The answer to this question hinges on what you define as the "numerical effect" for a Potion of Giant Strength. The Dungeon Master's Guide defines the effects as
When you drink this potion, your Strength score changes for 1 hour. The type of giant determines the score.
It is easy to see that the new potion will last for 2 hours, since we simply double the duration.
In the case of the numerical effect, we can interpret the wording in the following ways:
The numerical effect is a change in Strength: Under this definition, the numerical effect of the potion is however much the imbibing creature's Strength score changes. Then, the combined effect would be to increase the creature's Strength score by this amount again (e.g. a character with a Strength of 18 drinks a combined Potion of Cloud Giant Strength (sets Strength to 27). The increase in this case is +9, so the doubled effect is +18 and the character has a new Strength of 36 for 2 hours)).
The numerical effect is "setting" the new Strength score: Under this definition, the numerical effect is just the character's strength score being set to a new one. Then, the combined effect would be identical to the normal effect (with a 2 hour duration), because doubling the effect would "set" the Strength to the same value, twice.
The numerical effect is what the new Strength score is: This is the scenario you defined in the question. If we consider the new Strength score to be the numerical effect, then doubling it would yield a truly stupendous result. Your hapless, alchemy-major wizard would suddenly be able to go toe-to-toe with the Tarrasque in a wrestling match, and deal 23 damage with each unarmed strike. You could also long-jump over 50 feet (the world record is a measly 29).
If the book instead said "when you drink this potion, your Strength score is increased," then the answer would be very clearly be case #1, as the numerical effect would be the difference between original score and new score. Instead, it says that your Strength score "changes", which is much more open to interpretation. The most literal result is then case #2, which is not very fun at all. For your game, it's really up to the DM to decide which of these is the right one.
In my opinion, case #1 is the best and most fair interpretation, case #2 is too disappointing, and case #3 is a little off-the-wall (but maybe that's what you were going for).