Impact of radiation absorption on Caputo fractional fluid flow over an exponentially accelerated plate
DOI:
https://doi.org/10.15282/daam.v2i2.6834Keywords:
Fluid flow, Caputo derivative, Radiation absorption, Laplace transform, Zakian’s methodAbstract
With the advancement of nuclear energy as one of the top clean energy sources, studies on radiation effects are becoming more popular. Radiation absorption is an exothermic phenomenon where radiative energy is released to the surrounding environment. This occurrence can be seen widely in the field of manufacturing, biology, medicine, and fluid mechanics. In this study, the impact of radiation absorption of fluid flow over a vertical plate that is exponentially accelerating will be investigated. Heat and mass transfer flowing vertically over the y-axis for y>0 is considered in the presence of uniform magnetic field. At t>0, temperature and concentration gradient would also increase exponentially. Governing partial differential equations are modified into a fractional model via the Caputo fractional derivative. It is then reduced to an ordinary system with Laplace transform and later solved using Zakian’s inverse Laplace transform. Solutions of velocity, temperature and concentration profiles are presented graphically with varied values of fractional parameter, a, radiation absorption, Q, Prandtl number, Pr, Schmidt number, Sc, and magnetic parameter, M. Effect of radiation absorption is analysed for each varied result by comparing solutions with and without . It is observed that fluid velocity increases with and decreases with an increase in Pr, Sc, and M. Fluid tends to reach steady state faster as a increases. Velocity profile decreases with absence of Q. While Temperature profile is unaffected by change in Q. Obtained solutions are compared with published results and it is found that they are in agreement with each other.
References
Ibrahim FS, Elaiw AM, Bakr AA. Effect of the chemical reaction and radiation absorption on the unsteady MHD free convection flow past a semi infinite vertical permeable moving plate with heat source and suction. communications in Nonlinear science and Numerical simulation. 2008 Aug 1;13(6):1056-66.
Sreedevi G, Rao RR, Rao DP, Chamkha AJ. Combined influence of radiation absorption and Hall current effects on MHD double-diffusive free convective flow past a stretching sheet. Ain Shams Engineering Journal. 2016 Mar 1;7(1):383-97.
Sreedevi G, Prasada Rao DRV, Makinde OD, Venkata Ramana Reddy G. Soret and dufour effects on MHD flow with heat and mass transfer past a permeable stretching sheet in presence of thermal radiation. Indian J Pure Appl Phys. 2017;55(8):551-563.
Arifuzzaman SM, Khan MS, Mehedi MFU, Rana BMJ, Ahmmed SF, et al. MHD Maxwell fluid flow in presence of nano-particle through a vertical porous-plate with heat-generation, radiation absorption and chemical reaction. Front Heat Mass Transf. 2017;(2017):1-14.
Arifuzzaman SM, Khan MS, Mehedi MFU, Rana BMJ, Ahmmed SF, et al. Chemically reactive and naturally convective high speed MHD fluid flow through an oscillatory vertical porous plate with heat and radiation absorption effect. Eng Sci Technol Int J. 2018;21(2):215-228.
Prasad PD, Kiran Kumar RVMS, Varma SVK. Heat and mass transfer analysis for the MHD flow of nanofluid with radiation absorption. Ain Shams Eng J. 2018;9(4):801-813.
Krishna MV, Chamkha AJ. Hall and ion slip effects on MHD rotating boundary layer flow of nanofluid past an infinite vertical plate embedded in a porous medium. Results in Physics. 2019 Dec 1;15:102652.
Rao SR, Vidyasagar G, Deekshitulu GV. Unsteady MHD free convection Casson fluid flow past an exponentially accelerated infinite vertical porous plate through porous medium in the presence of radiation absorption with heat generation/absorption. Materials Today: Proceedings. 2021 Jan 1;42:1608-16.
Raju ABM, Chandra PR, Mallikarjuna B, Raju CSK. Radiation absorption and soret effects on mhd conducting fluid flow past an exponentially accelerated vertical plate. South East Asian J Math Math Sci. 2020;21(1):1-9.
Raza N. Unsteady rotational flow of a second grade fluid with non-integer caputo time fractional derivative. Punjab University Journal of Mathematics. 2020 Nov 25;49(3).
Raza N, Awan AU, Haque EU, Abdullah M, Rashidi MM. Unsteady flow of a Burgers’ fluid with Caputo fractional derivatives: A hybrid technique. Ain Shams Engineering Journal. 2019 Jun 1;10(2):319-25.
Raza N, Ullah MA. A comparative study of heat transfer analysis of fractional Maxwell fluid by using Caputo and Caputo–Fabrizio derivatives. Canadian Journal of Physics. 2020;98(1):89-101.
Anwar MS, Rasheed A. Simulations of a fractional rate type nanofluid flow with non-integer Caputo time derivatives. Computers & Mathematics with Applications. 2017 Nov 15;74(10):2485-502.
Imran MA, Khan I, Ahmad M, Shah NA, Nazar M. Heat and mass transport of differential type fluid with non-integer order time-fractional Caputo derivatives. Journal of Molecular Liquids. 2017 Mar 1;229:67-75.
Abdullah M, Butt AR, Raza N, Alshomrani AS, Alzahrani AK. Analysis of blood flow with nanoparticles induced by uniform magnetic field through a circular cylinder with fractional Caputo derivatives. Journal of Magnetism and Magnetic Materials. 2018 Jan 15;446:28-36.
Aman S, Khan I, Ismail Z, Salleh MZ, Tlili I. A new Caputo time fractional model for heat transfer enhancement of water based graphene nanofluid: An application to solar energy. Results in Physics. 2018 Jun 1;9:1352-62.
Khan I, Ali Shah N, Nigar N, Mahsud Y. MHD mixed convection Poiseuille flow in a porous medium: New trends of Caputo time fractional derivatives in heat transfer problems⋆. The European Physical Journal Plus. 2018 Aug 2;133(8):299.
Shah NA, Elnaqeeb T, Animasaun IL, Mahsud Y. Insight into the natural convection flow through a vertical cylinder using caputo time-fractional derivatives. International Journal of Applied and Computational Mathematics. 2018 Jun;4(3):80.
Shah NA, Khan I, Aleem M, Imran MA. Influence of magnetic field on double convection problem of fractional viscous fluid over an exponentially moving vertical plate: New trends of Caputo time-fractional derivative model. Advances in Mechanical Engineering. 2019 Jul;11(7):1687814019860384.
Imran MA, Shah NA, Khan I, Aleem M. Applications of non-integer Caputo time fractional derivatives to natural convection flow subject to arbitrary velocity and Newtonian heating. Neural Computing and Applications. 2018 Sep;30(5):1589-99.
Sarwar S, Nazar M, Imran MA. Influence of slip over an exponentially moving vertical plate with Caputo-time fractional derivative. Journal of Thermal Analysis and Calorimetry. 2021 Sep;145:2707-17.
Ali F, Sheikh NA, Khan I, Saqib M. Solutions with Wright function for time fractional free convection flow of Casson fluid. Arabian Journal for Science and Engineering. 2017 Jun;42:2565-72.
Khan I, Ali Shah N, Vieru D. Unsteady flow of generalized Casson fluid with fractional derivative due to an infinite plate. The European Physical Journal Plus. 2016 Jun;131:1-2.
Hassanzadeh H, Pooladi-Darvish M. Comparison of different numerical Laplace inversion methods for engineering applications. Applied Mathematics and Computation. 2007 Jun 15;189(2):1966-81.
Saqib M, Khan I, Shafie S. Application of fractional differential equations to heat transfer in hybrid nanofluid: modeling and solution via integral transforms. Advances in Difference Equations. 2019 Dec;2019(1):1-8.
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