I have an old electrical system. And I have a separate breaker set up for dryer and the box uses the round fuses. There are 3 wires. Red wire goes to one fuse, Black wire goes to a second fuse, and White wire looks to be ground. The 2 round fuses are 30 amp TL. Only the black one keeps blowing. My wife tried a 30a T and blew 2 in one day. We average blowing 1 a week from black. But there are days we can do 5 loads and have no problem. Last night the black one blew out again, and I took one from the red and put it in the black and the dryer turned on but didn't warm up the dryer(no fuse was in the red one). Ideas? Can I go down to a 20A reset one and it might blow more often but I can just reset it, or what would you recommend?

Can I go down to a 20A reset one
No.

In the past clothes dryers required a 240 volt circuit. All the components were engineered to use 240 volts. The more modern dryer require a 120/240 volt circuit.

I took one from the red and put it in the black and the dryer turned on but didn't warm up the dryer(no fuse was in the red one)
The heating element requires 240 volts (provided through the red and black hot conductors) and the other components require 120 volts (provide through one of the hot conductors (in your case the black) and the neutral.) That is why when you put a fuse in the black circuit only the motor would run but the heating element did not heat up. There was no 240 volt circuit because you did not fuse the red side.

I do not wish to be unkind but you need a better understanding of your electrical service. You have two hot conductors and a neutral conductor coming into your home. Each hot conductor has 120 volts, however they are in opposite halves of the cycle. You might think of them as, when one is positive the other is negative. Voltage is the difference in electrical potential. Since the neutral has no voltage, the difference in the neutral and 120 positive is 120 volts. Likewise the difference in the neutral and 120 negative is 120 volts. Therefore, the difference in electrical potential of 120 positive and 120 negative is 240 volts.

The components of you dryer that require 240 volts are connected to the two hot conductors (red and black) for a complete circuit. The components that require 120 volts are connected to one of the hots (in your case the black) and the neutral for a complete circuit. Obviously there is a greater amperage draw on the black leg.

The usual wiring for a residential dryer is 10/3 with ground cable and a 30 amp breaker or fuse. The rated amperage of the appliance determines the minimum size wiring and the wiring determines the maximum breaker. The purpose of the breaker or fuse is to protect the wiring. The amperage draw of the appliance would determine the minimum size breaker or fuse that would work.

You cannot increase the size of the breaker or fuse because the wiring is not rated for anything higher than 30 amps. You could decrease the size of the fuse but normal use of the dryer requires more than 20 amps. The 20 amp fuse would blow every time.

On the dryer, usually around the door, there will be an electrical nomenclature tag which specifies the voltage and the amperage draw. You will find the amperage draw to be 240 volts and about 25 amps.

You need to determine why you are blowing the fuse. It could be a fault in the dryer or it could be a fault in the wiring. Because it is consistently the black leg you will find a short to ground between the black and ground, a short between the black and neutral or a short between black and red. Because you do not blow the fuse every time the dryer is use it will most likely be caused by something that moves. Meaning that it is most likely in the dryer but could be in some wire that is moves during normal use of the dryer. Check inside the receptacle box.
Inside the dryer it could be some loose connection that is contacting the frame or it could be a defective part. Look for burn marks.

You must find the fault and correct, not try to work around it.

Not unkind at all. I don't know AC electricity at all DC I know there is a positive and negative. I am good with DC but never worked with AC. Your comment was helpful. I'll check all the connections are tight and get back with you. Thank you so much for replying. One other question, the dryer was fine at our old house where it had 4 prong outlet. Here there is only a 3 prone 220 outlet and we used a 3 prong wire. Could it be that? In the mean time I'll look for burn marks and tighten all connections. Thanks again.

The only difference between the 3 and 4 is an extra neutral wire, should not affect the power.

If you did not have this problem at previous residence, and you change plug from 4 prong to 3, check your work. Look for possibility of conductor touching one another. Next check inside the receptacle box. If box is metal make sure that terminals screws cannot touch box. It can be a pretty tight with a receptacle that large. Check wiring between fuse disconnect and receptacle.

If wiring is concealed and you are unable to find any defect, as a temporary measure you can purchase some 10/3 with ground cable and a plastic box. Remove receptacle connect the new cable to it in the new box. Remove fuses and connect the new cable just as the old cable is connected. Plug in the dryer and use the temporary cable for period to confirm whether the old cable is defective at some place you do not have access to.

Edit
In your post you said there was a red, black and white wire at the fuse disconnect. Assuming that there is also a ground, you could have replace the 3 prong receptacle with a 4 prong receptacle instead of replacing the cord. Pull receptacle and tell me what wires are there. You may find an unconnected ground or white wire that is moving around.