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A general analytical solution for fluid flow and heat convection through arbitrary-shaped triangular ducts: A
Amirhossein Hajiaghaei Tabalvandani1, Mahmood Norouzi1, Mohammad Hassan Kayhani1
1Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran.
Heliyon
|February 21, 2024
Summary
This study provides the first analytical solution for fluid flow and heat transfer in any triangular duct, crucial for industrial applications. It reveals how duct shape and Brinkman number impact heat transfer and flow characteristics.
Area of Science:
- * Fluid Dynamics
- * Heat Transfer
- * Applied Mathematics
Background:
- * Existing analytical solutions for fluid flow and heat transfer in ducts are limited to specific geometries, like isosceles triangles.
- * Non-circular channels, particularly triangular ducts, are prevalent in various industrial applications, necessitating a generalized solution.
- * There is a lack of analytical methods to address heat transfer in arbitrarily-shaped triangular ducts, considering viscous dissipation.
Purpose of the Study:
- * To develop the first analytical solution for fluid flow and heat transfer within arbitrarily-shaped triangular ducts.
- * To investigate the influence of duct geometry and the Brinkman number on flow and thermal behavior.
- * To analyze the critical Brinkman number's role in distinguishing cooling and heating regimes.
Main Methods:
- * Derivation of functionals for flow and heat transfer equations.
- * Application of the Ritz method to solve the resulting Euler-Lagrange equations.
- * Detailed analysis of velocity profiles, friction coefficients, temperature distributions, and Nusselt numbers.
Main Results:
- * An analytical solution for heat transfer in arbitrary triangular ducts with constant wall heat flux and viscous dissipation is presented.
- * The critical Brinkman number is identified as the point where the Nusselt number approaches infinity, differentiating cooling and heating.
- * Nusselt number decreases with increasing Brinkman number in both cooling and heating modes; equilateral triangles show minimal friction and maximal Poiseuille number.
Conclusions:
- * The developed analytical method provides a universal approach for heat transfer analysis in all triangular ducts.
- * Geometric parameters and viscous dissipation significantly influence fluid flow and heat transfer characteristics.
- * The findings offer valuable insights for optimizing thermal management in systems utilizing triangular channels.
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