How to calculate cooling time of a sphere when only knowing T_start, t_ambiant, and the material of the sphere? I'm helping an artist making a giant gel blob and we wanna know how long it takes for it to cool down. For simplicity let's assume its a uniformly heated (T_start = 70 degrees) water sphere (radius = 1 m) and the ambient temperature is constant all the way around it at say T_ambient = 25 degrees celciuls. How long would it take to cool it to 30 degrees?  I asume the gradiant will change over time and make a decreasing exponential function and asymptotically aproch 25 degrees eventualy. But how long for it to reach 30 degrees starting at 70?
Since I don't know aleady how long it will take I guess I can't use newtons cooling law since I can't calculate the cooling coeficient without knowing the cooling time or can I?. Or can I look up the coeficient up somewhere?
or is there an other way?
(it would be nice to know how time depends on radius or on mass? )
I found this video: https://www.youtube.com/watch?v=XEyOk4brcZg
But here i again need some coeficients.
 A: Sounds like a neat project.
The terms you want search for is probably Transient heat conduction of a sphere. The link is similar to the you tube video. In terms of heat transfer I think:

*

*Radiation terms are mostly negligible. You can check with this hyperphysics link.Hyperphysics cooling calculator


*Convection will be important - so if you cool with a fan you will get a different rate than if it is just natural conduction.


*Conduction could be important. - You don't describe how the gel is held. So if it is in a spherical shell you have an additional layer and boundary condition. If there is a lot of contact with the floor or some kind of base then you could lose heat through the base.


*Not knowing anything about how you make your gel if the sphere is large you could get some type of convection in the container initially.


*As the gel goes from being a liquid to a gel, the heat transfer properties are likely to change, so this in detail could be a nonlinear problem.


*If you spray cooler water on it, or otherwise speed up the cooling by using a fan analytically the problem is more difficult becasue of evaporation or the convection coefficient being different on different points of the sphere.
Since you are trying to make a blob, perhaps the above doesn't matter a lot if all you want is a quick estimate. In that case Newtons law of cooling is perhaps not a bad way to go, for at least smaller blobs. You also have the curves from the analytical solution, so you might be able to do a couple of experiments and get a rough idea.
Wolfram has a calculator but you would still need to figure out the coefficients you want to plug into the calculator.
I haven't used it for heat transfer, but Fusion 360 is free software and it has a thermal module that includes convection, it might be suitable for problem like this.
