Application of Combined Micro- and Macro-Scale Models to Investigate Heat and Mass Transfer through Textile Structures with Additional Ventilation
Abstract
:1. Introduction
2. Materials and Methods
2.1. The Representative Volume Element
2.2. Mathematical Model and Assumptions
2.2.1. Determination of Thermal Resistance
2.2.2. Mesh Analysis
2.3. Development of a Micro-Scale Model
Algorithm 1. Pseudocode of Newton’s method for nonlinear equations. |
1: Choose a starting guess x0 and accuracy є. 2: for k = 0, 1, 2, … do 3: compute the correction Solve by the direct solver. 4: update the solution guess . 5: if < є then 6: stop. 7: end if 8: end for Note. For highly nonlinear problems, a damped update of the form can be used, with 0 < α < 1 where α is a damping parameter. |
2.4. The Macro-Scale Model
3. Results and Discussion
3.1. Mesh Analysis
3.2. Thermal Resistance Evaluation at a Micro-Scale
3.3. Combined Forced Ventilation Micro- and Macro-Scale Models
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Model | Length and Width of Domain a × b (mm) | Height of Air Domain H (mm) | The Thickness of the Textile Layer h (mm) | Length and Width of Pore c × d (mm) | Distance between Two Layers of Textile e (mm) |
---|---|---|---|---|---|
Model 1_c | 1.1 × 1.1 | 10 | 0.439 | 0.263 × 0.263 | - |
Model 1_e | 1.1 × 1.1 | 10 | 0.439 | 0.263 × 0.263 | 3.06 |
Model 2_e | 0.98 × 0.98 | 10 | 0.438 | 0.195 × 0.195 | 3.06 |
Model 3_e | 0.85 × 0.85 | 10 | 0.468 | 0.155 × 0.155 | 3.06 |
Interface | Surface | Boundary Condition | Description |
---|---|---|---|
Fluid flow | on ∂Ωinlet | Qsv- standard flow rate is 0.8 dm3/min. | Inlet boundary condition was used to apply the mass flow rate, where stands for the fluid flow domain boundary thickness, the standard density is defined as In this investigation, the standard temperature Tst = 20 °C, mean molar mass of the fluid (0.032 kg/mol), R—the universal molar gas constant, and —the standard pressure 1 [atm] [40]. |
on ∂Ωoutlet_1, on ∂Ωoutlet_2. | , | Outlet on ∂Ωoutlet is a boundary where the fluid (net) outflows from the domain. The term stands for “suppress backflow”. | |
on ∂Ωt, on ∂Ωair | Wall condition: no-slip. The fluid velocity is zero. This boundary condition is used as the default. | ||
on ∂Ωe | Wall condition. The wall condition slip was applied on ∂Ωe surface. | ||
Heat flow | on ∂Ωinflow_1 | T = 37 °C | Temperature. The inlet constant temperature was set to represent human skin temperature. |
on ∂Ωinflow_2 | T = 20 °C | Temperature. The inlet constant temperature was set to represent generated from the thermoelectric module. | |
on ∂Ωoutflow_1 | Outflow. In a model with convective heat transfer, this condition states that the only heat transfer occurring across the boundary is by convection. The temperature gradient in the normal direction is zero [40]. | ||
on ∂Ωoutflow_2 | Heat flux. The h denotes a heat transfer coefficient. The h = 8.9646 W/(K·m2) was selected from Table 3, which was numerically predicted. is the external temperature. It was assumed that °C. | ||
Thermal insulation. This boundary condition is used as the default. |
Interface | Surface | Boundary Condition | Description |
---|---|---|---|
Fluid flow | on ∂Ωinlet | Qsv- 0.000014716 m3/s. | Inlet boundary condition was used to apply the mass flow rate, where the standard density is defined as mean molar mass of the fluid and —the standard molar volume. |
on ∂Ωoutlet_1 | Outlet on ∂Ωoutlet_1, the flow rate of 0.000014552 m3/s was applied. |
Model | Rct, K·m2/W | h, W/(K·m2) | One-Layer Thickness, mm | The Height of the Model x_e, mm |
---|---|---|---|---|
Model 1_e | 0.11725 | 8.5287 | 0.439 | 3.938 |
Model 2_e | 0.11455 | 8.7298 | 0.438 | 3.936 |
Model 3_e | 0.11155 | 8.9646 | 0.468 | 3.996 |
Mass Flow Rate | hmicrolayer, W/(K·m2) | htotal, W/(K·m2) |
---|---|---|
No ventilation | 25.61 | 6.6368 |
With ventilation | 25.603 | 19.747 |
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Gadeikytė, A.; Abraitienė, A.; Barauskas, R. Application of Combined Micro- and Macro-Scale Models to Investigate Heat and Mass Transfer through Textile Structures with Additional Ventilation. Mathematics 2023, 11, 2532. https://doi.org/10.3390/math11112532
Gadeikytė A, Abraitienė A, Barauskas R. Application of Combined Micro- and Macro-Scale Models to Investigate Heat and Mass Transfer through Textile Structures with Additional Ventilation. Mathematics. 2023; 11(11):2532. https://doi.org/10.3390/math11112532
Chicago/Turabian StyleGadeikytė, Aušra, Aušra Abraitienė, and Rimantas Barauskas. 2023. "Application of Combined Micro- and Macro-Scale Models to Investigate Heat and Mass Transfer through Textile Structures with Additional Ventilation" Mathematics 11, no. 11: 2532. https://doi.org/10.3390/math11112532