[Noel_C]

Hello

What is the most cost effective way to increase the viscosity of
Silicon Oil so that it becomes less like a fluid and more like a gel?
The only area's of concern are that:

1: Thermal Conductivity is not decreased significantly
2: Cant react to metals, particularly Cu, Al
3: Should not emit toxic fumes or be dangerous to the user in general.

My second question relates to thermal conductivity. What is the most
cost effective pure oil in regards to thermal conductivity? The only
area's of concern are that:

1: It does not emit toxic rf unwanted scents
2: Does not react to metals such as Cu and Ai

Cheers!
Noel

[Enthalpy]

Welcome, Noel_C!

Silicone oil is available from the producers is nearly any viscosity, from water-thin to fat-thick. This is adjusted at production by the chain length. Maybe you could thicken an available oil by cross-linking it a little bit; silicone resins are sold with hardeners that act on silicone oils just the same way - it's only less direct than buying the needed viscosity.
https://www.bluestarsilicones.com/EN/Our_offer/KEC/ListInstance_Brochure_Title/FLD47_Brochure.pdf
http://www.behlke.com/pdf/wacker_silicone_oil.pdf
For instance Wacker offers a viscosity between 0.65 and 1,000,000 mm²/s.

The thermal conductivity depends little on the viscosity, as both docs tell:
it increases from 0.1W×m^-1×K^-1 for 0.65mm²/s oils to 0.15W×m^-1×K^-1 for 50mm²/s (as thick as a motor oil), then it's constant to 1,000,000 mm²/s. This is essentially as much as a mineral oil.

Though, this conductivity is the whole picture only when the material is immobile. With convection, natural or forced, the viscosity has its own importance, the heat capacity too.

----------

Oil with biggest thermal conductivity: the differences are small. Making a film thin, or moving a liquid better, make more difference than the material.
http://www.engineeringtoolbox.com/thermal-conductivity-liquids-d_1260.html
So water is an excellent cooling fluid because is stores much heat and, being thin, it reaches well the surfaces to be cooled. NaK is excellent thanks to its heat conductivity. But among noncorrosive, lubricating fluids, there is no miracle.

Toxicity, fumes, scents: at reasonable temperature, many compositions are possible, be it vegetable oil, mineral oil, silicone fluid, brake fluid... And at unreasonable temperature there is none.

Cu, Al: not difficult. Choose the proper alloy: AlMgSi rather than AlCu.

You didn't tell an important criterium: whether this oil shall lubricate. Silicone oils are catastrophic at that, many other fluids are bad, only mineral oils are good, water+PEG too, vegetable oils if properly used.

My suggestion as a cooling fluid would be a water-based oil, especially a polyethylene-glycol (PEG) hydraulic fluid like Hydrolube or similar: 0.45W×m^-1×K^-1. They are fully optimized and characterized and documented as hydraulic fluids, with decent lubricant properties, anticorrosion additives, antifoaming and anti-manythings, good viscosity index, and so on.
http://www.ilco-chemie.de/downloads/BREOX_HYDROLUBES_E.pdf