Question

Why do we use a short wire in fuse and not long wire if we know that more is the length more is the heat produced

Answer 1

For a fuse the area to length ratio is important as resistance is directly proportional to l/A.
As a long wire requires a lot of space inside the fuse housing it is better to use a short thin wire instead of long thick wire as both have the same resistance. The shorter one saves space. For the design of a fuse the upper current limit, time for blowing and power dissipation inside the fuse body are important factors.