Answered: Explain the difference (in concept or…

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

Chapter1: Introduction

Section: Chapter Questions

Problem 1.1P

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

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 $\delta _{99}$ value is approximately given by

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

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

\mathrm {Re} _{x}

is the Reynold's number

u_{0}

is the freestream velocity,

u_{e}

is the asymptotic velocity,

x

is the distance downstream from the start of the boundary layer, and

\nu

is the kinematic viscosity.

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

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

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