First of all, we must analyze how we relate to the water being heated up in the tubes: is this cooking in the sun (permissible) or cooking with solar byproducts (forbidden)?

Permissive View: Cooking in the Sun

The Tzitz Eliezer (Vol. VII, ch. 19) writes that one should be allowed to use the water from a solar heater, since the water in it is considered to have become hot by the agency of the sun itself.  He explains in the name of Rav Yosef Kafih that there is a difference between hot sand (considered a solar byproduct, and therefore rabbinically prohibited) and a solar heater.  Hot sand, even if it is moved to another place, will stay hot for some time, and therefore one might come to mistake it for something heated by fire.  In a solar heater, on the other hand, if the tube is moved elsewhere, it will cool immediately.  Therefore, it is clear to everyone that this tube was heated directly by the sun.

Heating by Magnifying Glass — Permissible  

The Tzitz Eliezer adds that if we explain that the glass helps to focus the rays of the sun, it is considered the sun itself.  This is what he cites from the words of the Shevitat Ha-Shabbat (Mevashel, Be’er Rechovot, ch. 44), whose inclination is to allow heating by a magnifying glass that focuses the light of the sun: [1]

One cannot compare tubes to sand and dirt from the road… because sand and dirt from the road have already absorbed a lot of heat from the sun, and they can now heat and cook even in the absence of the sun: if one moves this sand to a shady part, its heat is still sufficient to cook food.  It is only in this case that they have banned solar byproducts because of igneous byproducts, because they are interchangeable.  However, if these substances could only make something hot while they were in the sunlight, what worry would there be of interchanging them?  We would see that the sun is the sole actor, and without it no action can take place.

Now, in our case, should we take one of these collecting tubes to another place, it could not heat up anything at all, and the thickness of its metal is not sufficient to heat other substance with its own heat, and it turns out that the water is heated directly from the sun.

In such a case, we certainly view it as being heated by the sun directly and not by solar byproducts, and it should be permissible.  Thus we should know that the glass panels on the collector do not act at all to heat the water, and they have no influence upon it, aside from preventing the wind and the cold air from cooling the water that passes over the collector tubes.  This is the view of the learned.[2]

This is what is appropriate to say about this matter.  I have seen something even greater than this in the book Shevitat Ha-Shabbat; that author is inclined to say that even when a metal vessel is heated by glass (and no flame is ignited, for if so, it would be true fire), which focuses the energy of the sun, and through this the food is cooked in it, this may be like the sun itself [and permissible]. 

Forbidden: Cooking with Solar Byproducts

However, this is not simple.  According to the Minchat Yitzchak (Vol. IV, ch. 44), [3] the collectors are considered solar byproducts because they absorb solar energy and afterwards heat the water.  On the contrary, this is actually a more sophisticated type of solar byproducts.

Additional Problem: Ancillary Water in the Heater

There is another problem, particularly in modern solar heaters.  When one opens the hot-water tap, hot water comes out of the heater, and new cold water enters from the main.  This water does not directly reach the collectors; rather, first it goes through the central heater (see the above diagram), and there they are heated by the water that is already in the heater, and that water has already been heated by the collectors.[4]  The hot water in the heater certainly should be classified as a solar byproduct (because they have been cooked by the sun), and if so, the cold water that is heated by this heated water should be considered to be cooked by solar byproducts.  According to this, it would be unanimously forbidden to use a solar heater on Shabbat because the cold water is heated by the hot water.

Is a Rabbinical Pesik Reisha Permitted?

Even so, there are those who permit using a solar heater on Shabbat.  Rav Ovadya Yosef (Yabbia Omer, Vol. IV, OC, ch. 34) struggles with the issue of a pesik reisha, an inevitable, albeit unintentional, result: [5]

There is a question whether one is allowed to use hot water on Shabbat if it was heated by the solar heater, because at the time that one opens the hot-water tap in one’s residence, cold water immediately comes into the heater, and this is like cooking on Shabbat…  Even though one opening the tap has no intent to heat the cold water (which flows immediately into the heater when the tap is opened), nevertheless, it should be a pesik reisha, and this is like cooking on Shabbat, because it is forbidden to cook via solar byproducts on Shabbat…

However, in our case, that one does not intend to heat and boil the water, we have come to a dispute among the halakhic authorities about the law of pesik reisha as it applies to rabbinical prohibitions, whether it is permitted or not. The Terumat Ha-deshen (ch. 64) writes that for a rabbinical prohibition, one should distinguish between full intent and a pesik reisha of an unintended consequence…  However, the Magen Avraham (314:5) has argued strenuously and impressively, overwhelming every occupant of the study hall with his brilliant and convincing proofs from a number of sources that a pesik reisha of a rabbinical prohibition is prohibited…  Nevertheless, the words of our master the Beit Yosef indicate that, halakhically, he believes that one should different between biblical and rabbinical pesik reisha…

The determination of the law with which we began and with which we conclude is that, by the letter of the law, one may open the tap for water that was heated in a solar heater and use it for washing dishes, washing hands, drinking or anything of the sort (and, similarly, it is permitted to close the tap after one has finished using it).  There is no need to be concerned with the flow of cold water into the heater and the tubes that come out from it where the water gets heated …[6]  However, one who wishes to act stringently and avoid using water that was heated in the solar heater because of the concern of boiling the cold water is praiseworthy; nevertheless, those who act leniently have upon whom to rely for practical purposes.  This is how we rule, God willing, for the tendency to permit must always be greater.  May the Holy One illuminate our eyes in His holy and pure Torah, amen. 

The main reason for Rav Ovadya Yosef to permit this is the fact that the person does not intend to heat the cold water that comes into the heater (it has enough hot water for his needs, so he does not need to heat additional cold water).  The assumption is that the water will indeed be heated, as a pesik reisha; however, because this is a rabbinical ban (against solar byproducts) we may, in his view, be lenient for a rabbinical pesik reisha. 

Magen Avraham: Rabbinical Pesik Reisha Is Forbidden

However, there is no consensus to allow this.  The Magen Avraham (314:5) argues and forbids even rabbinical pesik reisha (even if it is unwanted).  This is how Ashkenazim rule, following the Rema’s view (314:1, Mishna Berura ad loc. 11; Rema 340:3, Mishna Berura ad loc. 17; et cetera).  A number of Sephardic authorities also rule this way.

Perhaps There Is No Pesik Reisha

However, many times there is no certainty that the cold water will be heated by the hot water, since the cold water enters the solar heater from below, and many times the water that is already there in the bottom of the heater is cold (and that water will still need to be heated more by the collectors, so that it may be that it is considered like the sun and not like solar byproducts).  If so, it may be that there is no pesik reisha but rather a doubt (or chance) of a pesik reisha, and the Mishna Berura (316:16) permits a doubtful pesik reisha of rabbinical prohibition.

No Concern of Confusing with Igneous Byproducts

There are halakhic authorities who want to allow the use of a solar heater for another reason, based on the view of the Maharshal (Responsa, ch. 61). The Maharshal claims that the entire prohibition of cooking via solar byproducts applies only when there is a concern of confusion or error — i.e., when one may confuse a solar byproduct with a byproduct of fire.  However when it is clear to all that the heat comes from the sun, there is no prohibition in using the substance, even though we are talking about a solar byproduct.  Based on this, the Maharshal allows cooking food directly on a hot roof that has been heated by the sun, because it is obviously visible that the source of the heat is the sun.  Based on this allowance, there are those who believe that it is permitted to use a solar heater, since the heating is always being done by the sun, and the matter is similar to a hot roof, concerning which there is no concern for error (Shemirat Shabbat Ke-hilkhata, 1^st ed., 1:29, n. 67).

Rav Auerbach: Nowadays, a Concern Exists

However, this approach is also the subject of some dispute.  First of all, the Magen Avraham (318:10) writes that the words of the Maharshal are not conclusive; he cites Acharonim who dispute this view and forbid to cook on a hot roof.  Secondly, according to Rav S.Z. Auerbach (Shemirat Shabbat Ke-hilkhata, ch. 1, n. 127), even when it comes to a solar heater there is a concern for error.  Nowadays, the solar heater generally contains a heating element (even if there is no such element, generally the tap in one’s home is also attached to a water source heated by electricity).  Thus, there is a concern that a person may open the tap at home and think that the water is coming from the solar heater, when the water is in fact being heated via electricity (which has the halakhic status of fire).  The concern is very significant, since even if the boiler is currently off, if before Shabbat the water had been heated by the electricity (and it is still hot due to this), the water remains an igneous byproduct, and there is a concern of violating the biblical prohibition of bishul.[7]

In Practice

Practically, it is best to avoid using a solar heater on Shabbat because of the concern that this device has the status of a solar byproduct, as well as the concern that one will confuse the water heated by this device with water heated by a boiler.  However, in a time of need (e.g., for the ill or for minors), one who is lenient about this has upon whom to rely (particularly when we are talking about a rabbinical doubt).[8]