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A modified lumped capacitance method for transient heat transfer in a stirred tank with non-Newtonian fluid

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  • Tian, Fengguo
  • Zhan, Xiaoqiang
  • He, Hao
  • Liu, Shulei
  • Yang, Tao
  • Xiao, Honghai

Abstract

This work is focused on the transient heat transfer of non-Newtonian fluid in a coil-cooled stirred tank through experimental and numerical approaches. A modified lumped capacitance method was established for a more accurate definition of the time constant at a limited coolant flowrate. The modified method breaks down the time constant into two terms: the first term is based on the system heat transfer capability and the second one on the coolant heat transport capability. Limited by the assumption of an infinite cooling capability, the simple lumped capacitance method attributes all of the time constant solely to the first term. The significant difference between the two models results in fundamentally different derivations used to calculate the overall heat transfer coefficient. Theoretical analysis indicates that the modified method align harmoniously with its original form. The results manifest that: (1) Within the operating range of all tests, the second term contributes 26.5–12.9% to the total time constant as coolant flowrate increases, making it a significant factor that should not be overlooked. (2) The simple method underestimates the overall heat transfer capability by 15.4–29.2% compared to the modified one. It subsequently underestimates the coil external and internal convection coefficients by up to 12.8% and 70.6% in comparison to the modified model, respectively, compared to the modified model. (3) The CFD-predicted overall heat transfer coefficient, coil external convection coefficient, and coil internal convection coefficient deviate by a maximum of 15.2%, 7.2%, and 32.1% respectively compared to the experimental values obtained through the modified lumped capacitance method. By the way, the CFD-predicted coil internal convection coefficient closely aligns with the Nusselt correlation for straight tubes adjusted using Cr = 1.2. (4) A thorough analysis of CFD results reveals complex dynamics in stirred tanks, such as viscosity distribution patterns and areas of limited mass and heat exchange between middle and bottom impellers. This deep understanding enables root cause analysis crucial for optimizing configurations or designing uniquely structured tanks. (5) The revised lumped capacitance method expands on its original version by transitioning from assuming infinite cooling to accounting for limited transient cooling capacity. This shift is more realistic and crucial for thermal management and process control.

Suggested Citation

  • Tian, Fengguo & Zhan, Xiaoqiang & He, Hao & Liu, Shulei & Yang, Tao & Xiao, Honghai, 2024. "A modified lumped capacitance method for transient heat transfer in a stirred tank with non-Newtonian fluid," Applied Energy, Elsevier, vol. 368(C).
    • Handle: RePEc:eee:appene:v:368:y:2024:i:c:s0306261924008663
    DOI: 10.1016/j.apenergy.2024.123483
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