@Article{cmc.2020.011492,
AUTHOR = {Dolat Khan, Gohar Ali, Arshad Khan, Ilyas Khan, Yu-Ming Chu, Kottakkaran Sooppy Nisar},
TITLE = {A New Idea of Fractal-Fractional Derivative with Power Law  Kernel for Free Convection Heat Transfer in a Channel Flow  between Two Static Upright Parallel Plates},
JOURNAL = {Computers, Materials \& Continua},
VOLUME = {65},
YEAR = {2020},
NUMBER = {2},
PAGES = {1237--1251},
URL = {http://www.techscience.com/cmc/v65n2/39871},
ISSN = {1546-2226},
ABSTRACT = {Nowadays some new ideas of fractional derivatives have been used 
successfully in the present research community to study different types of mathematical 
models. Amongst them, the significant models of fluids and heat or mass transfer are on 
priority. Most recently a new idea of fractal-fractional derivative is introduced; however, 
it is not used for heat transfer in channel flow. In this article, we have studied this new 
idea of fractal fractional operators with power-law kernel for heat transfer in a fluid flow 
problem. More exactly, we have considered the free convection heat transfer for a 
Newtonian fluid. The flow is bounded between two parallel static plates. One of the 
plates is heated constantly. The proposed problem is modeled with a fractal fractional 
derivative operator with a power-law kernel and solved via the Laplace transform method 
to find out the exact solution. The results are graphically analyzed via MathCad-15 
software to study the behavior of fractal parameters and fractional parameter. For the 
influence of temperature and velocity profile, it is observed that the fractional parameter 
raised the velocity and temperature as compared to the fractal operator. Therefore, a 
combined approach of fractal fractional explains the memory of the function better than 
fractional only.},
DOI = {10.32604/cmc.2020.011492}
}