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Transactions on Engineering and Computing Sciences - Vol. 13, No. 1

Publication Date: February 25, 2025

DOI:10.14738/tecs.131.18300.

Koueni, T. C. A. (2025). Numerical Modeling of Temperature and Pressure Fields in an Enclosure with Two Openings in Natural

Convection. Transactions on Engineering and Computing Sciences, 13(1). 124-146.

Services for Science and Education – United Kingdom

Numerical Modeling of Temperature and Pressure Fields in an

Enclosure with Two Openings in Natural Convection

Koueni, Toko Christian Anicet

Department of Renewable Energy, ENSPM,

University of Maroua, P. O. Box 46 Maroua, Cameroon

ABSTRACT

This work numerically studies the temperature and pressure fields generated by a

solid heat source in an enclosure with an aspect ratio H/L = 0.82 having two

symmetrical low openings in natural convection. The enclosure has a height H = 520

mm, a length L = 630 mm and a width l = 210 mm. The heat source is cylindrical with

a diameter D0 = 20 mm and a length l = 210 mm. 04 values of the power per unit

length were imposed on the heat source corresponding to 04 reduced Rayleigh

numbers 0.59 × 1011, 1.78 × 1011, 2.19 × 1011 and 2.57 × 1011. 03 CAS 21, CAS 22,

CAS 23 enclosures different by the position of the heat source were studied. In CAS

21, the heat source is at position x+ = 0.24, in CAS 22 at x+ = - 0.24 and in CAS 23 at

position x+ = 0. The study was carried out in steady state. Numerical studies were

conducted by DNS considering that the heat source is at constant power per unit

length. Numerical results show that in CAS 23 and whatever the values of the

reduced Rayleigh number, the thermal plume is centered at a higher temperature

than that of the environment outside the plume. The thermal plume is generated by

turbulent natural convection. Its initial speed is a function of the speed of fresh air

entering the enclosure through the openings and its initial temperature is a

function of the reduced Rayleigh number. The gas movements at the openings are

created by the static pressure difference between the inside and outside of the

enclosure. In the CAS 21 enclosure, the thermal plume is deflected from x+ > 0 and

in CAS 22 from x+ < 0. This deflection of the thermal plume towards one of the side

walls of the enclosure may be due to the Coanda effect. The numerical results of the

temperature and the differential static pressure agree with the experimental

measurements.

Keywords: Enclosure with aspect ratio less than 1, Natural convection, Solid heat source,

Temperature fields, Pressure fields, Numerical calculation.

INTRODUCTION

Natural convection is a phenomenon of fluid mechanics, which occurs when a gradient induces

a movement in the fluid. The gradient can concern different intensive quantities such as

temperature ("thermal convection"). Since the density depends on the temperature, a

temperature gradient generates differences in density within the fluid, resulting in lateral

variations in the Archimedes' thrust which are at the origin of the movement. Such

displacements are called convection movements. These natural convection movements are

present in many industrial processes such as: pipes, electrical cabinets where they participate

in the cooling of electronic components, Le Masson et al. (2011) [1], transformers, sensors and

solar and electric dryers. They are also found in the building sector (offices, classrooms,

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Transactions on Engineering and Computing Sciences (TECS) Vol 13, Issue 1, February - 2025

Services for Science and Education – United Kingdom

Table 1: Rayleigh number reduced as a function of the power of the heat source

Φ (W/m) Ra*

100 0.59×1011

180 1.16×1011

275 1.78×1011

340 2.19×1011

400 2.57×1011

a b

c

Figure 1: Experimental devices a) CAS 23, b) CAS 22, c) CAS 21

These enclosures have a 03-dimensional orthonormal Cartesian axis system with center 0. The

(0x+) axis is the abscissa axis, the (0y+) axis is the ordinate axis and the (0z+) axis is

perpendicular to the plane formed by the (0x+) and (0y+) axes. The heat source is 3 mm above

the floor of the enclosures which are made of plexiglass of the same materials as all the other

walls of the enclosures. The floors have a thickness of 14 mm, identical to that of the ceilings of

the enclosures. The side walls are each 8 mm thick. The walls of the enclosures are assembled