Question

The velocity of flow over a flat plate is doubled. Assuming the flow remains laminar over the entire plate, what is the ratio of the new thermal boundary layer thickness to the original boundary layer thickness?

Answer 1

Given:

laminar flow

and since velocity of flow is doubled, we consider
`v_(n)` as new velocity and
`v_(o)` as original velocity

Explanation:

As per laminar flow, thickness, t is given by

t =
`(4.91x)/(\sqrt( R_(ex)) )`

t =
`\frac{4.91x}{\sqrt{(\rho vx)/(\mu )}}`

t =
`(4.91x\mu )/(√(\rho vx))`

where,

`R_(ex)` = Reynold's no.

therefore,

t ∝
`(1)/(√(v) )`

Now,

`(t_(n) )/(t_(o) )` =
`\sqrt{((v_(o) )/(v_(n) ))}`

`(t_(n) )/(t_(o) )` =
`\sqrt{((v_(o) )/(2v_(o) ) )} =(1)/(√(2) )`

therefore,

`t_(n):t_(o) = 1:√(2)`