scholarly journals A new general fractional-order derivataive with Rabotnov fractional-exponential kernel applied to model the anomalous heat transfer

2019 ◽  
Vol 23 (3 Part A) ◽  
pp. 1677-1681 ◽  
Author(s):  
Xiao-Jun Yang ◽  
Mahmoud Abdel-Aty ◽  
Carlo Cattani
Keyword(s):  
Heat Transfer ◽  
Fractional Order ◽  
Exponential Function ◽  
Power Law ◽  
Transfer Model ◽  
Mathematical Tool ◽  
Fractional Exponential Function ◽  
Anomalous Heat Transfer ◽  
First Time ◽  
Anomalous Heat

In this paper, we consider a general fractional-order derivataive of the Liouville-Caputo type with the non-singular kernel of the Rabotnov fractional-exponential function for the first time. A new general fractional-order derivataive heat transfer model is discussed in detail. The general fractional-order derivataive formula is a new mathematical tool proposed to model the anomalous behaviors in complex and power-law phenomena.

scholarly journals Group Invariant Solutions for Flow and Heat Transfer of Power-Law Nanofluid in a Porous Medium

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Saba Javaid ◽  
Asim Aziz
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Power Law ◽  
Internal Heat ◽  
Shear Thickening ◽  
Internal Heat Source ◽  
Heat Transfer Model ◽  
Transfer Model ◽  
Flow And Heat Transfer ◽  
Power Law Nanofluid

The present work covers the flow and heat transfer model for the power-law nanofluid in the presence of a porous medium over the penetrable plate. The flow is caused by the impulsive movement of the plate embedded in Darcy’s type porous medium. The flow and heat transfer model has been examined with the effect of linear thermal radiation and the internal heat source or sink in the flow regime. The Rosseland approximation is utilized for the optically thick nanofluid. To form the closed-form solutions for the governing partial differential equations of conservation of mass, momentum, and energy, the Lie symmetry analysis is used to get the reductions of governing equations and to find the group invariants. These invariants are then utilized to obtain the exact solution for all three cases, i.e., shear thinning fluid, Newtonian fluid, and shear thickening fluid. In the end, all solutions are plotted for the cu -water nanofluid and discussed briefly for the different emerging flow and heat transfer parameters.

scholarly journals The difference in the thermal conductivity of nanofluids measured by different methods and its rationalization

2016 ◽  
Vol 7 ◽  
pp. 2037-2044 ◽  
Author(s):  
Aparna Zagabathuni ◽  
Sudipto Ghosh ◽  
Shyamal Kumar Pabi
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Laser Flash ◽  
Flash Method ◽  
Transfer Model ◽  
Measuring Methods ◽  
Order Of Magnitude ◽  
Wire Method ◽  
The Difference ◽  
First Time

A suspension of particles below 100 nm in size, usually termed as nanofluid, often shows a notable enhancement in thermal conductivity, when measured by the transient hot-wire method. In contrast, when the conductivity of the same nanofluid is measured by the laser flash method, the enhancement reported is about one order of magnitude lower. This difference has been quantitatively resolved for the first time on the basis of the collision-mediated heat transfer model for nanofluids proposed earlier by our research group. Based on the continuum simulation coupled with stochastic analysis, the present theoretical prediction agrees well with the experimental observations from different measuring methods reported in the literature, and fully accounts for the different results from the two measuring methods mentioned above. This analysis also gives an indication that the nanofluids are unlikely to be effective for heat transfer in microchannels.

scholarly journals A new general fractional derivative Goldstein-Kac-type telegraph equation

2020 ◽  
Vol 24 (6 Part B) ◽  
pp. 3893-3898
Author(s):  
Ping Cui ◽  
Yi-Ying Feng ◽  
Jian-Gen Liu ◽  
Lu-Lu Geng
Keyword(s):  
Fractional Order ◽  
Telegraph Equation ◽  
Order Derivative ◽  
Mathematical Tool ◽  
Fractional Order Derivative ◽  
Derivative Formula ◽  
The Laplace Transform ◽  
The One ◽  
First Time ◽  
Derivatives Of

In this paper, we consider the Riemann-Liouville-type general fractional derivatives of the non-singular kernel of the one-parametric Lorenzo-Hartley function. A new general fractional-order-derivative Goldstein-Kac-type telegraph equation is proposed for the first time. The analytical solution of the considered model with the graphs is obtained with the aid of the Laplace transform. The general fractional-order-derivative formula is as a new mathematical tool proposed to model the anomalous behaviors in complex and power-law phenomena.

scholarly journals Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat transfer problems

2017 ◽  
Vol 21 (3) ◽  
pp. 1161-1171 ◽  
Author(s):  
Xiao-Jun Yang
Keyword(s):  
Heat Transfer ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Complex Phenomenon ◽  
Anomalous Relaxation ◽  
Comparative Results ◽  
Transfer Problems ◽  
First Time ◽  
Derivatives Of ◽  
Relaxation Models

In this paper, we address a class of the fractional derivatives of constant and variable orders for the first time. Fractional-order relaxation equations of constants and variable orders in the sense of Caputo type are modeled from mathematical view of point. The comparative results of the anomalous relaxation among the various fractional derivatives are also given. They are very efficient in description of the complex phenomenon arising in heat transfer.

scholarly journals A General fractional-order heat transfer model for Photovoltaic/Thermal hybrid systems and its observer design

2017 ◽  
Vol 139 ◽  
pp. 49-54 ◽  
Author(s):  
Lahoucine Ouhsaine ◽  
Yassine Boukal ◽  
Mohammed El Ganaoui ◽  
Mohammed Darouach ◽  
Michel Zasadzinski ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Hybrid Systems ◽  
Fractional Order ◽  
Heat Transfer Model ◽  
Observer Design ◽  
Transfer Model
Sign in / Sign up

Export Citation Format

Share Document