I have a failed obsolete adjustable voltage regulator (Motorola MFC 6030). Could this 6-terminal device be replaced with a modern 3-terminal voltage regulator? The regulator is used to drive the base of a pass transistor for a DC power supply. The power supply (Heatkit HWA-202-1) delivers 10 V DC to 15 V DC at 2 amps.
No, it will not.
For two reasons, one, which comes directly from the pinout/datasheet of the original device, and another that comes from experience.
The original device features a current sense pin, also hinted at by the low-value resistors across which it measures in the Heathkit schematic (oh, how I know those supplies well...). This protects from damage to the transistor as well as the transformer, because the original will drop the output voltage when the maximum current is exceeded. So, in the same setting the supply will no longer be sufficiently protected from damage.
The second reason is that a device designed to provide an output directly, proportionally measured through resistances or otherwise, is not optimised for an external pass-transistor.
The LM317 your title mentions is an excellent example of such a regulator. Its output is designed to be measured directly by its feedback pin. If you just willy-nilly add a pass-transistor before it's measured you may very well get instability and oscillations. These can cause your Transistor, Transformer or even Capacitors to blow up even before you try to take the full 2A from the device.
If you want to substitute the device, you need to find something that is indicated as a compatible substitute, or you need quite a bit more background information. You need to do analysis of the total effective resulting schematic and see if the phase-margin and total path gain across a range of frequencies are such that the device stays stable, or at least stable enough. And if not, add tuning paths to prevent oscillations at those frequencies that those values are not favourable.
Of course, you can simply try and see what happens, but you need to be fully prepared for unwanted consequences of any sort. And in any replacement not the actual original I would strongly suggest you use an oscilloscope to inspect all signals over several different known loads.
Most likely yes, your going from 20V-rms down to 13.8V so a 2A voltage regulator should be able to do that, but there is a caveat.
The voltage drop, which is 6.2V at full load with 2A that will be 12W (which may be a little lower if the 20VDC is really 20-18V or something like that). So if you do get a regulator, its going to have to need a package to handle the heat.
A simple (inefficient) AC to DC power supply circuit looks like this:
Which you already have the transformer and rectifier. The stage you will need to replace is the regulation stage, which in your case is done by Q1 and IC-1
There are probably better ways to handle this circuit, just ditch the whole thing and get a 13.8V wall wart that can source 2A, I'm willing to bet this circuit is not built up on a PCB to UL standards today. If you buy a wall wart this will be tested and will be less likely to kill you or burn your house down.
The last thing is they do have DC to DC regulators that are drop in replacements for voltage regulators, then you wouldn't have to deal with the heat.
You might find useful to use a fixed linear voltage regulator instead of an adjustable one. The LM78S15 gives 15V at 2A maximun, a little higher voltage than the 13.8V, but do the job without using adjusting resistors. Use this with a proper thermal dissipation and the proper caps at the input and output of regulator and it should work without any problem. If the 13.8V is a must then use the LM317, but in any case there's not a direct substitution to the MFC6030 and you will have to think how connect the new regulator to the circuit.