### Combined Free And Forced Convection In An Inclined Channel With Discrete Heat Sources

#### Abstract

It is studied in this work the mixed convection in an inclined rectangular channel.

Three constant heat sources q’ with finite lengths are flush mounted on the bottom surface of

a channel, while the remaining part of this surface is kept isolated. The upper wall is cooled

at a constant cold temperature Tc. At the inlet, the flow has constant velocity Uo and

temperature To profiles. The Reynolds number, the Grashof number, and the channel

inclination angle are ranged as follows: 1 ≤ Re ≤ 1000, 103 ≤ Gr ≤105, e 0° ≤ γ ≤ 90°,

respectively. The system of the governing equations is solved using the finite element method

with the Penalty formulation on the pressure terms and the Petrov-Galerkin perturbations on

the convective terms. Three comparisons are carried out to validate the computational code.

It is observed that the inclination angle has a stronger influence on the flow and heat transfer

for low Reynolds numbers, especially when it is between 0° and 45°. The cases which present

the lowest temperature distributions on the modules are those where the inclination angles

are 45° and 90° with little difference between them. The case where Gr = 105 and Re = 1000

is an exception where γ = 0° is the best channel inclination.

Three constant heat sources q’ with finite lengths are flush mounted on the bottom surface of

a channel, while the remaining part of this surface is kept isolated. The upper wall is cooled

at a constant cold temperature Tc. At the inlet, the flow has constant velocity Uo and

temperature To profiles. The Reynolds number, the Grashof number, and the channel

inclination angle are ranged as follows: 1 ≤ Re ≤ 1000, 103 ≤ Gr ≤105, e 0° ≤ γ ≤ 90°,

respectively. The system of the governing equations is solved using the finite element method

with the Penalty formulation on the pressure terms and the Petrov-Galerkin perturbations on

the convective terms. Three comparisons are carried out to validate the computational code.

It is observed that the inclination angle has a stronger influence on the flow and heat transfer

for low Reynolds numbers, especially when it is between 0° and 45°. The cases which present

the lowest temperature distributions on the modules are those where the inclination angles

are 45° and 90° with little difference between them. The case where Gr = 105 and Re = 1000

is an exception where γ = 0° is the best channel inclination.

#### Full Text:

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Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**