Explain the difference (in concept or definition) between boundary layer thickness and thermal boundary layer thickness?

Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
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Explain the difference (in concept or definition) between boundary layer thickness and thermal boundary layer thickness?
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difference (in concept or definition) between boundary layer thickness and thermal boundary layer thickness

 

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Boundary layer thickness

The boundary layer concept was originally developed by Ludwig Prandtl. The boundary layer refers to the thin transition layer between the wall and the bulk fluid flow. At the solid walls of the plate the fluid has zero velocity, but as one moves away from the wall, the velocity of the flow increases without peaking, and then approaches a constant mean velocity.

The boundary layer thickness, {\displaystyle \delta }, is the distance normal to the wall to a point where the flow velocity has essentially reached the 'asymptotic' velocity, {\displaystyle u_{e}}.  In terms of  the location {\displaystyle y_{99}}, denoted as {\displaystyle \delta _{99}} and given by

{\displaystyle u(x,y_{99})=0.99u_{e}(x)\quad ,}

as the boundary layer thickness.

For laminar boundary layer, flows along a flat plate channel, the {\displaystyle \delta _{99}} value is approximately given by

{\displaystyle \delta _{99}(x)\approx 5.0{\sqrt {{\nu x} \over u_{0}}}=5.0{x \over {\sqrt {\mathrm {Re} _{x}}}}\quad ,}

where {\displaystyle u_{e}\approx u_{0}} is constant, and where

{\displaystyle \mathrm {Re} _{x}} is the Reynold's number
{\displaystyle u_{0}} is the freestream velocity,
{\displaystyle u_{e}} is the asymptotic velocity,
{\displaystyle x} is the distance downstream from the start of the boundary layer, and
{\displaystyle \nu } is the kinematic viscosity.

For turbulent boundary layers along a flat plate channel, the boundary layer thickness, {\displaystyle \delta }, is given by

{\displaystyle \delta (x)\approx 0.37{x \over {\mathrm {Re} _{x}}^{1/5}}\quad .}
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