**1. Introduction**

The paper contains a summary of successful invited papers addressed to the Special Issue on 'Numerical Heat Transfer and Fluid Flow', which were published in 2021 in the scientific journal '*Energies*'. Invitations were addressed to specialists from all over the world who deal with mathematical modeling, simulations, and experiments on heat and/or fluid flow. The submitted papers regarded the solution of problems of scientific and industrial relevance in a specific field of heat transfer and fluid transportation, including natural resources, technical devices, industrial processes, etc. Papers addressed to the Special Issue not only solved specific engineering problems, but served as a catalyst on future directions and priorities in numerical heat transfer and fluid flow. Most papers dealt with heat transfer in single-phase flow of air, in particular technical devices, while part of them regarded liquid and solid–liquid flows. Reliable predictions require reliable measurements; therefore, the majority of the papers presented experimental data and validation of mathematical models.

The importance of heat and fluid flow is still growing in all aspects of our lives, starting from nature and ending with industrial processes. In the era of digital transformation, which includes converting any process into a quantified format suitable for analysis, there is an increasing demand for modeling, simulations, and experiments on heat exchange in fluid flow for a variety of single and multiphase flows, and also boundary conditions [1]. Thanks to computational fluid dynamics and its commercial packages, especially Ansys, we can design and optimize various industrial processes. The increasing understanding of heat and mass transfer phenomena has contributed significantly to the development of new methods and techniques for solving and effectively managing many engineering processes.

Formulating any problem of prediction of heat transfer and/or fluid flow requires developing a physical model first. The next step is developing a mathematical model which fulfills the assumptions stated in the physical model and defines boundary and initial conditions. The mathematical model should be based on general governing equations, like continuity, Navier-Stokes, and energy equations. The equation set can be solved analytically—which is complicated and impractical—or numerically. If numerical methods are considered, we can use approaches like direct numerical simulation (DNS), for instance. Such a method is time-consuming, expensive, and not practical for many engineering applications. Other methods like, for instance, modelling of turbulence, which uses random averaged Navier-Stokes equations (RANS), or large eddy simulation (LES) were proved for a variety of engineering applications and are less time consuming and less expensive; however, the set of equations require closure. The problem of closure requires additional equation or equations, like those proposed by turbulence models. Requirements for turbulence models, formulated by the honorable founder of computational fluid dynamics (CFD), that is, Dudley Brian Spalding, are the following: universality, economy, extensionality, and reality [2,3]. The ability to simulate heat transfer and/or fluid flow, which includes velocity, pressure, and temperature distributions, for engineering purposes, remains one of the main challenges in CFD.

**Citation:** Bartosik, A.S. Numerical Heat Transfer and Fluid Flow: A Review of Contributions to the Special Issue. *Energies* **2022**, *15*, 2922. https://doi.org/10.3390/ en15082922

Received: 11 April 2022 Accepted: 14 April 2022 Published: 15 April 2022

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1

Considering the heat exchange between a transported fluid and the surrounding, we recognize methods and techniques focused on the enhancement of heat transfer, named passive or active. Passive methods, such as increasing heat transfer area and/or temperature difference, shaping an insert with dedicated perforation, or mechanically deformed pipes, have been studied for several years and have become commercial solutions [4–9]. Active methods, such as air injection, bubble or vortex generation, or proper pulsation, can lead to increased heat transfer coefficient, and, finally, can produce increased heat transfer process [10–13]. Some of such methods have been demonstrated by contributors to the Special Issue.
