# Unsteady double-diffusive buoyancy-induced flow in a triangular solar collector shape enclosure with corrugated bottom wall: Effects of buoyancy ratio

M.M. Rahman (Department of Mathematics, BUET, Dhaka, Bangladesh and Department of Mathematical and Computing Sciences, Universiti Brunei Darussalam, Gadong, Brunei)
Sourav Saha (Department of Mechanical Engineering, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh)
Satyajit Mojumder (Department of Mechanical Engineering, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh)
Khan Md. Rabbi (Department of Mechanical Engineering, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh)
Hasnah Hasan (Department of Mathematical and Computing Sciences, Universiti Brunei Darussalam, Gadong, Brunei)
Talaat A. Ibrahim (Vice Presidency for Projects, King Saud University, Riyadh, Saudi Arabia and Mechanical Power Eng. Dept., Faculty of Engineering-Mattaria, Helwan University, Cairo, Egypt)

ISSN: 0961-5539

Article publication date: 5 June 2017

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## Abstract

### Purpose

The purpose of this investigation is to determine the nature of the flow field, temperature distribution and heat and mass transfer in a triangular solar collector enclosure with a corrugated bottom wall in the unsteady condition numerically.

### Design/methodology/approach

Non-linear governing partial differential equations (i.e. mass, momentum, energy and concentration equations) are transformed into a system of integral equations by applying the Galerkin weighted residual method. The integration involved in each of these terms is performed using Gauss’ quadrature method. The resulting non-linear algebraic equations are modified by the imposition of boundary conditions. Finally, Newton’s method is used to modify non-linear equations into the linear algebraic equations.

### Findings

Both the buoyancy ratio and thermal Rayleigh number play an important role in controlling the mode of heat transfer and mass transfer.

### Originality/value

Calculations are performed for various thermal Rayleigh numbers, buoyancy ratios and time periods. For each specific condition, streamline contours, isotherm contours and iso-concentration contours are obtained, and the variation in the overall Nusselt and Sherwood numbers is identified for different parameter combinations.

## Acknowledgements

The authors extend their appreciation to the International Scientific Partnership Program ISPP at King Saud University for funding this research work through ISPP# 0012.

## Citation

Rahman, M.M., Saha, S., Mojumder, S., Rabbi, K.M., Hasan, H. and Ibrahim, T.A. (2017), "Unsteady double-diffusive buoyancy-induced flow in a triangular solar collector shape enclosure with corrugated bottom wall: Effects of buoyancy ratio", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 6, pp. 1282-1303. https://doi.org/10.1108/HFF-03-2016-0085

## Publisher

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Emerald Publishing Limited