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In this paper, we derive a boundary-domain integral formulation for the energy transport equation under the assumption that the fluid properties, through which the energy is transported by diffusion and convection, are spatially and temporally changing. The energy transport equation is a second-order partial differential equation of a diffusion-convection type, with the fluid temperature as the independent variable. The presented formulation does not require a calculation of the temperature gradient, thus it is, for a known fluid velocity field, linear.
The final boundary-domain integral equation is discretized using a domain decomposition approach, where the equation is solved on each sub-domain, while subdomains are joined by compatibility conditions. The validity of the method is checked using several analytical examples. Convergence properties are studied yielding that the proposed discretization technique is second-order accurate.
The developed method is used to simulate flow and heat transfer of nanofluids, which exhibit properties that depend on the solid particle concentration. A Lagrange-Euler approach is used.
boundary element method, energy transport equation, nanofluids, variable material properties
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