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Investigations of heat transfer, entropy generation and pressure build up for upward flow in a vertical channel equipped with a fin array

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Abstract

The optimal thermal systems design criteria by maximizing the amount of heat transfer per pressure losses is a very important topic. In this work, flow and convection and radiation heat transfer characteristics are studied numerically for a flow in a vertical channel equipped with transverse fin array. The influences of fin height on heat transfer characteristics and fluid flow is investigated. Large number of fins is used (40 fins) in order to reach the fully developed conditions after few fins from the entrance. Based on the calculated data of temperature and velocity, the local entropy generation is calculated through the whole channel by solving the entropy generation equation. The results are validated against the available data in the literature and both results are in a good agreement. Optimizations for flow conditions and channel geometry are performed in order to obtain maximum heat transfer per pumping power losses. The results showed that the highest values of total heat transfer per pumping power losses are obtained at fin height to the gap width values of 0.1 and 0.3. The effect of heat transfer by radiation on entropy generation is examined and, the effect of the ratio, Gr/Re2, on the pressure field is also investigated. It was found that a positive pressure gradient appears downstream in the channel when the value of Gr/Re2 exceeds a certain limit. For Gr/Re2 values between 0 and 9, the pressure gradient is negative; however, when the value Gr/Re2 exceeds 9, the pressure starts to build up through the channel axis.

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Abbreviations

CFD:

Computational fluid dynamics

2-D:

Two dimensional

DO:

Discrete ordinates radiation model

Dh :

Hydraulic diameter (mm)

e:

Fin height (mm)

\(\Gamma_{\Phi }\) :

Diffusion coefficient (m2/s)

Gr:

\({\text{Grashofs}}\;{\text{number}} = \frac{{g\beta (T_{1} - T_{0} )D_{h}^{3} }}{{\upsilon^{2} }}\)

H:

Channel width (distance between the two plates) (mm)

Pr:

Prandtls number

Re:

Reynolds number

RTE:

Radiative transfer equation

I v :

The spectral radiation intensity

c:

The speed of electromagnetic wave in vacuum (m/s)

κ v :

The spectral absorption coefficient (1/m)

Φ v :

The phase function

n v :

The spectral index of refraction of the medium

I bv :

The Planck’s spectral blackbody intensity of radiation

σ v :

The scattering coefficient

\(S_{\Phi }\) :

Source term in the conservation equations (kg/m3/s)

To :

Ambient temperature (cold plate temperature) (K)

T1 :

Heated plate temperature (K)

\(\bar{U}_{j}\) :

The mean axial velocity (m/s)

\(u_{j}\) :

The fluctuating axial velocity (m/s)

\(\bar{\rho }\) :

Fluid density (Kg/m3)

uo :

Inlet velocity (m/s)

S′′′:

Rate of entropy generation (kW/K)

\(\overline{\theta }\) :

Dimensionless temperature

S″:

Entropy generation at each cross section (kW m2/K)

\(\Phi\) :

The dependent variable in the general conservation equation

Υ:

Kinematic viscosity (m2/s)

Φ v :

The phase function (isotropic function)

c :

Speed of electromagnetic wave in vacuum (m/s)

κ v :

Spectral absorption coefficient (1/m)

n v :

Spectral index of refraction of the medium (1)

σ v :

Scattering coefficient (1/m)

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Acknowledgments

This project was funded by the National Plan for Science, Technology and Innovation (MAARIFAH)-King Abdulaziz City for Science and Technology through the Science & Technology Unit at King Fahd University of Petroleum & Minerals (KFUPM)-the Kingdom of Saudi Arabia, award number (14-ENE58-04).

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Authors and Affiliations

  1. KACST TIC on CCS and Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Medhat A. Nemitallah

  2. Mechanical Engineering Department, Alexandria University, Alexandria, 21544, Egypt

    Medhat A. Nemitallah

  3. Mechanical Engineering Department, Tabbin Institute for Metallurgical Studies, Cairo, Egypt

    Alaa E. Zohir

Authors
  1. Medhat A. Nemitallah
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  2. Alaa E. Zohir
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Correspondence to Alaa E. Zohir.

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Nemitallah, M.A., Zohir, A.E. Investigations of heat transfer, entropy generation and pressure build up for upward flow in a vertical channel equipped with a fin array. Heat Mass Transfer 52, 1953–1961 (2016). https://doi.org/10.1007/s00231-015-1718-9

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