT (e34) and below the maximum oven temperature (e35, e36, f35, f36) is used to calculate how many days worth of cooking heat is stored in the heat retention material.
Lines 29a to 29d thru 39a to 39d: refer to the heat retention material and its ability to store heat for cooking during the evening, night, morning, and any cloudy days. Three common types of material are considered: table salt (NaCl), brick (the numbers are for fire clay brick, but almost any type of brick would work), and ceramic tiles. The specific heat capacity (SHC) is the number of kilojoules of energy per kilogram of mass per degree Kelvin (or Centigrade) that the material can store. The mass in kilograms times the SHC times the difference in temperature from ambient temperature to MCT gives us the amount of energy needed to raise the heat retention material (HRM) to minimum cooking temperature.
Any stored energy above MCT can be used to cook and is found in Line 37, the Energy towards Maximum Cooking Energy (MCE). MCE is determined by the maximum cooking temperature. Once the maximum cooking temperature is reached, it is considered that the raise in temperature will have increased heat loss to the point where energy input is decreased and the oven temperature will no longer climb. This can be checked by adjusting the value for interior oven temperature (c14). Once the value in line 37 equals the value in line 39, then the maximum amount of stored cooking heat is reached. This will also give the maximum number of days that one can cook on cloudy days (with the oven covered), in line 38.
These calculations assume that the oven is covered 24 hours a day due to cloudy weather, but that the oven is still used for cooking. Therefore, the additional heat loss through the insulation and the additional heat loss from cooking are accounted for in lines 34 and 35. Back to the Mathematical page. Think harder.... Disclaimer: The drawings, procedures, and words on this site are for information purposes only. No claims are expressed or implied as to the safety, usefulness, or accuracy of this information. This site does not contain recommendations or actual plans for building a Heat Retention Solar Oven. This particular solar oven design is theoretical and experimental. |