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Heat Transfer Research
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Heat Transfer Research

DOI: 10.1615/HeatTransRes.2018016177
pages 1299-1321

EFFECTS OF HEAT FLUX ON NATURAL CONVECTION OF WATER-BASED NANOFLUIDS IN A TRAPEZOIDAL ENCLOSURE

Xiaofeng Wang
School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang, Henan 453003, PR China; School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian 363000, PR China
Juntao Wang
School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang, Henan 453003, PR China
Weizhong Dai
Mathematics and Statistics, College of Engineering and Science, Louisiana Tech University, Ruston, LA 71272, USA

ABSTRACT

This study investigates natural convection heat transfer of water-based nanofluids in a trapezoidal enclosure where the left vertical side is heated with constant heat flux both partially and throughout the entire wall, the inclined wall is cooled, and the rest walls are kept adiabatic. The dimensionless governing equations were solved using a higher-order compact finite difference method, and solutions for algebraic equations were obtained through pesudo-time algorithms. Investigations of four types of nanofluids were made at different values of Rayleigh number Ra in the range 102 ≤ Ra ≤ 105, for the heat flux Ht lying in the range 0.2 ≤ Ht ≤ 0.8, enclosure aspect ratio AR within 1.5 ≤ AR ≤ 3.0, center position of a heater Υp in 0.3 ≤ Υp ≤ 0.7, solid volume fraction parameter Φ of nanofluids in the range 0% ≤ Φ ≤ 20%, and at the fixed angle φ = 45°. The results show that the maximum value of the local Nusselt number NuΥ and average Nusselt number Nu can be achieved for the highest Rayleigh number Ra, the smallest center position of the heater Υp, and the smallest enclosure aspect ratio AR. In addition, it was observed that the enhancement in heat transfer in the trapezoidal enclosure is much improved with increase of the solid volume fraction parameter Φ of nanofluids at a low volume fraction (Φ ≤ 10%), but opposite effects appear when the solid volume fraction parameter Φ is high (Φ > 10%). Moreover, multiple correlations in terms of the Rayleigh number Ra and the solid volume fraction Φ of nanoparticles have been established.


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