Note the very very (lfe savingly) important aspect of HRC = "High rupture capacity" fuses, discussed at the end.
You have done a fairly good job of summarising both the reasons and the dilemmas involved.
Fast blow are used where possible, where the fuse can be sized such that typical faults will always cause it to blow but nuisance blowing is rare. Suh situations have little or no startup surges or large occasional current excursions.
Slow blow are used where large short term transients are known to occur and if sizing of the fuse to accommodate the transients will result in inadequate protectionm against typical faults.
Where neither fast or slow blow fuses offer adequate protection (transients are very high but faults may be relatively low compared to maximum usual) then a cicuit breaker can be used, whose characteristics can be mapped accurately to a desired time/current profile.
Fast blow is the "more ideal" where possible.
Circuit current is well defined within known limits,
Start up transients are not so large compared to typical current that allowing for them is going to cause problems.
Fault currents are liable to be much much larger normal operate current and much larger than expected transients.
Slow blow is a compromise that allows protection while accommodating expected transient behaviour.
Startup or other transients may occur which cause much higher than average currents but for short periods.
Sizing a fast-blow fuse to allow the transients would result in a fuse which may not provide protection during some expected fault conditions.
The ideal may be both a fast and slow blow fuse in series (very unusual and possibly also illegal for regulatory reasons) or a circuit breaker with a well defined current versus time "envelope".
Regulatory requirements often make it clear which sort of fuse must be used.
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HRC / High Rupture capacity.
In some situations fault conditions can develop which can result in fault currents vastly in excess of the normal operating current and so high that massive destruction to property or loss of life may occur. An excellent example is a multimeter intended or measuring AC mains voltages of 230 VAC or higher. A meter measuring nominal 230 VAC mains voltages may easily be exposed to over 330 VDC peak, and transients on the waveform may cause much higher voltages to occur. A domestic range/stove/oven may be supplied with two phases with phase to phase voltages of 400 VAC or approaching 600 VDC peak to peak.
In either case above, if these voltages break down circuitry in the meter, an arc may occur followed rapidly by carbonisation of components, PCB, nearby case etc and a relatively low resistance across mains short may occur. The mains may then be supplying a high energy load vastly in excess of what is expected or designed - at least kilowatts with ease and tens of kilowatts in some cases. The onset of arc formation and generation of heat can be so rapid as to cause an explosion of th equipment with debris being ejected violently and with electric shock hazard also increasing.
Standing in the gap to this happening is "the fuse".
Edit: Actually, the fuses in multimeters are used to protect the current measuring circuitry. The voltage measurement stuff is protected by MOVS and PTCs.
If the fuse is able to blow and stay functionally blown when such a fault occurs the meter etc 'just stops working". if the fuse holder arcs and the PCB carbonises or the fuse otherwise fails to interrupt current, then the above scenario can occur. And does.
People have died due to this scenario and will die in future
An answer is the use of an HRC fuse which is designed to "rupture" in suh a way that a damaging arc does not form and the circuit is cleanly broken.
HRC fuses are usually ceramic bodied, usually white.
Not all white or ceramic fuses are HRC.
Not all HRC fuses are white or ceramic.
Image below shows fuses said by makers to be HRC. note that one is glass bodied.
( From here.)
Many HRC fuse images and links here.
Test equipment intended for AC mains use will usually specify HRC fuses. DO NOT SUBSTITUTE inferior types.
I have only ever had one meter fail under high voltage high energy conditions.
That was on a 1000 VDC range with a 1200 ior so VDC transmitting power supply being measured.
Very impressive.
A good lesson.
Long long ago.
Cheap multimeters often have their high end ACV ranges marked "not for mains use" or similar. That's why.
If you use them on mains you usually won't die.
But if you do, you won't be able to say that you weren't warned.
Remember that before you can't !!!
The "speed", rupture capability, and voltage spec of a fuse are each separate traits that aren't necessarily related. They will be specified according to the nature of the application.
Many cheap multimeters (i.e. <50$us) will only have glass fuses, because they're cheaper. But 'high rupture' capability (the ability to break a circuit up to a rated voltage, when a high fault current is flowing) is important in a multimeter (and in a circuit breaker), especially in a DC scenario, because DC >40V can easily form an arc and continue the current flow, even though the fuse has blown.
For the "20A" fuse in your meter, a HRC type would be wise, and rated for the max V rating of your multimeter, and same speed as the original.
Best Answer
The breaking capacity of a fuse specifies the maximum current which the fuse is guaranteed to be able to interrupt if a fault should occur.
The fuse you use must have a breaking capacity greater than the maximum possible current which can be delivered from the source it is connected to.
This has little or no relation to the amount of current normally consumed by the device being fused!
You haven't specified whether it is the input or the output of your buck converter which you are fusing, and the considerations are different for each case.
So if you're fusing the output, then the breaking capacity of the fuse should be greater than the maximum amount of current which your buck converter can supply.
If you're fusing the input to the converter, then the breaking capacity should be greater than the maximum amount of current which the source of that supply can deliver.
If your supply is a normal mains power outlet, then you can safely assume that there is a circuit breaker somewhere upstream of you and it is probably rated for something in the region of 20A - so your fuse must have a breaking capacity of no less than this.
If you use a fuse with a lower breaking capacity value than the amount of current which the source can supply, you risk the possibility that when an over-current condition occurs, you fuse will 'blow' but the current will arc over the blown fuse and continue to flow until it is manually shut off.
I discovered all of this the hard way much earlier in my career when I used a tiny fuse (100mA rating with a breaking capacity of maybe 50A) because the device I had built only drew a small current from the mains supply.
Unfortunately for me I didn't take into account that my tiny circuit would be connected to some very heavy industrial supplies and the one time something went wrong, the breaking capacity of the fuse I had chosen was woefully inadequate to interrupt the huge fault current (many 100's or even 1000's of A) - my little circuit was turned into a charred lump and the entire factory's electricity was shut off ...