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Question:

how to power a 400 watt heater with solar panels and batteries?

want to run 400 watt heater 8 hrs a day how many solar panels do i need and batteries

Answer:

You could do that, but it would be an expensive way to go. If what you really want is heat, consider heating water directly with conventional solar water heaters, and storing it in a large, insulated tank. You can then circulate the water through a conventional radiator at night.
Get the rating from the manufacturer, they will give you the watts per m2 of their panels. divide 400 into the rating and will have the total area, then get the area of the panel that physically fits better the project and divide the total area into that of the panel selected, you will have how many panels you need. For the batteries is more complicated because of the available light hours of your location and what time of day are you going to use the heater, to be safe make a bank of batteries to store 600 watts to have a 50% stored power for emergency
well, you need to produce 3200 watt-hours per day with your solar panels how many you need depends on the type of panel and size and how much sun you get (the energy of the rays depends on your latitude and the time of year) the amount of batteries you need again depends on your requirements and your insolation if you only need to heat when the sun is shining then you don't need any batteries at all if you want to heat for 8 hours after the sun has quit shining then you obviously need batteries to hold 3200 watt-hrs of electricity to actually size a 3200+ watt-hr solar system you need a lot more information

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