![]() Heat conduction, also called diffusion, is the direct microscopic exchanges of kinetic energy of particles (such as molecules) or quasiparticles (such as lattice waves) through the boundary between two systems. While these mechanisms have distinct characteristics, they often occur simultaneously in the same system. Engineers also consider the transfer of mass of differing chemical species (mass transfer in the form of advection), either cold or hot, to achieve heat transfer. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy ( heat) between physical systems. A hot, less-dense lower boundary layer sends plumes of hot material upwards, and cold material from the top moves downwards. Colors span from red and green to blue with decreasing temperatures. For test (v), the computed surface-averaged Nusselt numbers agree well with published results.Simulation of thermal convection in the Earth's mantle. Comparison between numerical results and analytical solutions in tests (i)–(iv) shows that the heat transfer is second-order accurate for straight boundaries perpendicular to one of the discrete lattice velocity vectors, and first-order accurate for curved boundaries due to the irregularly distributed lattice fractions intersected by the curved boundary. Several numerical tests are conducted to validate the applicability and accuracy of the proposed heat transfer evaluation scheme, including: (i) two-dimensional (2D) steady-state thermal flow in a channel, (ii) one-dimensional (1D) transient heat conduction in an inclined semi-infinite solid, (iii) 2D transient heat conduction inside a circle, (iv) three-dimensional (3D) steady-state thermal flow in a circular pipe, and (v) 2D steady-state natural convection in a square enclosure with a circular cylinder at the center. The proposed heat transfer evaluation scheme does not require a determination of the normal heat flux component or a surface area approximation on the boundary thus, it is very efficient in curved-boundary simulations. For lattice models with square or cubic structures and uniform lattice spacing the effective surface area is constant for each discrete heat flux, thus the heat flux integration becomes a summation of all the discrete heat fluxes with constant effective surface area. Integration of the discrete boundary heat fluxes with effective surface areas gives the heat flow rate across the boundary. The boundary heat fluxes in the discrete velocity directions of the TLBE model are obtained using the given thermal boundary condition and the temperature distribution functions at the lattice nodes close to the boundary. Journal of Verification, Validation and Uncertainty QuantificationĪn efficient and accurate approach for heat transfer evaluation on curved boundaries is proposed in the thermal lattice Boltzmann equation (TLBE) method.Journal of Thermal Science and Engineering Applications.Journal of Offshore Mechanics and Arctic Engineering.Journal of Nuclear Engineering and Radiation Science.Journal of Nondestructive Evaluation, Diagnostics and Prognostics of Engineering Systems.Journal of Nanotechnology in Engineering and Medicine.Journal of Micro and Nano-Manufacturing.Journal of Manufacturing Science and Engineering.Journal of Engineering Materials and Technology.Journal of Engineering for Sustainable Buildings and Cities.Journal of Engineering for Gas Turbines and Power.Journal of Engineering and Science in Medical Diagnostics and Therapy.Journal of Electrochemical Energy Conversion and Storage.Journal of Dynamic Systems, Measurement, and Control. ![]()
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