2. Air at 50°C and essentially atmospheric pressure is flowing through a 10 cm x 10 cm rectangular duct at avelocity of 10 m/s. If the wall temperature of the duct is 25 °C, and the length of the duct is 50 m, calculatethe drop in the air temperature.

Answered: 2. Air at 50°C and essentially…

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

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2. Air at 50°C and essentially atmospheric pressure is flowing through a 10 cm x 10 cm rectangular duct at a
velocity of 10 m/s. If the wall temperature of the duct is 25 °C, and the length of the duct is 50 m, calculate
the drop in the air temperature.

Expert Solution

Step 1

Given that-

Length of duct, L=50 m

Average velocity, v_avg=10 m/s

Wall temperature, T_s=25⁰C

Cross-sectional area of duct, A=10cm x10cm =0.1mx0.1m=0.01 m²

Hence, the perimeter of the duct is-

$P = 2 \times (0.1 m + 0.1 m) = 0.4 m$

The initial temperature of air, T_i=50⁰C

The properties of air ( from standard data)-

$\begin{array}{rcl} ρ & = & 1.127 k g / m^{3} \\ C_{P} & = & 1007 J / k g^{0} C \\ k & = & 0.02662 W / m^{0} C \\ P_{r} & = & 0.7255 \\ v & = & 1.702 \times 10^{- 5} m^{2} / s \end{array}$

Further, the characteristic length is calculated as-

$D_{h} = \frac{4 A}{P} = \frac{4 \times 0.01 m^{2}}{0.4 m} = 0.1 m$

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2. Air at 50°C and essentially atmospheric pressure is flowing through a 10 cm x 10 cm rectangular duct at a velocity of 10 m/s. If the wall temperature of the duct is 25 °C, and the length of the duct is 50 m, calculate the drop in the air temperature.