Numerical analysis of time-fractional non-Fourier heat conduction in porous media based on Caputo fractional derivative
- PDF / 1,230,143 Bytes
- 11 Pages / 595.276 x 790.866 pts Page_size
- 81 Downloads / 252 Views
ORIGINAL
Numerical analysis of time-fractional non-Fourier heat conduction in porous media based on Caputo fractional derivative under short heating pulses Milad Mozafarifard 1 & Davood Toghraie 2 Received: 21 April 2020 / Accepted: 14 July 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this research, the heat transport in porous media (sand particles and interstitial gas) under short heating pulses is examined, taking into account the non-Fourier effects. The time-fractional heat conduction equation based on the Caputo definition is proposed to examine the thermal response of porous media in short-time scales. The results of the time-fractional model are compared to experimental data, which proves the accuracy of this model as well as its capability to describe the fast transient thermal process, the local thermal nonequilibrium condition, and the energy exchange between the solid and gaseous phases. Additionally, the influence of variation in the different parameters, including the order of fractionality and heating pulse widths are investigated, and it has been proved that the gas-solid interactions in the fast transient process play a vital role in heat transfer mechanism of porous media, especially in the near-field locations to the heater with short pulse width. Keywords Non-Fourier heat transfer . Time-fractional model . Porous material . Short-pulse heating
1 Introduction In the last few decades, the problem of heat transfer in porous media especially at small temporal scales and short heating periods has been conducted by many researchers. For a material volume including hundreds of pores, the heat conduction can be described by the effective thermal conductivity because of the existence of low-conducting pores. We can point to the works of [1–4], in which authors determined the effective thermal conductivity of porous materials, gas in the pores and also studied the effect of geometrical parameters of porous media on dimensionless thermal conductivity. Wei et al. [5] indicated that the machine learning methods can lead to the fast prediction of effective thermal conductivity, and also it can be applied to predict the other thermo-physical properties of composite materials and porous media. Nouri-Borujerdi et al. [6] studied the effect of the local thermal nonequilibrium * Davood Toghraie [email protected] 1
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
2
Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran
state on the temperature field in a semi-infinite porous medium. The effects of pore micro-geometric structure on heat conduction in porous media were examined by Lv et al. [7]. The theoretical results proved that the decrease in pore size and porosity can lead to enhancement of heat transfer in porous media. Vadasz [8] employed a set of energy equations for both solid and liquid phases, and the energy exchange between two phases was characterized through the coupling fa
Data Loading...
