Papers by Muhammad Ramzan
In this paper, unsteady flow of fractionalized Maxwell fluid over an inclined vertical plate is c... more In this paper, unsteady flow of fractionalized Maxwell fluid over an inclined vertical plate is considered by using thermo diffusion and slip effects. The flow model is solved using Constant proportional Caputo fractional derivative. Initially, the governing equations are made non-dimensional and then solved by Laplace transform. To see the impact of different flow parameters on the velocity, temperature and concentration, we have drawn some graphs. In addition, it is observed that magnetic field has decreasing effect on fluid motion whereas thermo-diffusion have increasing effect on fluid motion.
The study investigates the combined impact of heat and mass transfer on a vertical plate, conside... more The study investigates the combined impact of heat and mass transfer on a vertical plate, considering factors such as an applied magnetic field, thermal radiation, heat absorption, and a first-order chemical reaction. The fluid under examination is assumed to be an electrically conducting Cunanofluid based on water. Thermophysical properties are derived from Table 1 for both the base fluid (water) and nanoparticles (Cu), with the nanoparticle volume fraction chosen within the range of 0.01 to 0.02. A novel aspect of this study involves considering both passive and active control of the Maxwell nanofluid. The governing equations are solved using the Laplace transform technique to obtain uniform closed-form solutions. Graphical representations illustrate the velocity, temperature, concentration, and Bio-Convection profiles under various flow parameters. Remarkably, the velocity profile exhibits consistent behavior for both stationary g ¼ 0 and moving g ¼ 1 plates, as depicted in Figures 2-10. The obtained semi-analytical solutions successfully fulfill all initial and boundary conditions. Moreover, manipulating the nanoparticle volume fraction demonstrates significant control over the flow and heat transfer characteristics.
In this article, Caputo and Prabhakar fractional derivatives are used to analyze the influence of... more In this article, Caputo and Prabhakar fractional derivatives are used to analyze the influence of heat flux on fractionalized second grade flow. The fluid model is generalized by Fick's and Fourier's laws. Moreover, radiation and slip effects are also taken into account additionally. Fractional governing models are solved semi-analytically by using Caputo and Prabhakar fractional derivatives. The method of Laplace method is applied to solve the dimensional model for temperature, velocity, and concentration profiles. The results are contrasted visually. A variety of graphs are used to illustrate the impacts of several parameters, including the heat absorption Q, fractional parameter, magnetic parameter M, and chemical reaction R. It is evident from the figure that the velocity distribution is affected less by chemical and magnetic field, while the fluid velocity is affected more by diffusion-thermodynamics and mass Grashoff number. Furthermore, comparisons among classical and fractional fluid models are made to check the validity of the result. It is noted that the classical approach is less convenient as compared to the fractional approach.
Fractional order derivatives are often regarded as extremely complex mathematical instruments tha... more Fractional order derivatives are often regarded as extremely complex mathematical instruments that may be used to find practical solutions in numerous fields of engineering and science. This article examined the nonlinear Casson fluid fractional order model because of the widespread use of fractional derivatives. In the different physical situations of mass transfer, the temperature gradient force affects the mass flux. In this situation, lightweight molecules move to the region of higher temperature, and heavy molecules move to the region of lower temperature. The governing equations in the equations of the present flow model are partial differential equations (PDEs), where the temperature, velocity, and concentration distributions are calculated numerically using the Crank-Nicolson method. Furthermore, the graphs of the field of interest are used to illustrate the physical characteristics of material parameters and flow parameters.
Fractional order derivatives are often regarded as extremely complex mathematical instruments tha... more Fractional order derivatives are often regarded as extremely complex mathematical instruments that may be used to find practical solutions in numerous fields of engineering and science. This article examined the nonlinear Casson fluid fractional order model because of the widespread use of fractional derivatives. In the different physical situations of mass transfer, the temperature gradient force affects the mass flux. In this situation, lightweight molecules move to the region of higher temperature, and heavy molecules move to the region of lower temperature. The governing equations in the equations of the present flow model are partial differential equations (PDEs), where the temperature, velocity, and concentration distributions are calculated numerically using the Crank-Nicolson method. Furthermore, the graphs of the field of interest are used to illustrate the physical characteristics of material parameters and flow parameters.
The objective of this model is to examine the Dufour effect on unsteady free convection second-gr... more The objective of this model is to examine the Dufour effect on unsteady free convection second-grade fluid flow past an accelerated moving plate subjected to the magnetic field through a porous medium. The thermal radiation and chemical reactions are also taken into account. The constitutive governing equations of the model with all levied initial and boundary conditions are written in non-dimensional form. The non-dimensional equations that govern the flow model are transformed into a time-fractional model using the Caputo, Caputo-Fabrizio, and Atangana-Baleanu time-fractional derivatives. The Laplace transform technique is applied to the differential equations of the flow model to obtain the exact solution for concentration, temperature, and velocity fields. The expression for the Sherwood number, the Nusselt number, and skin friction are also derived analytically. The effects of diffusion-thermo, chemical reactions, second-grade parameterfractional parameter (), porosity, magnetic parameter, heat absorption/generation, and thermal radiation on velocity profiles are studied through various figures. It is observed that the velocity profiles for Caputo-Fabrizio fractional derivatives are higher as compared to Caputo and Atangana-Baleanu fractional derivatives. It is also seen that for the value of fractional parameter → 1, the velocity profiles obtained via Caputo, Caputo-Fabrizo, and Atangana-Baleanu derivatives are identical.
The objective of this paper is to analyze the influence of heat absorption/generation and mass di... more The objective of this paper is to analyze the influence of heat absorption/generation and mass diffusion on magnetohydrodynamics(MHD) Jeffrey fluid flow over a perpendicular plate moving exponentially immersed in a porous media. The Newtonian heating condition are udes for the fluid motion. The impact of thermal radiation is used in the energy equation. The two types of magnetic field have been evaluated. The main purpose of present work is to acquire the analytical solution with the help of Atangana-Baleanu (AB), Caputo, and Caputo-Fabrizio fractional derivatives. We have drawn a graphical comparison between the solutions of these three types of fractional models of jeffery fluid. Graphs of different parameters have been also plotted using MathCad software. Furthermore, comparison among ordinary and fractionalized velocity fields are made to observe the impact of fractional parameter. It is clear from graph that velocity obtained with ordinary derivative is higher than that obtained with fractional derivatives. It is also found that velocity obtained with Atangana-Baleanu (AB) fractional derivative is smaller than that obtained with Caputo and Caputo-Fabrizio fractional derivatives. Therefore, Atangana-Baleanu fractional derivative is the best choice to obtain controlled velocity.
In this paper, unsteady flow of fractionalized Maxwell fluid over an inclined vertical plate is c... more In this paper, unsteady flow of fractionalized Maxwell fluid over an inclined vertical plate is considered by using thermo diffusion and slip effects. The flow model is solved using Constant proportional Caputo fractional derivative. Initially, the governing equations are made non-dimensional and then solved by Laplace transform. To see the impact of different flow parameters on the velocity, temperature and concentration, we have drawn some graphs. In addition, it is observed that magnetic field has decreasing effect on fluid motion whereas thermo-diffusion have increasing effect on fluid motion.
Analytical solution of thermo diffusion effect on magnetohydrodynamics flow of fractionalized Cas... more Analytical solution of thermo diffusion effect on magnetohydrodynamics flow of fractionalized Casson fluid over a vertical plate immersed in a porous media is obtained. Moreover, in the model of the problem, additional effects, like a chemical reaction, heat source/sink, and thermal radiation are also considered. The model is solved by three approaches, namely, Atangana-Baleanu, Caputo-Fabrizio, and Caputo fractional derivative of non-integer order γ. The governing dimensionless equations for temperatures, concentrations, and velocities are solved using Laplace transform method and compared graphically. The effects of different parameters like fractional parameter γ, Thermo diffusion Sr, and magnetic parameter M are discussed through numerous graphs. Furthermore, comparisons among ordinary and fractionalized velocity fields are also drawn. It is found that the velocity obtained with Atangana-Baleanu fractional derivative is less than that obtained by Caputo, Caputo-Fabrizio, or ordinary derivatives.
The objective of this paper is to analyze the influence of thermo-diffusion on magnetohydrodynami... more The objective of this paper is to analyze the influence of thermo-diffusion on magnetohydrodynamics (MHD) flow of fractional second grade fluid immersed in a porous media over an exponentially accelerated vertical plate. In addition, other factors such as heat absorption and chemical reaction are used in the problem. More exactly, the fractional model has been developed using the generalized Fick's and Fourier's laws. The Caputo-Fabrizio (CF) fractional derivative has been used to solved the model. Initially, the flow modeled system of partial differential equations are transformed into dimensional form through suitable dimensionless variable and then Laplace transform technique has been used to solved the set of dimensionless governing equations for velocity profile, temperature profile, and concentration profile. The influence of different parameters like diffusion-thermo, fractional parameter, magnetic field, chemical reaction, heat obsorption, Schmidt number, time, Prandtl number and second grade parameter are discussed through numerous graphs. From figures, it is observed that fluid motion decreases with increasing values of Schmidt number, Prandtl number, magnetic parameter, and chemical reaction, whereas velocity field decreases with decreasing values of diffusion-thermo and mass grashof number. In order to check the athenticity of present work, we compare the present work with already published model graphically.
The objective of this model is to examine the Dufour effect on unsteady free convection second-gr... more The objective of this model is to examine the Dufour effect on unsteady free convection second-grade fluid flow past an accelerated moving plate subjected to the magnetic field through a porous medium. The thermal radiation and chemical reactions are also taken into account. The constitutive governing equations of the model with all levied initial and boundary conditions are written in non-dimensional form. The non-dimensional equations that govern the flow model are transformed into a time-fractional model using the Caputo, Caputo-Fabrizio, and Atangana-Baleanu time-fractional derivatives. The Laplace transform technique is applied to the differential equations of the flow model to obtain the exact solution for concentration, temperature, and velocity fields. The expression for the Sherwood number, the Nusselt number, and skin friction are also derived analytically. The effects of diffusion-thermo, chemical reactions, second-grade parameterfractional parameter (), porosity, magnetic parameter, heat absorption/generation, and thermal radiation on velocity profiles are studied through various figures. It is observed that the velocity profiles for Caputo-Fabrizio fractional derivatives are higher as compared to Caputo and Atangana-Baleanu fractional derivatives. It is also seen that for the value of fractional parameter → 1, the velocity profiles obtained via Caputo, Caputo-Fabrizo, and Atangana-Baleanu derivatives are identical.
Numerous researchers have been drawn to the rheology of non-Newtonian fluids because of their div... more Numerous researchers have been drawn to the rheology of non-Newtonian fluids because of their diverse uses in the engineering and manufacturing fields, such as lubrication, plastic processing, and mining. Additionally, the characteristics of magnetohydrodynamics non-Newtonian fluids permit its widespread application in computer hard drives, loudspeakers, magnetic resonance imaging, the administration of magnetic medicines, and magnetic hyperthermia. The current work is focused on the analysis of heat and mass transfer in a magnetohydrodynamics Brinkman nanofluid flows across a vertical plate because of these possible uses. The modeling also takes into account the passive and active control of the Brinkman nanofluid. Using suitable nondimensional variables, ordinary differential equations are created from the modeling equations, and the Laplace transform method is used to solve these equations. Semi-analytical solutions for temperature, concentration, and velocity are found after employing the Laplace transform approach to address the issue.
Numerous researchers have been drawn to the rheology of non-Newtonian fluids because of their div... more Numerous researchers have been drawn to the rheology of non-Newtonian fluids because of their diverse uses in the engineering and manufacturing fields, such as lubrication, plastic processing, and mining. Additionally, the characteristics of magnetohydrodynamics non-Newtonian fluids permit its widespread application in computer hard drives, loudspeakers, magnetic resonance imaging, the administration of magnetic medicines, and magnetic hyperthermia. The current work is focused on the analysis of heat and mass transfer in a magnetohydrodynamics Brinkman nanofluid flows across a vertical plate because of these possible uses. The modeling also takes into account the passive and active control of the Brinkman nanofluid. Using suitable nondimensional variables, ordinary differential equations are created from the modeling equations, and the Laplace transform method is used to solve these equations. Semi-analytical solutions for temperature, concentration, and velocity are found after employing the Laplace transform approach to address the issue.
Unsteady magnetohydrodynamics (MHD) flow of fractionalized Brinkman-type fluid over a vertical pl... more Unsteady magnetohydrodynamics (MHD) flow of fractionalized Brinkman-type fluid over a vertical plate is discussed. In the model of problem, additional effects such as heat generation/absorption and chemical reaction are also considered. e model is solved by using the Caputo fractional derivative. e governing dimensionless equations for velocity, concentration, and temperature profiles are solved using the Laplace transform method and compared graphically. e effects of different parameters like fractional parameter, heat generation/absorption Q, chemical reaction R, and magnetic parameter M are discussed through numerous graphs. Furthermore, comparison among ordinary and fractionalized velocity fields are also drawn. From the figures, it is observed that chemical reaction and magnetic field have decreasing effect on velocity profile, whereas thermal radiation and mass Grashof numbers have increasing effect on the velocity of the fluid.
The generalized magnetohydrodynamics (MHD) free convection flow of a Casson fluid through a chann... more The generalized magnetohydrodynamics (MHD) free convection flow of a Casson fluid through a channel immersed in a porous media with mass and heat transfer is considered. With heat generation, the contribution of concentration gradient is taken into account for heat flux (Dufour effect), and chemical reaction of order first for species balance is also considered. Initially, governing equations of flow model are reduced to nondimensional equations and then solved analytically. The transformed solutions for concentration, temperature, and velocity are written in summation form to invert by Laplace transform easily. The closed form solution of field variables has been plotted graphically due to different parametric variations to analyze the behavior of concentration, temperature, and flow fields against the physical parameters. Furthermore, comparisons among fractionalized and ordinary concentration, temperature,
The study investigates the combined impact of heat and mass transfer on a vertical plate, conside... more The study investigates the combined impact of heat and mass transfer on a vertical plate, considering factors such as an applied magnetic field, thermal radiation, heat absorption, and a first-order chemical reaction. The fluid under examination is assumed to be an electrically conducting Cunanofluid based on water. Thermophysical properties are derived from Table 1 for both the base fluid (water) and nanoparticles (Cu), with the nanoparticle volume fraction chosen within the range of 0.01 to 0.02. A novel aspect of this study involves considering both passive and active control of the Maxwell nanofluid. The governing equations are solved using the Laplace transform technique to obtain uniform closed-form solutions. Graphical representations illustrate the velocity, temperature, concentration, and Bio-Convection profiles under various flow parameters. Remarkably, the velocity profile exhibits consistent behavior for both stationary g ¼ 0 and moving g ¼ 1 plates, as depicted in Figures 2-10. The obtained semi-analytical solutions successfully fulfill all initial and boundary conditions. Moreover, manipulating the nanoparticle volume fraction demonstrates significant control over the flow and heat transfer characteristics.
Fractal-fractional derivative has numerous significance in real world problems. The main goal of ... more Fractal-fractional derivative has numerous significance in real world problems. The main goal of this derivative is the use of memory effects to formulate the model. Due to extensive applications of fractional derivatives, in the present article fractional order model of Brinkman fluid has been analyzed. The governing equations of the present flow model are solved numerically by using Cranck-Nicolson method to obtain the solutions for mass, energy, and momentum equations. In additions the physical aspects of material and flow parameters like as Prandtl number, magnetic force, Schmidt number, Grashof thermal number, Grashof mass number, especially the fractional operators are studied by drawing the graphs of field of interest.
Acta Crystallographica Section E Structure Reports Online, 2010
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Papers by Muhammad Ramzan