# Natural convection process endorsed in coaxial duct with Soret/Dufour effect

Syed Saqib Shah (Department of Computer Science, Bahria University, Islamabad, Pakistan)
Hakan F. Öztop (Department of Mechanical Engineering, Technology Faculty, Firat Universitesi, Elazig, Turkey and Department of Mechanical Engineering, King Abdulaziz University, Jeddah, Saudi Arabia)
Rizwan Ul-Haq (Department of Electrical Engineering, Bahria University Islamabad Campus, Islamabad, Pakistan)
Nidal Abu-Hamdeh (Department of Mechanical Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia; K.A. CARE Energy Research and Innovation Center, King Abdulaziz University, Jeddah, Saudi Arabia and Energy Efficiency Group/Center of Research Excellence in Renewable Energy and Power Systems, King Abdulaziz University, Jeddah, Saudi Arabia)

ISSN: 0961-5539

Article publication date: 23 May 2022

Issue publication date: 3 January 2023

39

## Abstract

### Purpose

The purpose of this paper is to analyse the buoyancy flow, mass and heat transfer in coaxial duct under Soret and Dufour effect. The combined effects of the thermal-diffusion and diffusion-thermo coefficients, as well as the Schmidt number, on natural convection in a heated lower coaxial curve were explored using the proposed physical model. The Dufour and Soret effects are taken into consideration in the energy and concentration equations, respectively.

### Design/methodology/approach

The dominating mathematical models are converted into a set of non-linear coupled partial differential equations, which are solved using a numerical approach. The controlling non-linear boundary value problem is numerically solved using the penalty finite element method with Galerkin’s weighted residual scheme over the entire variety of essential parameters.

### Findings

It was observed that different parameters were tested such as heat generation or absorption coefficient, buoyancy ratio, Soret coefficient, Dufour coefficient, Lewis number and Rayleigh number. Effect of Rayleigh number, absorption/generation and Dufour coefficient on isotherm are significantly reported. For greater values of Lewis number, maximum mass transfer in duct in the form of molecular particles is produced. Buoyancy ratio parameter decreases the average rate of heat flow and increases its mass transfer.

### Originality/value

The main originality of this work is to make an application of Soret and Dufour effects in a coaxial duct in the presence of source sink.

## Acknowledgements

Data availability statement: The data that support the findings of this study are available from the corresponding author upon reasonable request.

## Citation

Shah, S.S., Öztop, H.F., Ul-Haq, R. and Abu-Hamdeh, N. (2023), "Natural convection process endorsed in coaxial duct with Soret/Dufour effect", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 1, pp. 96-119. https://doi.org/10.1108/HFF-02-2022-0106

## Publisher

:

Emerald Publishing Limited

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