In this paper, we study the semi-Hyers–Ulam–Rassias stability and the generalized semi-Hyers–Ulam–Rassias stability of some partial differential equations using Laplace transform. One of them is the convection partial differen...
A computational approach with the aid of the Linear Multistep Method (LMM) for the numerical solution of differential equations with initial value problems or boundary conditions has appeared several times in the literature due to its good accuracy a...
This paper mainly consists of two parts: (i) We study the uniqueness, existence, and stability of a new fractional nonlinear partial integro-differential equation in Rn with three-point conditions and variable coefficients in a Banach space using inv...
The paper presents two effective methods for discovering process models in the form of partial differential equations based on an evolutionary algorithm and an algorithm for the best subset selection. The methods are designed to work with sparse and...
We are developing a Virtual Eye for in silico therapies to accelerate research and drug development. In this paper, we present a model for drug distribution in the vitreous body that enables personalized therapy in ophthalmology. The standard treatme...
The space fractional advection–diffusion equation is a crucial type of fractional partial differential equation, widely used for its ability to more accurately describe natural phenomena. Due to the complexity of analytical approaches, this pap...
Most weather and climate models simulate circulations by numerically approximating a complex system of partial differential equations that describe fluid flow. These models also typically use one of a few standard methods to parameterize the effects...
The noteworthiness of double-diffusive convection with magneto-Jeffrey nanofluid on a peristaltic motion under the effect of MHD and porous medium through a flexible channel with the permeable wall has been theoretically examined. A non-linearized Ro...
The Lie symmetry group transformation method was used to investigate the partial differential equations that model the motion of a natural convective unsteady flow past to a non-isothermal vertical flat surface. The one-parameter Lie group transforma...
The transient temperature distribution through a convective-radiative moving rod with temperature-dependent internal heat generation and non-linearly varying temperature-dependent thermal conductivity is elaborated in this investigation. Symmetries a...
It is generally known that classical point and potential Lie symmetries of differential equations (the latter calculated as point symmetries of an equivalent system) can be different. We question whether this is true when the symmetries are extended...
This study investigates mixed convection flow over a vertical thin needle with variable surface heat, mass, and microbial flux, incorporating the influence of gyrotactic microorganisms. The governing partial differential equations are transformed int...
In this investigation, the compressibility effects are visualized on the flow of non-Newtonian fluid, which obeys the stress–strain relationship of an upper convected Maxwell model in a microchannel. The fundamental laws of momentum and mass co...
In this paper, we present a fully Lagrangian method based on the radial basis function (RBF) finite difference (FD) method for solving convection–diffusion partial differential equations (PDEs) on evolving surfaces. Surface differential operato...
In this paper, we investigate functional inverse operators associated with a class of fractional integro-differential equations. We further explore the existence, uniqueness, and stability of solutions to a new integro-differential equation featuring...
In this article, the impact of effective Prandtl number model on 3D incompressible flow in a rotating channel is proposed under the influence of mixed convection. The coupled nonlinear system of partial differential equations is decomposed into a hig...
In this paper, a technique generally known as meshless method is presented for solving fractional partial differential equations (FPDEs). Some physical linear and nonlinear experiments such as time-fractional convective-diffusion equation, timefracti...
The durability of subsea tunnels under the coupled action of stress and chloride ions was analyzed to estimate the service life and provide a theoretical foundation for durability design. The influence coefficient of the stress on chloride ion transm...
This analysis emphasizes the significance of radiation and chemical reaction effects on the boundary layer flow (BLF) of Casson liquid over a linearly elongating surface, as well as the properties of momentum, entropy production, species, and thermal...
In this study we numerically examine the mixed convection stagnation-point flow of a nanofluid over a vertical stretching/shrinking sheet in the presence of suction, thermal radiation and a heat source/sink. Three distinct types of nanoparticles, cop...
In this study, we explore fractional partial differential equations as a more generalized version of classical partial differential equations. These fractional equations have shown promise in providing improved descriptions of certain phenomena under...
A mathematical model for the unsteady, two-dimensional mixed convection stagnation point flow over a Riga plate is presented in this study. Convective boundary conditions, time-dependent derivatives, mixed convection, radiation effects, and the Grinb...
The current analysis discusses Jeffery nanofluid’s thermally radiative flow with convection over a stretching wedge. It takes into account the Brownian movement and thermophoresis of the Buongiorno nanofluid model. The guiding partial different...
This study explored the impact of double diffusive convection and inclined magnetic field in nanofluids on the peristaltic pumping of fourth grade fluid in non-uniform channels. Firstly, a brief mathematical model of fourth grade fluid along inclined...
A study on mixed convection boundary layer flow with thermal radiation and nanofluid over a permeable vertical cylinder lodged in a porous medium is performed in this current research by considering groupings of a variety nanoparticles, consisting of...
The proposed investigation concerns the impact of inclined magnetohydrodynamics (MHD) in a Casson axisymmetric Marangoni forced convective flow of nanofluids. Axisymmetric Marangoni convective flow has been driven by concentration and temperature gra...
This study investigates the effects of an unsteady mixed convection nanofluid flow in a rotating vertical cone submerged in spinning nanofluid. Our analysis considered the impacts of heat flux, chemical reactions, and thermal radiation, with the ther...
In this paper, a local meshless differential quadrature collocation method based on radial basis functions is proposed for the numerical simulation of one-dimensional Klein–Gordon, two-dimensional coupled Burgers’, and regularized long wa...
The convective micropolar fluid flow over a permeable shrinking sheet in the presence of a heat source and thermal radiation with the magnetic field directed towards the sheet has been studied in this paper. The mathematical formulation considers the...
Increasing heat transfer is an important part of industrial, mechanical, electrical, thermal, and biological sciences. The aim of this study is to increase the thermal competency of a conventional fluid by using a ternary hybrid nanofluid. A magnetic...
The main purpose of this study is to investigate the multislip effects on the magneto-hydrodynamic (MHD) mixed convection unsteady flow of micropolar nano-fluids over a stretching/shrinking sheet along with radiation in the presence of a heat source....
In the present study, the magnetohydrodynamics (MHD) bio-convective flow and heat transfer of nanofluid, due to the swimming of the gyrotactic micro-organisms over a curved stretched sheet, is examined. In addition, thermophoresis and Brownian motion...
The key objective of the study under concern is to probe the impacts of Brownian motion and thermophoresis diffusion on Casson nanofluid boundary layer flow over a nonlinear inclined stretching sheet, with the effect of convective boundaries and ther...
This study presents a novel fifth-order iterative method for solving nonlinear systems derived from a modified combination of Jarratt and Newton schemes, incorporating a frozen derivative of the Jacobian. The method is applied to approximate solution...
The main goal of the current work was to study the coupled mechanism of thermophoretic transportation and mixed convection flow around the surface of the sphere. To analyze the characteristics of heat and fluid flow in the presence of thermophoretic...
The present analysis has interesting applications in physiology, industry, engineering and medicine. Peristaltic pumps acquire an elliptical cross-section during motion. Peristaltic pumps, roller pumps and finger pumps also have highly useful applica...
The main contribution of this article is to propose a compact explicit scheme for solving time-dependent partial differential equations (PDEs). The proposed explicit scheme has an advantage over the corresponding implicit compact scheme to find solut...
In this research article, we investigated a comprehensive analysis of time-dependent free convection electrically and thermally conducted water-based nanofluid flow containing Copper and Titanium oxide (Cu and TiO 2 ) past a moving porous vert...
Current disquisition is presented to excogitate heat and mass transfer features of second grade fluid flow generated by an inclined cylinder under the appliance of diffusion, radiative heat flux, convective and Joule heating effects. Mathematical mod...
The rapid advancement in technology in recent years has shown that nanofluids are very vital to further development in science and technology. Moreover, many industrial specifications cannot be met by allowing natural convection only, hence the need...
Pressure is a physical quantity that is indispensable in the study of transport phenomena. Previous studies put forward a pressure constitutive law and constructed a partial differential equation on pressure to study the convection with or without he...
Numerical techniques for approximate solution of a system of reaction-diffusion-convection partial differential equations modeling the evolution of temperature and fuel density in a wildfire are proposed. These schemes combine linearly implicit-expli...
Recently, the topic of convection of heat transfer has created an interest among researchers because of its numerous applications in the daily life. The objective of this paper was to study theoretically the problem of mixed convection boundary layer...
The present inquiry studies the influence of mass transfer in magnetohydrodynamics (MHD) upper-convected Maxwell (UCM) fluid flow on a stretchable, porous subsurface. The governing partial differential equations for the flow problem are reformed to o...
In this research work, our goal is to scrutinize the case, where water-based nanofluids having single-wall and multi-wall carbon nanotubes (CNTs) flow through a vertical cone. The second law of thermodynamic is taken for the aim of scheming effective...
The MHD convective Walters-B memory liquid flow past a permeable accelerating surface with the mechanism of Soret-Dufour is considered. The flow equation constitutes a set of partial differential equations (PDEs) to elucidate the real flow of a non-N...
The fluid flow through inclined plates has several applications in magneto-aerodynamics, materials processing and magnetohydrodynamic propulsion thermo-fluid dynamics. Inspired by these applications, the rate of entropy production in a bio-convective...
This paper investigated the magnetohydrodynamic (MHD) mixed convection flow of Fe3O4-water ferrofluid over a nonlinearly moving surface. The present work focused on how the state of suction on the surface of the moving sheet and the effects of therma...
We investigate the partial differential equation system which describes the double-diffusion convection phenomena with the reduction formalism. Double-diffusion refers to when two scalar quantities with different diffusivity, such as heat and solute...
This article analyzes heat transfer enhancement in incompressible time dependent magnetohydrodynamic (MHD) convective flow of Oldroyd-B nanofluid with carbon nanotubes (CNTs). Single wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWC...
of 4