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Heat Conduction Problems for Half-Spaces with Transversal Isotropic Gradient Coating Cover

Heat Conduction Problems for Half-Spaces with Transversal Isotropic Gradient Coating

Acta Mechanica et Automatica
Volume 19 (2025): Issue 2 (June 2025)
By: Roman KULCHYTSKYY-ZHYHAILO  
Open Access
|Jun 2025

Figures & Tables

Fig. 1.

The scheme of considered problem
The scheme of considered problem

Fig. 2.

The scheme of considered problem
The scheme of considered problem

Fig. 3.

Distributions of the temperature over the surface z = h (black lines and rhombi) and over z = 0 (grey lines and rhombi), dashed lines – the distributions of the temperature for the homogeneous half-space: 1 – κ2 = 1; 2 – κ2 = 5; n = 20
Distributions of the temperature over the surface z = h (black lines and rhombi) and over z = 0 (grey lines and rhombi), dashed lines – the distributions of the temperature for the homogeneous half-space: 1 – κ2 = 1; 2 – κ2 = 5; n = 20

Fig. 4.

Distributions of the radial heat flux along the surface z = h, dashed line – the distributions of the radial heat flux for the homogeneous half-space: 1 – κ2 = 1; 2 – κ2 = 5; n = 20.
Distributions of the radial heat flux along the surface z = h, dashed line – the distributions of the radial heat flux for the homogeneous half-space: 1 – κ2 = 1; 2 – κ2 = 5; n = 20.

Fig. 5.

Distributions of the temperature over the plane z = h (black lines and rhombi) and over the plane z = 0 (grey lines and rhombi), dashed lines – the distributions of the temperature for the isotropic homogeneous half-space with the heat conductivity coefficient K0: 1 – K2/K0 = 1; 2 – K2/K0 = 5 ; m = 10
Distributions of the temperature over the plane z = h (black lines and rhombi) and over the plane z = 0 (grey lines and rhombi), dashed lines – the distributions of the temperature for the isotropic homogeneous half-space with the heat conductivity coefficient K0: 1 – K2/K0 = 1; 2 – K2/K0 = 5 ; m = 10

Fig. 6.

Distributions of the radial heat flux on the cylindrical surface r = 1 (black lines and rhombi): fig. a) – K2/K0 = 1; fig. b) – K2/K0 = 5; grey line – the distribution of the average radial heat flux; vertical dashed line – the interface of the coating and base; m = 20; z′ = h – z
Distributions of the radial heat flux on the cylindrical surface r = 1 (black lines and rhombi): fig. a) – K2/K0 = 1; fig. b) – K2/K0 = 5; grey line – the distribution of the average radial heat flux; vertical dashed line – the interface of the coating and base; m = 20; z′ = h – z

Fig. 7.

Graphs of the function κ(z): continuous lines – coatings described in section C: 1 – K1/K0 = 0.2, K2/K0 = 1; 2 – K1/K0 = 0.2, K2/K0 = 5; dashed lines – coatings described in section A: 1 – κ2 = 1; 2 – κ2 = 5
Graphs of the function κ(z): continuous lines – coatings described in section C: 1 – K1/K0 = 0.2, K2/K0 = 1; 2 – K1/K0 = 0.2, K2/K0 = 5; dashed lines – coatings described in section A: 1 – κ2 = 1; 2 – κ2 = 5

Fig. 8.

Distributions of the average radial heat flux on the cylindrical surface r = 1 (coatings described in section C): 1 – K1/K0 = 0.2, K2/K0 = 1; 2 – K1/K0 = 0.2, K2/K0 = 5; m = 20; z′ = h – z
Distributions of the average radial heat flux on the cylindrical surface r = 1 (coatings described in section C): 1 – K1/K0 = 0.2, K2/K0 = 1; 2 – K1/K0 = 0.2, K2/K0 = 5; m = 20; z′ = h – z

Dependence of the dimensionless parameters Tsurmax=T(0,h)K0aq0 , Tintmax=T(0,0)K0aq0 , qr,surmax=qr(1,h)q0 on the dimensionless parameter κ2and number of the layers n

κ2nTsurmax εTsur,%Tintmax εTint,%qr,surmax εqsur,%
1∞1.4723 0.5847 0.4733
160 -0.0011 -0.0002 0.5103
80 -0.0036 -0.0007 0.9445
40 -0.0135 -0.0028 1.7952
20 -0.0537 -0.0113 3.4317
10 -0.2146 -0.0451 6.5039
5∞1.0200 0.3158 13256
160 -0.0017 -0.0007 0.4731
80 -0.0064 -0.0017 0.9078
40 -0.0252 -0.0054 1.7408
20 -0.1005 -0.0204 3.2928
10 -0.4007 -0.0799 6.0922

Dependence of the dimensionless parameters Tsurmax=T(0,h)K0aq0 , Tintmax=T(0,0)K0aq0 on the dimensionless parameter K2/K0 and number of the representative cells m

K2/K0mTsurmax εTsur,%Tintmax εTint,%
1∞1.5630 0.5420
80 0.1613 0.0992
40 0.3173 0.1965
20 0.6171 0.3854
10 1.1698 0.7407
5 2.1096 1.3661
5∞1.1164 0.3217
80 0.4999 0.2566
40 0.9858 0.5106
20 1.9225 0.9844
10 3.6628 2.0010
5 6.6678 3.8612
DOI: https://doi.org/10.2478/ama-2025-0023 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088
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Language: English
Page range: 197 - 204
Submitted on: Sep 5, 2024
Accepted on: Mar 23, 2025
Published on: Jun 6, 2025
Published by: Bialystok University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
heat conduction problem,
temperature,
heat flux,
transversal isotropic gradient coating,
multi-layered structure
Related subjects:
Engineering,
Electrical engineering,
Electronics,
Mechanical engineering,
Mechanics,
Bioengineering and biomedical engineering,
Biomechanics,
Civil engineering,
Environmental engineering

© 2025 Roman KULCHYTSKYY-ZHYHAILO, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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