There is both theoretical and practical interest in the investigation of time dependent heat flows which is motivated by their applications in several technological fields including micro-electromechanical systems and microelectronics ranging from microprocessor chip heating to ultrafast temperature variations encountered in the laser industry as well as in the design of microsensors and microactuators. The response of a rarefied gas between two parallel plates due to instantaneous changes in the wall temperature of one plate has been studied first in [1] and more recently in [2], while the periodic behaviour of a rarefied gas caused by the oscillatory heating of one plate has been recently investigated based on the linearized Boltzmann equation in [3]. In the present work, the response of a gas in a slab due to various time-dependent boundary heating configurations is investigated in the whole range of the Knudsen number based on the linear Shakhov kinetic model. In particular, in addition to the sudden change of the wall temperature the cases of linear and arctangential variation of the temperature at the boundary with some cut-off is investigated. In all three cases the time response of the gas including the evolution of the heat flow field in terms of the Knudsen number is examined. The total response time to reach steady-state conditions is estimated deducing a non-monotonic behaviour in terms of the gas rarefaction. This type of information may be important in the design and optimization of the Pirani sensors enlarging the range of their applicability. The case of oscillatory heating of one boundary is also studied. The solution is given in terms of two parameters namely the Knudsen number and the dimensionless oscillation frequency. The results based on the Shakhov model is in very good agreement with the corresponding ones in [3] both in the mass and energy flow fields demonstrating the validity of the implementation of the kinetic model equations instead of the Boltzmann equation in order to reduce the involved computational effort.
Buchina O., Valougeorgis D., Morini G.L. (2012). The response of a rarefied gas in a slab due to various time-dependent boundary heating configurations. Zaragoza : s.n.
The response of a rarefied gas in a slab due to various time-dependent boundary heating configurations
MORINI, GIAN LUCA
2012
Abstract
There is both theoretical and practical interest in the investigation of time dependent heat flows which is motivated by their applications in several technological fields including micro-electromechanical systems and microelectronics ranging from microprocessor chip heating to ultrafast temperature variations encountered in the laser industry as well as in the design of microsensors and microactuators. The response of a rarefied gas between two parallel plates due to instantaneous changes in the wall temperature of one plate has been studied first in [1] and more recently in [2], while the periodic behaviour of a rarefied gas caused by the oscillatory heating of one plate has been recently investigated based on the linearized Boltzmann equation in [3]. In the present work, the response of a gas in a slab due to various time-dependent boundary heating configurations is investigated in the whole range of the Knudsen number based on the linear Shakhov kinetic model. In particular, in addition to the sudden change of the wall temperature the cases of linear and arctangential variation of the temperature at the boundary with some cut-off is investigated. In all three cases the time response of the gas including the evolution of the heat flow field in terms of the Knudsen number is examined. The total response time to reach steady-state conditions is estimated deducing a non-monotonic behaviour in terms of the gas rarefaction. This type of information may be important in the design and optimization of the Pirani sensors enlarging the range of their applicability. The case of oscillatory heating of one boundary is also studied. The solution is given in terms of two parameters namely the Knudsen number and the dimensionless oscillation frequency. The results based on the Shakhov model is in very good agreement with the corresponding ones in [3] both in the mass and energy flow fields demonstrating the validity of the implementation of the kinetic model equations instead of the Boltzmann equation in order to reduce the involved computational effort.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
