Q:

What is a tesla turbine and how is it different from other turbines(like pelton or francis turbine)?

I came accross this word tesla turbine while reading about the applications of boundary layer flow but couldn't find much details of such turbine anywhere.

A:

While "conventional turbines operate by imparting impulse or reaction energy from an incoming fluid using "buckets" or spiral surfaces on the turbine "runner", a "Tesla Turbine" is a bladeless or "drag turbine". A Tesla turbine's disks are bladeless and essentially smooth and the "drag" from boundary layer interaction of the fluid passing over the essentially smooth disk surfaces imparts energy from the fluid flowing across the disk surface. 
A simplistic view of boundary layer effect is that in a stream of fluid flowing across a surface, immediately adjacent to the surface the fluid is stationary, at some distance away from the surface the fluid is at or close to its mean velocity and the velocity varies from zero to mean across the intervening "boundary layer".  Moving from a simplistic to "somewhat accurate" model of boundary later effects can take as much of your life as you are willing to give it - but good approximations are available.
Wikipedia
Many useful glimpses ...
In practice a Tesla Turbine consists of two or more rotating disks mounted on one shaft with fluid injected between the disks.   Fluid is injected (usually) tangentially at the disk outer edge and spirals towards the centre as it imparts energy by "drag" to the disks either side of it that it is flowing between.
The inverse of the turbine is the Tesla pump, which imparts energy to the fluid by boundary layer drag as the disk rotates as fluid is supplied to the disk surface. 
As with most of Tesla's legacy, there are some good practical useful ideas involved and/but there is a lot of hype rubbish and misinformation surrounding them.
A Tesla Turbine or pump is able to achieve reasonably good efficiency compared to an impulse or reaction transfer equivalent, providing flow is essentially laminar across the disk surfaces. When flow is turbulent efficiency falls. Laminar flow is maintained only at relatively low interdisk spacings which also limits the absolute flow rate or power available for a given size. Many devices which use the basic principle claim laminar flow while not achieving it. This includes a relatively recent Kickstarter project which claimed laminar flow and quite a lot of other "magic stuff" but just reading their own provided material revealed the contradictions.

Phoenix [Tesla] Turbine builder club - USEFUL CHARTS & DATA - Much from Tesla directly.  USE WITH CARE. His comment cited from that site confirms my above comments about throughput and efficiency, without mentioning laminar flow per se. 

"Owing to a number of causes affecting the performance, it is difficult to frame a precise rule which would be generally applicable, but it may be stated that within certain limits, and other conditions being the same, the torque is directly proportionate to the square of the velocity of the fluid relatively to the runner and to the effective area of the disks and, inversely, to the distance separating them. The machine will, generally, perform its maximum work when the effective speed of the runner is one-half of that of the fluid; but to attain the highest economy, the relative speed or slip, for any given performance should be as small as possible. This condition may be to any desired degree approximated by increasing the active area of and reducing the space between the disks."

Their links page - TTs and more - useful. 

Wikipedia - TTs - reasonable.

I've only skimmed it quickly but it looks like quite a good practical feel for the TT could be obtained from this 1950 PhD thesis - typewritten and rather hard to read, but looks useful.
THE DESIGN, CONSTRUCTION AND INVESTIGATION OF A TESLA TURBINE

PESWIKI
Instructables DIY using hard disk platters.

