scholarly journals A direct method of moving spheres on fractional order equations

2017 ◽  
Vol 272 (10) ◽  
pp. 4131-4157 ◽  
Author(s):  
Wenxiong Chen ◽  
Yan Li ◽  
Ruobing Zhang
Keyword(s):  
Fractional Order ◽  
Direct Method ◽  
Moving Spheres ◽  
A Direct Method

2D PROBLEM FOR A SPHERE IN THE FRACTIONAL ORDER THEORY THERMOELASTICITY TO AXISYMMETRIC TEMPERATURE DISTRIBUTION

2022 ◽  
Vol 11 (1) ◽  
pp. 1-15
Author(s):  
S.G. Khavale ◽  
K.R. Gaikwad
Keyword(s):  
Temperature Distribution ◽  
Fractional Order ◽  
Direct Method ◽  
Order Theory ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Copper Material ◽  
Mathcad Software ◽  
Axisymmetric Temperature ◽  
A Direct Method

In the present article, we implement the fractional thermoelasticity theory to a 2D issue for a sphere whose surface is free from traction, subject to a provided axisymmetric temperature distribution of heat. The medium is supposed to be quiescent initially. A direct method is used to get a solution and the Laplace transform technique is used. Mathematical models for copper material are designed as a particular instance. Numerical results are computed with help of Mathcad software and graphically represented and the fractional-order parameter effect has been explained.

scholarly journals Plastic waste to fuels by hydrocracking at mild conditions

2021 ◽  
Vol 7 (17) ◽  
pp. eabf8283
Author(s):  
Sibao Liu ◽  
Pavel A. Kots ◽  
Brandon C. Vance ◽  
Andrew Danielson ◽  
Dionisios G. Vlachos
Keyword(s):  
Direct Method ◽  
Acid Sites ◽  
Liquid Fuels ◽  
High Yield ◽  
Tandem Catalysis ◽  
Hy Zeolite ◽  
Environmental Threat ◽  
Single Use ◽  
Initial Activation ◽  
A Direct Method

Single-use plastics impose an enormous environmental threat, but their recycling, especially of polyolefins, has been proven challenging. We report a direct method to selectively convert polyolefins to branched, liquid fuels including diesel, jet, and gasoline-range hydrocarbons, with high yield up to 85% over Pt/WO3/ZrO2 and HY zeolite in hydrogen at temperatures as low as 225°C. The process proceeds via tandem catalysis with initial activation of the polymer primarily over Pt, with subsequent cracking over the acid sites of WO3/ZrO2 and HY zeolite, isomerization over WO3/ZrO2 sites, and hydrogenation of olefin intermediates over Pt. The process can be tuned to convert different common plastic wastes, including low- and high-density polyethylene, polypropylene, polystyrene, everyday polyethylene bottles and bags, and composite plastics to desirable fuels and light lubricants.

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