I wonder why you are not intersted in a possible interaction between "time" and "number". I would consider this relevant (but I am not an expert here!). But maybe it is worth giving it a thought anyway...

You best use a mixed effects model, using "time" and "number" as fixed effects and "subject" as random effect.

Make sure that the assumptions about the errors are resonable. This depends on the kind of DV you have. You say that it is "continuous", but this says nothing about what error model would be appropriate (gamma? beta? gaussian? something else?). Some rational basis to find an appropriate error model may be to know if your DV are concentrations, rates, proportions, angles, etc. and/or if there are limits of the variable (like "values must be positive" or "values must be smaller than 100" etc.). Finally a residual analysis can give additional hints. You may also consider transformations, to linearize relationships or to get feasable error model (like logarithms of the DV turn a multiplicative error model [that is difficult to treat] into an additive [that is simple to treat]).

I agree that the best option is to run a mixed effect model. Just in case you are not familiarize with  the spss way of doing mixed, which is very unfriendly I paste you a link that maybe help you .... I usually run R or Rstudio in my analyses and use a web that we developed to help our student to run their analyses..

https://sites.google.com/site/ullrtoolboxeng/

1. Check the installation page

2. Check the Anova multi-factorial page

3. Check the Mixed page for doing the best possible analyses

If you have any query please contact me..

Thank you very much for your replies!

My DV is a rate between 0-1.

I am also interested in the interaction between time and number, but my main interest is to understand the differences of Number conditions for each Time; and how each Number Condition evolves among Time Condition.

For these goals, would it be wrong/invalid to conduct separate Friedman tests?

For example: For Time 2, compare the 3 Number conditions. For Time 3, compare the 3 Number conditions. And so on. And then, for Number 1, compare the Time conditions; and the same for the others?

I know I would not obtain the interaction between these two variables across all the experiment, but would it be valid?

Regarding the mixed effects model, since Time*Number result in 15 conditions, would the number of participants (30) be a problem?

Seperate anayses won't anser the question for interaction and they would make suboptimal use of the available data.

Friedman tests are rank-based (as far as I recall) so they won't you tell anything sensible about the relevant things (i.e. about effect sizes).

Rates (with values bounded between 0 and 1) are best nalyzed using the beta error model (search for "beta-regression"). If these rates are based on known numbers of events, a binomial model could be used instead.

Definitely a mixed model regression is called for.  Regarding your dv, I suggest a logit transform as a reasonable alternative to beta regression, but you'll have to see if it works for your rate data.  Don't do separate Friedmans without an omnibus test first (which you can only do with a mixed model).