Research

Open AccessArticle

The Heat Transfer Problem in a Non-Convex Body—A New Procedure for Constructing Solutions

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Axioms 2023, 12(4), 338; https://doi.org/10.3390/axioms12040338 - 30 Mar 2023

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The subject of this work is the coupled steady-state conduction-radiation-convection heat transfer phenomenon in a non-convex blackbody, which is represented by a second-order partial differential equation (representing the heat conduction inside the body) subjected to nonlinear (and non-local) boundary conditions (due to the [...] Read more.

The subject of this work is the coupled steady-state conduction-radiation-convection heat transfer phenomenon in a non-convex blackbody, which is represented by a second-order partial differential equation (representing the heat conduction inside the body) subjected to nonlinear (and non-local) boundary conditions (due to the thermal radiation heat transfer). Moreover, anon-convex body emits thermal radiant energy to itself, which must be taken into account in the boundary conditions when high temperatures are involved. The unknown is the absolute temperature. A procedure is proposed for constructing the solution tothe problem by means of a sequence whose elements are obtained from linear problems, such asthe classical ones involving linear Robin boundary conditions. Full article

(This article belongs to the Special Issue Computational Heat Transfer and Fluid Dynamics)

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Open AccessArticle

A Coupled PDE-ODE Model for Nonlinear Transient Heat Transfer with Convection Heating at the Boundary: Numerical Solution by Implicit Time Discretization and Sequential Decoupling

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Axioms 2023, 12(4), 323; https://doi.org/10.3390/axioms12040323 - 24 Mar 2023

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Abstract

This article considers heat transfer in a solid body with temperature-dependent thermal conductivity that is in contact with a tank filled with liquid. The liquid in the tank is heated by hot liquid entering the tank through a pipe. Liquid at a lower [...] Read more.

This article considers heat transfer in a solid body with temperature-dependent thermal conductivity that is in contact with a tank filled with liquid. The liquid in the tank is heated by hot liquid entering the tank through a pipe. Liquid at a lower temperature leaves the tank through another pipe. We propose a one-dimensional mathematical model that consists of a nonlinear PDE for the temperature along the solid body, coupled to a linear ODE for the temperature in the tank, the boundary and the initial conditions. All equations are converted into a dimensionless form reducing the input parameters to three dimensionless numbers and a dimensionless function. A steady-state analysis is performed. To solve the transient problem, a nontrivial numerical approach is proposed whereby the differential equations are first discretized in time. This reduces the problem to a sequence of nonlinear two-point boundary value problems (TPBVP) and a sequence of linear algebraic equations coupled to it. We show that knowing the temperature in the system at time level n − 1 allows us to decouple the TPBVP and the corresponding algebraic equation at time level n. Thus, starting from the initial conditions, the equations are decoupled and solved sequentially. The TPBVPs are solved by FDM with the Newtonian method. Full article

(This article belongs to the Special Issue Computational Heat Transfer and Fluid Dynamics)

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Open AccessArticle

Turbulent Free Convection and Thermal Radiation in an Air-Filled Cabinet with Partition on the Bottom Wall

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Igor V. Miroshnichenko

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Mikhail A. Sheremet

Axioms 2023, 12(2), 213; https://doi.org/10.3390/axioms12020213 - 17 Feb 2023

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Abstract

Computational analysis is performed for turbulent free convection and surface thermal radiation in an air-filled cavity with solid obstacle on the bottom wall. A partition of finite thickness is considered, the position, length, and heat conductivity of which vary for certain values of [...] Read more.

Computational analysis is performed for turbulent free convection and surface thermal radiation in an air-filled cavity with solid obstacle on the bottom wall. A partition of finite thickness is considered, the position, length, and heat conductivity of which vary for certain values of the Rayleigh number. The coupled heat transmission by thermal radiation, free convection and heat conduction through the solid obstacle and walls is studied. The governing equations are solved by the finite difference method. This work also contains a detailed description of the computational grid thickening procedure. Temperature patterns and airflow field are scrutinized for some specific conditions using streamlines and isotherms. The overall heat transfer within the cavity is analyzed in terms of the mean convective and radiative Nusselt numbers, and many of the data are presented in detail for various partition positions, heat conductivities of the partition and walls of the cavity, and Rayleigh numbers. The results report that the participation of partitions within the cavities in the heat exchange processes decreases the overall heat transfer rate compared to the simpler case of cavities without partitions. Full article

(This article belongs to the Special Issue Computational Heat Transfer and Fluid Dynamics)

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Open AccessArticle

Geometrical Structure in a Relativistic Thermodynamical Fluid Spacetime

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Axioms 2023, 12(2), 138; https://doi.org/10.3390/axioms12020138 - 29 Jan 2023

Cited by 1 | Viewed by 546

Abstract

The goal of the present research paper is to study how a spacetime manifold evolves when thermal flux, thermal energy density and thermal stress are involved; such spacetime is called a thermodynamical fluid spacetime (TFS). We deal with some geometrical characteristics of [...] Read more.

The goal of the present research paper is to study how a spacetime manifold evolves when thermal flux, thermal energy density and thermal stress are involved; such spacetime is called a thermodynamical fluid spacetime (TFS). We deal with some geometrical characteristics of

T F S

and obtain the value of cosmological constant

Λ

. The next step is to demonstrate that a relativistic

T F S

is a generalized Ricci recurrent

T F S

. Moreover, we use

T F S

with thermodynamic matter tensors of Codazzi type and Ricci cyclic type. In addition, we discover the solitonic significance of

T F S

in terms of the Ricci metric (i.e., Ricci soliton

R S

). Full article

(This article belongs to the Special Issue Computational Heat Transfer and Fluid Dynamics)

Open AccessArticle

Swirling Flow of Chemically Reactive Viscoelastic Oldroyd-B Fluid through Porous Medium with a Convected Boundary Condition Featuring the Thermophoresis Particle Deposition and Soret–Dufour Effects

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Axioms 2022, 11(11), 608; https://doi.org/10.3390/axioms11110608 - 01 Nov 2022

Viewed by 603

Abstract

In this study, an analysis of the rotating flow of viscoelastic Oldroyd-B fluid along with porous medium featuring the Soret–Dufour effects is explored. The heat transport mechanism is discussed with the involvement of thermal radiation and heat source/sink. Additionally, the thermophoresis of particle [...] Read more.

In this study, an analysis of the rotating flow of viscoelastic Oldroyd-B fluid along with porous medium featuring the Soret–Dufour effects is explored. The heat transport mechanism is discussed with the involvement of thermal radiation and heat source/sink. Additionally, the thermophoresis of particle deposition and chemical reaction are taken into the concentration equation in order to investigate the mass transportation in the liquid. To formulate the non-linear ordinary differential equations, the von Karman similarity approach is used in the system of partial differential equations and then integrated numerically by the bvp midrich scheme in Maple programming. Results are provided by graphical framework and tabular form. A quick parametric survey is carried out concerning flow field, thermal, and solutal distributions through graph representation. The curves show that increasing the values of the retardation time parameter decreases the radial velocity while increasing the angular velocity. Additionally, when the relaxation time parameter becomes powerful, the magnitude of the velocity curves decreases considerably in the radial and axial directions. The presence of a radiation parameter indicates that the fluid will absorb a greater amount of heat, which is equivalent to a higher temperature. Further, an increase in the stretching parameter leads to a reduction in the temperature components. Full article

(This article belongs to the Special Issue Computational Heat Transfer and Fluid Dynamics)

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Open AccessArticle

A Shortcut Method to Solve for a 1D Heat Conduction Model under Complicated Boundary Conditions

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Axioms 2022, 11(10), 556; https://doi.org/10.3390/axioms11100556 - 14 Oct 2022

Cited by 1 | Viewed by 671

Abstract

The function of boundary temperature variation with time, f(t) is generally defined according to measured data. For f(t), which has a complicated expression, a corresponding one-dimensional heat conduction model was constructed under the first type of boundary [...] Read more.

The function of boundary temperature variation with time, f(t) is generally defined according to measured data. For f(t), which has a complicated expression, a corresponding one-dimensional heat conduction model was constructed under the first type of boundary conditions (Dirichlet conditions) in a semi-infinite domain. By taking advantage of the Fourier transform properties, a theoretical solution was given for the model, under the condition that f(t) does not directly participate in the transformation process. The solution consists of the product of erfc(t) and f(0) and the convolution of erfc(t) and the derivative of f(t). The piecewise linear interpolation equation of f(t), based on the measured data of temperature, was substituted into the theoretical solution, thus quickly solving the model and deriving a corresponding analytical solution. Based on the analytical solution under the linear decay function boundary condition, the inflection point method and curve fitting method for calculating the thermal diffusivity were introduced and exemplified, and the variation laws of the appearance moment of the inflection point were discussed. The obtained results show that the values of thermal diffusivity calculated by the two methods are basically consistent, and that the inflection point values rise with the increasing values of the initial temperature variation of the boundary, the decrease in boundary temperature velocity, and the distance from the boundary, respectively. Full article

(This article belongs to the Special Issue Computational Heat Transfer and Fluid Dynamics)

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Open AccessArticle

A Comparative Study of Models for Heat Transfer in Bidisperse Gas–Solid Systems via CFD–DEM Simulations

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Axioms 2022, 11(4), 179; https://doi.org/10.3390/axioms11040179 - 15 Apr 2022

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Abstract

In this study, flow and heat transfers in bidisperse gas–solid systems were numerically investigated using the computational fluid dynamics–discrete element method (CFD–DEM). Three different models to close the gas–solid heat transfer coefficient for each species of bidisperse systems were compared in the simulations. [...] Read more.

In this study, flow and heat transfers in bidisperse gas–solid systems were numerically investigated using the computational fluid dynamics–discrete element method (CFD–DEM). Three different models to close the gas–solid heat transfer coefficient for each species of bidisperse systems were compared in the simulations. The effect of the particle diameter ratio and particle number ratio between large and small particles on the particle mean temperature and temperature distribution of each species were systematically investigated. The simulation results show that differences in the particle mean temperature and temperature distribution profiles exist among the three heat transfer models at a higher particle number ratio. The differences between the effects of three heat transfer models on heat transfer properties in bidisperse systems with particle diameter ratios of up to 4 are marginal when the particle number ratio between small and large particles is 1. Full article

(This article belongs to the Special Issue Computational Heat Transfer and Fluid Dynamics)

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Open AccessArticle

Analysis and Prediction of Flow-Induced Vibration of Convection Pipe for 200 t/h D Type Gas Boiler

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Axioms 2022, 11(4), 163; https://doi.org/10.3390/axioms11040163 - 05 Apr 2022

Viewed by 1436

Abstract

This paper is aimed at the analysis and prediction of the fluid-induced vibration phenomenon in the convection tube bundle area caused by Karman vortex street shedding in the background of a 200 t/h large-capacity D-type gas boiler. Based on the numerical simulation of [...] Read more.

This paper is aimed at the analysis and prediction of the fluid-induced vibration phenomenon in the convection tube bundle area caused by Karman vortex street shedding in the background of a 200 t/h large-capacity D-type gas boiler. Based on the numerical simulation of flue heat state flow field and fast Fourier transform, the lift coefficient curve of different monitoring areas and the corresponding Karman vortex street shedding frequency are obtained. The accuracy of the analysis model is validated by comparing Karman vortex shedding frequency with acoustic equipment standing wave frequency. In order to meet the design requirements of the 200 t/h D-type gas boiler for reliable and stable operation, the vibration characteristics and variation rules of a convection tube bundle in a D-type boiler under different working conditions are predicted. Full article

(This article belongs to the Special Issue Computational Heat Transfer and Fluid Dynamics)

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Open AccessArticle

Numerical Analysis of Heat Transfer through Hollow Brick Using Finite-Difference Method

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Igor V. Miroshnichenko

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Nikita S. Gibanov

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Mikhail A. Sheremet

Axioms 2022, 11(2), 37; https://doi.org/10.3390/axioms11020037 - 19 Jan 2022

Cited by 2 | Viewed by 1561

Abstract

The goal of the present work is to develop and test in detail a numerical algorithm for solving the problem of complex heat transfer in hollow bricks. The finite-difference method is used to solve the governing equations. The article also provides a detailed [...] Read more.

The goal of the present work is to develop and test in detail a numerical algorithm for solving the problem of complex heat transfer in hollow bricks. The finite-difference method is used to solve the governing equations. The article also provides a detailed description of the procedure for thickening the computational grid. The flow regime inside the hollow brick is turbulent, which is a distinctive feature of this work. As a rule, if the size of the cavities in the brick is greater than 20 cm and the temperature difference in the considered solution region is significant, then the numerical solution can be obtained in the turbulent approximation. The effect of surface emissivities of internal walls on the thermal transmission and air flow inside hollow brick is investigated. The distributions of isolines of the stream function and temperature are obtained. The results report that the emissivity of interior surfaces significantly affects the heat transfer through hollow bricks. Full article

(This article belongs to the Special Issue Computational Heat Transfer and Fluid Dynamics)

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