# Effect of surface radiation on natural convection in an asymmetrically heated channel-chimney system

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## Abstract

In this paper, a more realistic numerical approach that takes into account the effect of surface radiation on the laminar air flow induced by natural convection in a channel-chimney system asymmetrically heated at uniform heat flux is used. The aim is to enrich the results given in Nasri et al. (Int J Therm Sci 90:122–134, 2015) by varying all the geometric parameters of the system and by taking into account the effect of surface radiation on the flows. The numerical results are first validated against experimental and numerical data available in the literature. The computations have allowed the determination of optimal configurations that maximize the mass flow rate and the convective heat transfer and minimize the heated wall temperatures. The analysis of the temperature fields with the streamlines and the pressure fields has helped to explain the effects of surface radiation and of the different thermo-geometrical parameters on the system performances to improve the mass flow rate and the heat transfer with respect to the simple channel. It is shown that the thermal performance of the channel-chimney system in terms of lower heated wall temperatures is little affected by the surface radiation. At the end, simple correlation equations have been proposed for quickly and easily predict the optimal configurations as well as the corresponding enhancement rates of the induced mass flow rate and the convective heat transfer.

## Nomenclature

*Ar*channel aspect ratio (

*Ar*=*h*/*b*)*b*channel width (m)

*b*^{'}chimney width (m)

*B*expansion ratio (

*B*=*b*^{'}/*b*)*Er*extension ratio (

*Er*=*h*^{'}/*h*)*g*acceleration due to the gravity (m.s

^{−2})*G*dimensionless mass flow rate

*h*channel height (m)

*h*^{'}chimney height (m)

*h*_{c}convective heat transfer coefficient (W.m

^{−2}.K^{−1})*h*_{r}radiative heat transfer coefficient (W.m

^{−2}.K^{−1})*n*_{x},*n*_{z}numbers of grid points in

*x*− and*z*−directions*Nu*_{c}local convective Nusselt number

*Nu*_{r}local radiative Nusselt number

*Nu*_{ac}average convective Nusselt number

*Nu*_{ar}average radiative Nusselt number

*p*pressure (Pa)

*P*dimensionless pressure

*Ρr*Prandtl number

*q*heat flux (W.m

^{−2})*q*_{r}radiative heat flux (W.m

^{−2})*Ra*Rayleigh number

*Ra*^{∗}modified Rayleigh number (

*Ra*^{∗}=*Ra*/*Ar*)*t*dimensionless time

*t*^{'}time (s)

*T*dimensionless temperature

*u*,*w*velocity component along (

*x*,*z*)-direction (m.s^{−1})*U*,*W*dimensionless velocity components

*x*,*z*cartesian coordinates (m)

*X*,*Z*dimensionless coordinates

## Greek symbols

*α*thermal diffusivity (m

^{2}.s^{−2})*β*coefficient of volumetric expansion (K

^{−1})- Δ
difference between two values

*ε*emissivity

*θ*temperature (K)

*υ*kinematic viscosity (m

^{2}.s^{−1})*ρ*density (Kg.m

^{−3})*λ*thermal conductivity (W.m

^{−1}.K^{−1})

## Subscripts

*0*ambient

*a*average

*c*convective

- max
maximum value

*opt*optimum value

*r*radiative

*Sc*Simple channel

*w*wall

## Notes

### Acknowledgements

We thank the reviewers for their remarks which allow to improve the paper. We also thank Mr. Xavier Chesneau (Maître de Conférence à l’UPVD) for his advice.

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