Eur. Phys. J. Plus (2017) 132: 278
https://doi.org/10.1140/epjp/i2017-11583-8

Regular Article

Physical optimization of a wavy porous cavity filled by nanofluids in the presence of solar radiations using the Box-Behnken design (BBD)

¹ Department of Industrial Engineering, Esfarayen University of Technology (EUT), Esfarayen, North Khorasan, Iran
² Department of Material Engineering, Esfarayen University of Technology (EUT), Esfarayen, North Khorasan, Iran
³ Department of Mechanical Engineering, Esfarayen University of Technology (EUT), Esfarayen, North Khorasan, Iran

^* e-mail: m.hatami@xjtu.edu.cn

Received: 6 May 2017
Accepted: 4 June 2017
Published online: 26 June 2017

Abstract

In this paper, the physical optimization of a wavy porous cavity is evaluated while it is filled with nanofluids and under the solar radiation heat flux by using numerical and statistical methods. The effect of four parameters is discussed on the Nusselt number: Wavy amplitude ( , solar heat flux, Darcy number and Rayleigh number. To find the effect and interaction of these parameters on the heat transfer, a Box-Behnken design (BBD) is used and analysis is performed on the 27 experiments proposed by BBD. Analysis of variance (ANOVA) of the results revealed that solar heat flux and wave amplitude have a strong effect on the Nusselt number compared to Darcy and Rayleigh numbers. Finally, the response surface methodology (RSM) was applied to find the optimized case while its error was 0.002% in predicting the Nusselt number for the optimized case which confirms the high accuracy of results.