A sweating model for the internal ventilation of a motorcycle helmet. (English) Zbl 1452.76006
Summary: We present a thermodynamic model for the evolution of sweat in a porous medium in contact with a part of the human body, capable of describing the evaporation-related heat transfer phenomena. This is suitable for the analysis and optimization of the internal ventilation of a motorcycle helmet, with the purpose of enhancing the comfort and ultimately the safety of the rider. The model is based on a set of evolution equations for the three scalar unknowns temperature, absolute humidity and sweat. Its mathematical properties as well as those of the numerical counterpart are thoroughly investigated, and an efficient solution algorithm is devised. Simulations show the onset of a free-boundary separating the wet and dry regions and highlight the zones where sweat accumulates.
MSC:
| 76-10 | Mathematical modeling or simulation for problems pertaining to fluid mechanics |
| 76S05 | Flows in porous media; filtration; seepage |
| 80A19 | Diffusive and convective heat and mass transfer, heat flow |
Keywords:
internal fluid-dynamics; human body ventilation; sweating model; free-boundary problem; finite elementsSoftware:
FreeFem++References:
| [1] | Pinnoji P, Mahajan P. Impact analysis of helmets for improved ventilation with deformable head model. In: IRCOBI conference, Madrid, Spain; 2006. p. 159-70.; Pinnoji P, Mahajan P. Impact analysis of helmets for improved ventilation with deformable head model. In: IRCOBI conference, Madrid, Spain; 2006. p. 159-70. |
| [2] | Bogerd C. Physiological and cognitive effects of wearing a full-face motorcycle helmet, Ph.D. thesis, ETH Zurich, Zurich, Switzerland; 2009.; Bogerd C. Physiological and cognitive effects of wearing a full-face motorcycle helmet, Ph.D. thesis, ETH Zurich, Zurich, Switzerland; 2009. |
| [3] | Cimolin F. Analysis of the internal ventilation for a motorcycle helmet, Ph.D. thesis, Politecnico di Torino, Italy; 2010.; Cimolin F. Analysis of the internal ventilation for a motorcycle helmet, Ph.D. thesis, Politecnico di Torino, Italy; 2010. · Zbl 1452.76006 |
| [4] | Discacciati M. Domain decomposition methods for the coupling of surface and groundwater flows, Ph.D. thesis, Ecole Polytechnique Fédérale de Lausanne, Switzerland; 2004.; Discacciati M. Domain decomposition methods for the coupling of surface and groundwater flows, Ph.D. thesis, Ecole Polytechnique Fédérale de Lausanne, Switzerland; 2004. |
| [5] | Discacciati, M.; Quarteroni, A., Navier-Stokes/Darcy coupling: modeling, analysis, and numerical approximation, Rev Mat Complut, 22, 2, 315-426 (2009) · Zbl 1172.76050 |
| [6] | Bruneau, C.; Mortazavi, I., Numerical modelling and passive flow control using porous media, Comput Fluids, 37, 488-498 (2008) · Zbl 1237.76189 |
| [7] | Cimolin F, Discacciati. Navier-Stokes/Forchheimer models for filtration through porous media, Tech. Rep. 5, Dipartimento di Matematica, Politecnico di Torino; 2010.; Cimolin F, Discacciati. Navier-Stokes/Forchheimer models for filtration through porous media, Tech. Rep. 5, Dipartimento di Matematica, Politecnico di Torino; 2010. · Zbl 1394.76122 |
| [8] | Thorvaldsson, K.; Janestad, H., A model for simultaneous heat, water and vapour diffusion, J Food Eng, 40, 167-172 (1999) |
| [9] | Huang, H.; Lin, P.; Zhou, W., Moisture transport and diffusive instability during bread baking, SIAM J Appl Math, 68, 1, 222-238 (2007) · Zbl 1388.76205 |
| [10] | Zhou, W., Application of FDM and FEM in solving the simultaneous heat and moisture transfer inside bread during baking, Int J Comput Fluid Dyn, 19, 1, 73-77 (2005) · Zbl 1286.76097 |
| [11] | Huang, H.; Ye, C.; Sun, W., Moisture transport in fibrous clothing assemblies, J Eng Math, 61, 35-54 (2008) · Zbl 1138.76063 |
| [12] | Ye, C.; Huang, H.; Fan, J.; Sun, W., Numerical study of heat and moisture transfer in textile materials by a finite volume method, Commun Comput Phys, 4, 4, 929-948 (2008) · Zbl 1364.76122 |
| [13] | Laws N, Parry J. Mathematical modelling of heat and mass transfer in agricultural grain drying. In: Proceeding of the royal society of London, vol. 385; 1983. p. 169-87.; Laws N, Parry J. Mathematical modelling of heat and mass transfer in agricultural grain drying. In: Proceeding of the royal society of London, vol. 385; 1983. p. 169-87. |
| [14] | Smith, E.; Jayas, D., Air traverse time in grain bins, Appl Math Model, 28, 1047-1062 (2004) · Zbl 1147.76612 |
| [15] | IV, J. L.; V, J. L., A heat transfer textbook (2003), Phlogiston Press |
| [16] | Nield, D.; Bejan, A., Convection in porous media (1998), Springer: Springer New York · Zbl 0924.76001 |
| [17] | Boltz, R.; Tuve, G., Book of tables for applied engineering science (1976), CRC Press |
| [18] | Jones, F., Evaporation of water (1991), CRC Press |
| [19] | Olivieri J, Geshwiler M, Singh T, Lovodocky S. Psychrometrics: theory and practice, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., 1996.; Olivieri J, Geshwiler M, Singh T, Lovodocky S. Psychrometrics: theory and practice, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., 1996. |
| [20] | Smoller, J., Shock waves and reaction-diffusion equations (1994), Springer · Zbl 0807.35002 |
| [21] | Showalter, R., Monotone operators in banach space and nonlinear partial differential equations (1997), American Mathematical Society · Zbl 0870.35004 |
| [22] | Brézis, H., Problèmes unilatéraux, J Math Pures Appl, 51, 1-168 (1972) · Zbl 0237.35001 |
| [23] | Ekeland, I.; Temam, R., Convex analysis and variational problems (1999), SIAM: SIAM Paris · Zbl 0939.49002 |
| [24] | Rossi, R.; Savaré, G., Gradient flows of non convex functionals in hilbert spaces and applications, ESAIM: Control, Opt Calc Variat, 12, 564-614 (2006) · Zbl 1116.34048 |
| [25] | Díaz, J.; Hernández, J.; Mancebo, F., Branches of positive and free boundary solutions for some singular quasilinear elliptic problems, J Math Anal Appl, 352, 449-474 (2009) · Zbl 1173.35055 |
| [26] | Brézis H. Solutions à support compact d’inéquations variationnelles. Collège de France; 1974.; Brézis H. Solutions à support compact d’inéquations variationnelles. Collège de France; 1974. |
| [27] | Nochetto, R.; Savaré, G.; Verdi, C., A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations, Commun Pure Appl Math, 53, 525-589 (2000) · Zbl 1021.65047 |
| [28] | Hecht F, Pironneau O, Le Hyaric A, Ohtsuka K. FreeFEM++ Manual, 2nd ed.; 2008.; Hecht F, Pironneau O, Le Hyaric A, Ohtsuka K. FreeFEM++ Manual, 2nd ed.; 2008. |
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