Optimising thermal design for cross flow heat exchanger in fan coil units

ABSTRACT

Analytical and numerical solutions for determining the dimensions of a cross-flow heat exchanger under different conditions have been developed in this study. The analytical solution using the ε-NTU method is used to find the initial dimensions of the cross-flow heat exchanger. The numerical solution is used to validate the analytical solution and optimise the cooling coil dimensions. The ε-NTU design results show the effect of water mass flow rate, air inlet velocity, and the outer tube diameter of the cooling coil. The distribution of air and water temperatures through the heat exchanger can be predicted by solving the basic Navier-Stokes equation and energy equation using numerical methods.

KEYWORDS:

• Cross flow
• heat exchanger
• ε-NTU
• fan coil unit
• thermal design

Nomenclature

A	=	Area [m2]
C	=	Heat capacity rate [W/oC]
C1, C2, m	=	Constant
cp	=	Specific heat [J/kg.oC]
d	=	Diameter [m]
H	=	Height of the heat exchanger [m]
h	=	Heat transfer coefficient [W/m2. oC]
k	=	Thermal conductivity [W/m. oC]
L	=	Length of the tube [m]
$\dot{m}$	=	Mass flow rate [kg/s]
Nr	=	Number of rows
Nui	=	Inner Nusselt number
Nuo	=	Outer Nusselt number
Pr	=	Prandtl number
q	=	Heat transfer rate [W]
Re	=	Reynolds number
SL	=	Longitudinal distance between tubes [m]
ST	=	Transverse distance between tubes [m]
T	=	Temperature [oC]
u	=	Velocity [m/s]
U	=	Overall heat transfer coefficient [W/m2. oC]
W	=	Depth of the heat exchanger [m]
Greek symbols	=
∇	=	Laplace operator
Pr	=	Prandtel number
Δ	=	Difference
ε	=	Effectiveness
μ	=	Dynamic viscosity [N.s/m2]
ν	=	Kinematic viscosity [m2/s]
ρ	=	Density [kg/m3]
Subscripts	=
a	=	Air
c	=	Cold fluid
h	=	Hot fluid
i	=	Inner surface
in	=	Inlet
o	=	Outer
out	=	Outlet surface
w	=	Water
Abbreviations	=
ADTM	=	Actual dry bulb temperature method
CFD	=	Computational fluid dynamic
EDTM	=	Equivalent dry bulb temperature method
FCU	=	Fan coil units
HVAC	=	Heat ventilation air-condition
LMED	=	Log mean enthalpy difference
NTU	=	Number of thermal unit

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data presented in this study are available in this article.

Additional information

Funding

This research received no external funding.

Notes on contributors

Ahmed M. Hassan

Ahmed M. Hassan is a Ph.D. research scholar at Mechanical Engineering Department, University of Al-Qadisiyah, Al-Diwaniyah, 58001, Iraq. He holds M.Sc. (2019) and Ph.D. (2023) degree in Mechanical Engineering from the University of Babylon. Research Activity includes: Heat transfer, Solar energy, Phase change, and Heat exchanger.

Adil Abbas Alwan

Adil A. Alwan was born in Hilla city, Babylon, Iraq in year 1956. He obtained his B.Sc. degree in Mechanical Eng. from University of Technology, Iraq, at 1978. His M.Sc. degree from Glasgow University, Scotland, UK.at 1989. His Ph.D. degree from University of Technology, Iraq, at 2002. He published more than 75 papers in the field of Heat transfer and laser applications. He supervisors more than 40 students for Ph.D. and M.Sc. degree. He is working as professor in National University of Science and Technology, Dhi Qar, Iraq

Hameed K. Hamzah

Hameed K. Hamzah was born in Babylon city in 1976. He obtained his B.Sc. degree in Mechanical Engineering from university of Babylon, IRAQ 1999, MSc. Degree from university of Babylon, IRAQ in 2002, and PhD. degree from university of Babylon, IRAQ in 2016. He published more than 50 paper in top level journals in the fields of heat transfer and fluid flow. He Worked now as professor of Mechanical engineering at the university of Babylon, IRAQ.