Consider a fluid flowing in turbulent flow at velocity (v), inside a pipe diameter (D) and undergoing heat transfer to the wall. Find the dimensionless groups relating the heat transfer coefficient (h), to the variables diameter (D), density (, viscosity (, heat capacity (c), thermal conductivity (k) and velocity (v). (a) Use four variables D, k, and v as the core variables common to all the dimensionless groups and identify some of them by known names of Nusselt number (Nu), Reynolds number (Re) and Prandtl number (Pr). That is, show that Nusselt Number = f (Reynolds Number, Prandtl Number). (b) State without proof, a similar dimensionless numbers expression (equation) for mass transfer process involving the diffusivity (D) of A and B components terms of the Sherwood number (Sh) and Schmidt number (Sc) to estimate the mass transfer coefficient as Nu 2.0+ 0.60 (NR)°³ (Npr)" for a flow past a single sphere for the estimation of the mass transfer coefficient. = Re 0.5 Hint: See section 4-14-1 of the fourth edition or section 15.1C of the fifth edition of the class text on using Buckingham theorem for finding dimensionless groups that relate to variables involve.
Consider a fluid flowing in turbulent flow at velocity (v), inside a pipe diameter (D) and undergoing heat transfer to the wall. Find the dimensionless groups relating the heat transfer coefficient (h), to the variables diameter (D), density (, viscosity (, heat capacity (c), thermal conductivity (k) and velocity (v). (a) Use four variables D, k, and v as the core variables common to all the dimensionless groups and identify some of them by known names of Nusselt number (Nu), Reynolds number (Re) and Prandtl number (Pr). That is, show that Nusselt Number = f (Reynolds Number, Prandtl Number). (b) State without proof, a similar dimensionless numbers expression (equation) for mass transfer process involving the diffusivity (D) of A and B components terms of the Sherwood number (Sh) and Schmidt number (Sc) to estimate the mass transfer coefficient as Nu 2.0+ 0.60 (NR)°³ (Npr)" for a flow past a single sphere for the estimation of the mass transfer coefficient. = Re 0.5 Hint: See section 4-14-1 of the fourth edition or section 15.1C of the fifth edition of the class text on using Buckingham theorem for finding dimensionless groups that relate to variables involve.
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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Transcribed Image Text:Consider a fluid flowing in turbulent flow at velocity (v), inside
a pipe diameter (D) and undergoing heat transfer to the wall.
Find the dimensionless groups relating the heat transfer
coefficient (h), to the variables diameter (D), density (, viscosity
(, heat capacity (c), thermal conductivity (k) and velocity (v).
(a) Use four variables D, k, and v as the core variables common
to all the dimensionless groups and identify some of them by
known names of Nusselt number (Nu), Reynolds number (Re)
and Prandtl number (Pr). That is, show that Nusselt Number = f
(Reynolds Number, Prandtl Number).
(b) State without proof, a similar dimensionless numbers
expression (equation) for mass transfer process involving the
diffusivity (D) of A and B components terms of the Sherwood
number (Sh) and Schmidt number (Sc) to estimate the mass
transfer coefficient as Nu 2.0+ 0.60 (NR)°³ (Npr)" for a flow
past a single sphere for the estimation of the mass transfer
coefficient.
=
Re
0.5
Hint: See section 4-14-1 of the fourth edition or section 15.1C of
the fifth edition of the class text on using Buckingham theorem
for finding dimensionless groups that relate to variables involve.
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