Parallel and Counterflow Heat Exchangers

Mass flow rates (kg/s): Hot

0.3

Cold

0.3

Heat exchanger length (m):

Hot fluid:

Flow type:

Directions

Details

About

Directions

This simulation calculates the heat transfer rate and temperature profiles in a concentric tube heat exchanger that can be operated in either parallel or countercurrent flow (selected with Flow type dropdown menu). The cold fluid, liquid water fed at 300K, flows through the center of the tube, and the hot fluid, which is fed at 400K, flows through the annular region. The type of hot fluid (liquid water, air, or liquid sodium) is selected from the dropdown menu. Hot and cold fluid flow rates are selected with sliders. The heat exchanger length is changed using the slider.

Details

The temperatures of the hot stream $T_h $ and the cold stream $T_c $ of the heat exchanger are calculated from these differential equations:

$$ C_h\frac{dT_h}{dz} = -U\pi d_i(T_h \ - \ T_c) $$

for parallel flow:

$$ C_c\frac{dT_c}{dz} = U\pi d_i(T_h \ - \ T_c) $$

for countercurrent flow:

$$ C_c\frac{dT_c}{dz} = -U\pi d_i(T_h \ - \ T_c) $$

where $C_j = \dot{m}_jCp_j $, with $\dot{m}_j $ is the mass flow rate $(kg/s)$, $Cp_j $ is heat capacity $(J/[kg K] )$. $z $ is the length down the heat exchanger $(m)$, $U $ is the overall heat transfer coefficient ($W/[m^2 K]$) and $d_i$ is the inner diameter $(m)$.

The overall heat transfer coefficient is calculated using the heat transfer coefficients of the cold $\eta_c$ and hot $\eta_h$ streams:

$$ U = (\frac{1}{\eta_c} \ + \ \frac{1}{\eta_h})^{-1} $$

The heat transfer coefficients are calculated from Nusselt correlations. The Reynolds number is:

$$ Re_j = \frac{\dot{m}_j}{\mu_j \ \pi/4 \ d_j} $$

where $\mu_j$ is the dynamic viscosity $([N \ s]/m^2)$, $d_j$ is the diameter $(m)$ where $j$ is $c$ or $h$ for the cold or hot streams. The diameter of the tube that the cold fluid flows through is $d_c \ = \ d_i$, and the hydraulic diameter of the annulus that the hot fluid flows through is $d_h \ = \ d_o \ - \ d_i$, where $d_o$ is the outer diameter.

For turbulent flow $(Re_j \ \gt \ 10,000)$, the Dittus-Boelter correlation for the Nusselt number is used:

$$ Nu_j \ = \ 0.023Re_j^{4/5}Pr_j^n $$

otherwise, $Nu_j = 4.36$ is used for laminar flow.

Where $Pr_j^n = \frac{Cp_j \ \mu_j}{k_j}$ is the Prandtl number, $k_j$ is the thermal conductivity $(W/[m \ K])$, $n = 0.4$ for heating and $n = 0.3$ for cooling.

The heat transfer coefficients for each stream are calculated from $Nu_j = \frac{\eta_j \ d_j}{k_j}$

References:

T. L. Bergman, A. S. Lavine, F. P. Incropera and D. P. DeWitt, Introduction to Heat Transfer, 6th ed., Hoboken: John Wiley and Sons, 2011.

About

This simulation was created in the Department of Chemical and Biological Engineering, at University of Colorado Boulder for LearnChemE.com by Rachael Baumann under the direction of Professor John L. Falconer, with additional contributions Nathan S. Nelson, and was converted to HTML5 by Patrick Doyle, with additional contributions by Neil Hendren. Address any questions or comments to learncheme@gmail.com. All of our simulations are open source, and are available on our LearnChemE Github repository.

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