Yaqing Liu^a,*, Jinyu Ma^b

Frontiers in Heat and Mass Transfer, Vol.6, pp. 1-5, 2015, DOI:10.5098/hmt.6.17

Abstract This paper presents an exact solution for the magnetohydrodynamic (MHD) flow of an incompressible generalized Oldroyd-B fluid due to an infinite accelerating plate. The fractional calculus approach is introduced to establish the constitutive relationship of the Oldroyd-B fluid. The solutions in terms of Fox H-function are obtained by using the Laplace transform. When N = 0 the solutions corresponds to the generalized Oldroyd-B fluids, while θ → 0 and λ → 0 describes the Maxwell fluid and the generalized second fluid, as limiting cases of our general results, respectively. More >

K.V. Chandra Sekhar^*

Frontiers in Heat and Mass Transfer, Vol.16, pp. 1-6, 2021, DOI:10.5098/hmt.16.10

Abstract The behavior of unsteady MHD flow of Jeffrey fluid over an inclined porous plate was analyzed in the present article. The governing partial differential equations of the flow phenomena were solved by using powerful mathematical tool Laplace transforms. The variations of velocity, temperature of the flow with respect to dissimilar physical parameters are analyzed through graphs. The parameters of engineering interest are skin friction and Nusselt number. For better understanding of the problem, variations of skin friction and Nusselt number with respect to critical parameters are tabulated. More >

Utpal Jyoti Das^a , Mira Das^b,*

Frontiers in Heat and Mass Transfer, Vol.17, pp. 1-8, 2021, DOI:10.5098/hmt.17.18

Abstract An unsteady mixed convection flow of an electrically conducting, viscous, incompressible fluid over an oscillating vertical surface in a Darcian porous regime in presence of heat generation/absorption and thermal radiation have been studied. The liquid and the surface is moving with constant angular velocity as a rigid body about an axis. The fluid is taken here to be gray, absorbing/emitting radiation but non scattering medium. Here firstorder chemical reaction and a transverse magnetic field have been considered. The presence of Hall current and Soret effect are considered. The governing coupled partial differential equations are solved by using Laplace transform technique… More >

Muhammad Samraiz¹, Muhammad Umer¹, Thabet Abdeljawad^2,3,*, Saima Naheed¹, Gauhar Rahman⁴, Kamal Shah^2,5

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.1, pp. 901-919, 2023, DOI:10.32604/cmes.2023.024029

Abstract In this paper, we establish the new forms of Riemann-type fractional integral and derivative operators. The novel fractional integral operator is proved to be bounded in Lebesgue space and some classical fractional integral and differential operators are obtained as special cases. The properties of new operators like semi-group, inverse and certain others are discussed and its weighted Laplace transform is evaluated. Fractional integro-differential free-electron laser (FEL) and kinetic equations are established. The solutions to these new equations are obtained by using the modified weighted Laplace transform. The Cauchy problem and a growth model are designed as applications along with graphical… More >

Kamran¹, Siraj Ahmad¹, Kamal Shah^2,3,*, Thabet Abdeljawad^2,4,*, Bahaaeldin Abdalla²

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2743-2765, 2023, DOI:10.32604/cmes.2023.023705

Abstract Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects. Using the Laplace transform for solving differential equations, however, sometimes leads to solutions in the Laplace domain that are not readily invertible to the real domain by analytical means. Thus, we need numerical inversion methods to convert the obtained solution from Laplace domain to a real domain. In this paper, we propose a numerical scheme based on Laplace transform and numerical inverse Laplace transform for the approximate solution of fractal-fractional differential equations with order . Our proposed numerical scheme is based on… More > Graphic Abstract

Fairouz Tchier¹, Hassan Khan^2,3,*, Shahbaz Khan², Poom Kumam^4,5, Ioannis Dassios⁶

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2137-2153, 2023, DOI:10.32604/cmes.2023.022855

Abstract The nonlinearity in many problems occurs because of the complexity of the given physical phenomena. The present paper investigates the non-linear fractional partial differential equations’ solutions using the Caputo operator with Laplace residual power series method. It is found that the present technique has a direct and simple implementation to solve the targeted problems. The comparison of the obtained solutions has been done with actual solutions to the problems. The fractional-order solutions are presented and considered to be the focal point of this research article. The results of the proposed technique are highly accurate and provide useful information about the… More >

Thabet Abdeljawad^1,2, Awais Younus^3,*, Manar A. Alqudah⁴, Usama Atta⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.3, pp. 2163-2191, 2023, DOI:10.32604/cmes.2022.020915

Abstract The Laplace transformation is a very important integral transform, and it is extensively used in solving ordinary differential equations, partial differential equations, and several types of integro-differential equations. Our purpose in this study is to introduce the notion of fuzzy double Laplace transform, fuzzy conformable double Laplace transform (FCDLT). We discuss some basic properties of FCDLT. We obtain the solutions of fuzzy partial differential equations (both one-dimensional and two-dimensional cases) through the double Laplace approach. We demonstrate through numerical examples that our proposed method is very successful and convenient for resolving partial differential equations. More >

Aziz-Ur-Rehman¹, Muhammad Bilal Riaz^1,2, Syed Tauseef Saeed³, Shaowen Yao^4,*

CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.2, pp. 689-703, 2021, DOI:10.32604/cmes.2021.014980

Abstract Convective flow is a self-sustained flow with the effect of the temperature gradient. The density is non-uniform due to the variation of temperature. The effect of the magnetic flux plays a major role in convective flow. The process of heat transfer is accompanied by a mass transfer process; for instance, condensation, evaporation, and chemical process. Due to the applications of the heat and mass transfer combined effects in a different field, the main aim of this paper is to do a comprehensive analysis of heat and mass transfer of MHD unsteady second-grade fluid in the presence of ramped boundary conditions… More >

Syed Tauseef Saeed¹, Muhammad Bilal Riaz^2,3, Dumitru Baleanu^4,5,7,*, Ali Akgül⁶, Syed Muhammad Husnine¹

Intelligent Automation & Soft Computing, Vol.28, No.2, pp. 547-559, 2021, DOI:10.32604/iasc.2021.015982

Abstract Convective flow is a self-sustained flow with the effect of the temperature gradient. The density is non-uniform due to the variation of temperature. The effect of the magnetic flux plays a major role in convective flow. The process of heat transfer is accompanied by mass transfer process; for instance condensation, evaporation and chemical process. Due to the applications of the heat and mass transfer combined effects in different field, the main aim of this paper is to do comprehensive analysis of heat and mass transfer of MHD unsteady second-grade fluid in the presence of time dependent generalized boundary conditions. The… More >

Saqib Murtaza¹, Farhad Ali^2,3,*, Nadeem Ahmad Sheikh¹, Ilyas Khan⁴, Kottakkaran Sooppy Nisar⁵

CMC-Computers, Materials & Continua, Vol.67, No.3, pp. 2915-2932, 2021, DOI:10.32604/cmc.2021.013757

Abstract The present article aims to examine the heat and mass distribution in a free convection flow of electrically conducted, generalized Jeffrey nanofluid in a heated rotatory system. The flow analysis is considered in the presence of thermal radiation and the transverse magnetic field of strength B₀. The medium is porous accepting generalized Darcy’s law. The motion of the fluid is due to the cosine oscillations of the plate. Nanofluid has been formed by the uniform dispersing of the Silver nanoparticles in regular engine oil. The problem has been modeled in the form of classical partial differential equations and then generalized… More >