Computational Heat Transfer and Fluid Dynamics

Modern advances in numerical methods have led to the rapid development of various fields of human activity, including microelectronics, mechanical engineering and medicine. A numerical analysis of heat transfer and fluid flow is extremely important to study the efficiency and overall performance of various types of energy system. Numerical simulations allow for real physical systems to be analyzed in detail without conducting a large number of expensive experiments. A comprehensive understanding of fluid flow and heat transfer mechanisms is necessary to the efficient and sustainable development of modern energy systems. In this regard, this Special Issue (SI) “Computational Heat Transfer and Fluid Dynamics” was proposed to highlight new advances in heat transfer and fluid flow.

This SI includes nine research papers focusing on heat transfer in single-phase or multi-phase systems (Contributions 1 to 3), vibration problems (Contribution 4), heat transfer in porous medium (Contribution 5), relativistic problems (Contribution 6), and new numerical approaches (Contributions 7 to 9). As a Guest Editor, I was pleased to receive articles from authors from different countries. The geographical distribution of the authors is presented in Figure 1.

To obtain a better understanding of the content of the SI, a word cloud was compiled. This cloud is a visual representation of the most frequently occurring phrases and words from the titles and abstracts of nine articles. The word cloud is shown in Figure 2. The content of this SI reflects the scientific community’s commitment to solving various problems through high-quality research. The main results of the published articles are presented below.

The numerical simulation of heat and mass transfer processes plays an important role in the construction industry. Thanks to modern computing capabilities, it is possible to carry out numerical calculations that help make modern buildings more energy-efficient. Natural convection and surface radiation inside a hollow brick consisting of four air voids were investigated by Miroshnichenko et al. (Contribution 1). The inner surfaces of the brick walls are considered diffuse gray; the air inside is considered diathermic. The authors used the finite difference method as a solution method. The paper considers the combined effect of convection, thermal conductivity, and radiation on heat transfer and the flow structure. The authors found that an increase in the emissivity of surfaces leads to an insignificant decrease in the intensity of the convective heat exchange, and a significant increase in the average radiation Nusselt number. Therefore, it is recommended to reduce the emissivity of the walls to reduce the overall heat transfer.

Huang et al. (Contribution 2) numerically studied heat transfer in bidisperse gas–solid systems using the discrete element method. The influence of the ratio of particle diameters and the ratio og large and small particles on the average particle temperature and the temperature distribution of each kind is studied in detail. The authors considered three different models of interfacial heat transfer in gas–solid bidisperse systems. They found that differences between the impact of these models on thermal transmission in bidisperse systems with a particle diameter ratio of up to 4 are negligible when the ratio of small and large particles is 1. Miroshnichenko and Sheremet (Contribution 3) numerically investigated turbulent heat transfer in a cavity with partition located on the bottom wall. The influence of the thermal conductivity coefficient of walls and baffle, surface emissivities, the Rayleigh number, and the height of the partition on heat transfer in the solution region was studied. It is shown that the average Nusselt numbers are increasing functions of the Rayleigh number and decreasing functions of the partition height. This paper also demonstrates the significant effect of radiation on heat transfer inside the cavity.

A numerical analysis of the phenomenon of liquid-induced vibration in the area of a bundle of convection tubes was carried out by Yao et al. (Contribution 4). The accuracy of the calculation model was confirmed by comparing the frequency of the formation of Karman vortices with the frequency of the standing wave of acoustic equipment. The main novelty of the work is that the frequency of formation of Karman vortices, obtained by numerical simulation in this work, is closer to the true value than that obtained by traditional calculation methods. Al Elaiw et al. (Contribution 5) studied the rotating flow of viscoelastic fluid together with a porous medium with Soret–Dufour effects. Thermophoresis and chemical reaction were taken into account in the concentration equation to study mass transfer in a liquid. The work carried out a comprehensive analysis of the influence of Biot, Soret and Dufour numbers. Possible technical applications of the work include hard disks, turbine systems and jet engines.

Siddiqi et al. (Contribution 6) investigated how a thermodynamical fluid space–time manifold develops when heat flux, heat energy density and heat stress are involved. The goal of this work was to analyze the thermodynamical development of the space–time manifold under the influence of some specific thermal characteristics. A simplified method for solving a one-dimensional heat conduction model under complicated boundary conditions was proposed by Wei et al. (Contribution 7). If the law of temperature change at the boundary is extremely complicated, then the authors propose using a new model developed by them, which makes it possible to obtain the correct results more efficiently.

A new approach to solving the problem of heat exchange in a solid body with temperature-dependent thermal conductivity in contact with a container filled with a liquid was proposed by Filipov et al. (Contribution 8). The authors propose reducing the problem to a one-dimensional one and considering only the stationary formulation. To solve the coupled PDE-ODE system, a new numerical method was proposed that reduces the system to the sequence of two-point boundary value problems. Saldanha da Gama (Contribution 9) proposed a new procedure for solving the problem of convective–radiative heat transfer in a non-convex body. It is known that a non-convex body can radiate radiant energy onto itself, so the authors considered fact when formulating the boundary conditions. This paper presents a very simple procedure for constructing a solution to a nonlinear heat transfer problem.

List of Contributions:

• Miroshnichenko, I.V.; Gibanov, N.S.; Sheremet, M.A. Numerical Analysis of Heat Transfer through Hollow Brick Using Fi-nite-Difference Method. Axioms 2022, 11, 37. https://doi.org/10.3390/axioms11020037
• Huang, Z.; Huang, Q.; Yu, Y.; Li, Y.; Zhou, Q. A Comparative Study of Models for Heat Transfer in Bidisperse Gas–Solid Systems via CFD–DEM Simulations. Axioms 2022, 11, 179. https://doi.org/10.3390/axioms11040179.
• Miroshnichenko, I.V.; Sheremet, M.A. Turbulent Free Convection and Thermal Radiation in an Air-Filled Cabinet with Partition on the Bottom Wall. Axioms 2023, 12, 213. https://doi.org/10.3390/axioms12020213.
• Yao, S.; Huang, X.; Zhang, L.; Mao, H.; Sun, X. Analysis and Prediction of Flow-Induced Vibration of Convection Pipe for 200 t/h D Type Gas Boiler. Axioms 2022, 11, 163. https://doi.org/10.3390/axioms11040163.
• Al Elaiw, A.; Hafeez, A.; Khalid, A.; AL Nuwairan, M. Swirling Flow of Chemically Reactive Viscoelastic Oldroyd-B Fluid through Porous Medium with a Convected Boundary Condition Featuring the Thermophoresis Particle Deposition and So-ret–Dufour Effects. Axioms 2022, 11, 608. https://doi.org/10.3390/axioms11110608.
• Siddiqi, M.D.; Mofarreh, F.; Siddiqui, A.N.; Siddiqui, S.A. Geometrical Structure in a Relativistic Thermodynamical Fluid Spacetime. Axioms 2023, 12, 138. https://doi.org/10.3390/axioms12020138.
• Wei, T.; Tao, Y.; Ren, H.; Lin, F. A Shortcut Method to Solve for a 1D Heat Conduction Model under Complicated Boundary Conditions. Axioms 2022, 11, 556. https://doi.org/10.3390/axioms11100556.
• Filipov, S.M.; Hristov, J.; Avdzhieva, A.; Faragó, I. A Coupled PDE-ODE Model for Nonlinear Transient Heat Transfer with Convection Heating at the Boundary: Numerical Solution by Implicit Time Discretization and Sequential Decou-pling. Axioms 2023, 12, 323. https://doi.org/10.3390/axioms12040323.
• Saldanha da Gama, R.M. The Heat Transfer Problem in a Non-Convex Body—A New Procedure for Constructing Solu-tions. Axioms 2023, 12, 338. https://doi.org/10.3390/axioms12040338.