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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

Fig. 2.

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

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.

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

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

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

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

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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