From: muratlanne@gmail.com   
      
   "Wu Ming"  wrote in message news:vk35pg$3b5s8$1@dont-email.me...   
      
   Wu Ming  wrote:   
   > Energy payback: W1*(t-tcool)+Wh =W2*t   
   >   
   > Where:   
   > W1 is the average wattage at lower T   
   > W2 is the average wattage at 98°   
   > t is the number of hours   
   > tcool is the time to cool down from 98° to T   
   > Wh is the energy required to re-heat from T to 98°   
   >   
   > W1, W2 are known from my previous   
   > tcool is unknown and I tried to guesstimate it   
   > Wh is calculated as:   
   >   
   > T° C to 98° C Wh Wh *1.25   
   > 90 37.24 46.55   
   > 80 83.8 104.75   
   > 60 176.91 221.14   
   > After 6 hrs 21° 358.48 448.1   
   >   
   > Second column from an online calculator. Wolfram Alpha as example. Third   
   > accounts for the not perfect energy transfer.   
   >   
   > Solving for t is simple. Then the fun begins.   
   >   
      
   Formatting appears to be a mess. On my client at least. Doesn’t know how to   
   keep LF.   
   ----------------------------------------   
   You are on the right track.   
      
   Convection and air currents from the heating system and nearby people throw   
   off the calculation of cooling rate which would be exponential to an   
   asymptote at ambient by conduction alone. The professional way to get a good   
   result is to record time and temperature and fit an equation to the   
   observation, piecewise between power inputs. When I became a scientist in   
   the 1960's we used paper chart recorders with mechanical ball integrators to   
   give area under the curve, now spreadsheets can total automated readings.   
      
   The multimeter method I mentioned is my cheap home substitute for a   
   datalogger, since I haven't found an inexpensive one that can record   
   temperature, voltage and current. The meters are optically coupled to the   
   laptop and don't create short circuits, allowing me to measure battery   
   current with a shunt.   
      
   Water temperature is tricky to measure accurately even with an immersion   
   probe. It will fluctuate due to convection cells in the water, rapidly   
   during heating and slowly during cooling. I see this on the remote readout   
   above my computer monitor for the temperature of food cooking downstairs on   
   the wood stove. A probe on the outer surface is nearly useless unless in   
   good contact and well insulated from the air.   
      
   The simple way is to guess a convenient procedure and measure the total   
   energy consumed with a Wattmeter like the KAW or another smart plug. If you   
   have only a few choices and can't spend hours watching and recording data it   
   should be adequate. I've added PZEM-061s to several outlet strips to measure   
   the energy demand of 120V and 240V appliances and machine tools during   
   typical use.   
      
   I bought a thermal imager to find heat leaks on the house that I used to   
   monitor a roasting chicken. It showed me the coolest areas immediately after   
   I cut it open, where to insert a temperature probe near the breastbone, but   
   wasn't otherwise better than an IR thermometer for cooking.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)