scholarly journals Heat and Mass Transfer Impact on Differential Type Nanofluid with Carbon Nanotubes: A Study of Fractional Order System

2021 ◽  
Vol 5 (4) ◽  
pp. 231
Author(s):  
Fatima Javed ◽  
Muhammad Bilal Riaz ◽  
Nazish Iftikhar ◽  
Jan Awrejcewicz ◽  
Ali Akgül
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Fractional Derivatives ◽  
Differential Operators ◽  
Fluid Velocity ◽  
Order System ◽  
Inversion Algorithm ◽  
Thermal Generation ◽  
Nano Fluid ◽  
First Order Chemical Reaction

This paper is an analysis of flow of MHD CNTs of second grade nano-fluid under the influence of first order chemical reaction, suction, thermal generation and magnetic field. The fluid is flowing through a porous medium. For the study of heat and mass transfer, we applied the newly introduced differential operators to model such flow. The equations for heat, mass and momentum are established in the terms of Caputo (C), Caputo–Fabrizio (CF) and Atangana–Baleanu in Caputo sense (ABC) fractional derivatives. This shows the novelty of this work. The equations for heat, mass and momentum are established in the terms of Caputo (C), Caputo–Fabrizio (CF) and Atangana–Baleanu in Caputo sense (ABC) fractional derivatives. The solutions are evaluated by employing Laplace transform and inversion algorithm. The flow in momentum profile due to variability in the values of parameters are graphically illustrated among C, CF and ABC models. It is concluded that fluid velocity showed decreasing behavior for χ, P, ℏ2, Mo, Pr, ℵ and Sc while it showed increasing behavior for Gr, Gm, κ and Ao. Moreover, ABC fractional operator presents larger memory effect than C and CF fractional operators.

scholarly journals Comparative study of heat and mass transfer of generalized MHD Oldroyd-B bio-nano fluid in a permeable medium with ramped conditions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Fuzhang Wang ◽  
Sadique Rehman ◽  
Jamel Bouslimi ◽  
Hammad Khaliq ◽  
Muhammad Imran Qureshi ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Prandtl Number ◽  
Heat And Mass Transfer ◽  
Differential Operators ◽  
Fluid Model ◽  
Nano Particles ◽  
Order Derivative ◽  
Grashof Number ◽  
Integer Order ◽  
Nano Fluid

AbstractThis article aims to investigate the heat and mass transfer of MHD Oldroyd-B fluid with ramped conditions. The Oldroyd-B fluid is taken as a base fluid (Blood) with a suspension of gold nano-particles, to make the solution of non-Newtonian bio-magnetic nanofluid. The surface medium is taken porous. The well-known equation of Oldroyd-B nano-fluid of integer order derivative has been generalized to a non-integer order derivative. Three different types of definitions of fractional differential operators, like Caputo, Caputo-Fabrizio, Atangana-Baleanu (will be called later as $$C,CF,AB$$ C , C F , A B ) are used to develop the resulting fractional nano-fluid model. The solution for temperature, concentration, and velocity profiles is obtained via Laplace transform and for inverse two different numerical algorithms like Zakian’s, Stehfest’s are utilized. The solutions are also shown in tabular form. To see the physical meaning of various parameters like thermal Grashof number, Radiation factor, mass Grashof number, Schmidt number, Prandtl number etc. are explained graphically and theoretically. The velocity and temperature of nanofluid decrease with increasing the value of gold nanoparticles, while increase with increasing the value of both thermal Grashof number and mass Grashof number. The Prandtl number shows opposite behavior for both temperature and velocity field. It will decelerate both the profile. Also, a comparative analysis is also presented between ours and the existing findings.

Effect of Magnetic Field with Parabolic Motion on Fractional Second Grade Fluid

2021 ◽  
Vol 5 (4) ◽  
pp. 163
Author(s):  
Nazish Iftikhar ◽  
Muhammad Bilal Riaz ◽  
Jan Awrejcewicz ◽  
Ali Akgül
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Analytical Solutions ◽  
Differential Operators ◽  
Fluid Velocity ◽  
Rate Of Change ◽  
Second Grade ◽  
Dynamical Process ◽  
Second Grade Fluid ◽  
Grade Fluid

This paper is an analysis of the flow of magnetohydrodynamics (MHD) second grade fluid (SGF) under the influence of chemical reaction, heat generation/absorption, ramped temperature and concentration and thermodiffusion. The fluid was made to flow through a porous medium. It has been proven in many already-published articles that heat and mass transfer do not always follow the classical mechanics process that is known as memoryless process. Therefore, the model using classical differentiation based on the rate of change cannot really replicate such a dynamical process very accurately; thus, a different concept of differentiation is needed to capture such a process. Very recently, new classes of differential operators were introduced and have been recognized to be efficient in capturing processes following the power law, the decay law and the crossover behaviors. For the study of heat and mass transfer, we applied the newly introduced differential operators to model such flow. The equations for heat, mass and momentum are established in the terms of Caputo (C), Caputo–Fabrizio (CF) and Atangana–Baleanu in Caputo sense (ABC) fractional derivatives. The Laplace transform, inversion algorithm and convolution theorem were used to derive the exact and semi-analytical solutions for all cases. The obtained analytical solutions were plotted for different values of existing parameters. It is concluded that the fluid velocity shows increasing behavior for κ, Gr and Gm, while velocity decreases for Pr and M. For Kr, both velocity and concentration curves show decreasing behavior. Fluid flow accelerates under the influence of Sr and R. Temperature and concentration profiles increase for Sr and R. Moreover, the ABC fractional operator presents a larger memory effect than C and CF fractional operators.

Exploration of Chemical Reaction Effects on Entropy Generation in Heat and Mass Transfer of Magneto-Jeffery Liquid

2018 ◽  
Vol 16 (9) ◽  
Author(s):  
R. Mohapatra ◽  
B. Mahanthesh ◽  
B.J. Gireesha ◽  
S.R. Mishra
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Chemical Engineering ◽  
Numerical Solutions ◽  
Ceramic Materials ◽  
Transverse Magnetic ◽  
Cross Diffusion ◽  
Order Chemical Reaction ◽  
First Order Chemical Reaction

AbstractIn many chemical engineering processes, a chemical reaction between a foreign mass and the fluid does occur. These processes find relevance in polymer production, oxidation of solid materials, ceramics or glassware manufacturing, tubular reactors, food processing, and synthesis of ceramic materials. Therefore, an exploration of homogeneous first-order chemical reaction effects on heat and mass transfer along with entropy analysis of Jeffrey liquid flow towards a stretched isothermal porous sheet is performed. Fluid is conducting electrically in the company of transverse magnetic field. Variations in heat and mass transfer mechanisms are accounted in the presence of viscous dissipation, heat source/sink and cross-diffusion aspects. The partial differential equations system governing the heat transfer of Jeffery liquid is reformed to the ordinary differential system through relevant transformations. Numerical solutions based on Runge-Kutta shooting method are obtained for the subsequent nonlinear problem. A parametric exploration is conducted to reveal the tendency of the solutions. The present study reveals that the Lorentz force due to magnetism can be used as a key parameter to control the flow fields. Entropy number is larger for higher values of Deborah and Brinkman numbers. It is also established that the concentration species field and its layer thickness of the Jeffery liquid decreases for a stronger chemical reaction aspect. To comprehend the legitimacy of numerical results a comparison with the existing results is made in this exploration and alleged an admirable agreement.

Heat and Mass Transfer of a MHD Flows of An Oldroyd 8-Constant Nano-Fluid Through a Non-Darcy Porous Medium

2017 ◽  
Vol 14 (1) ◽  
pp. 321-329
Author(s):  
Abeer A Shaaban
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Prandtl Number ◽  
Heat And Mass Transfer ◽  
Induced Magnetic Field ◽  
Linear Ordinary Differential Equations ◽  
Nano Fluid ◽  
Non Linear

Explicit finite-difference method was used to obtain the solution of the system of the non-linear ordinary differential equations which transform from the non-linear partial differential equations. These equations describe the steady magneto-hydrodynamic flow of an oldroyd 8-constant non-Newtonian nano-fluid through a non-Darcy porous medium with heat and mass transfer. The induced magnetic field was taken into our consideration. The numerical formula of the velocity, the induced magnetic field, the temperature, the concentration, and the nanoparticle concentration distributions of the problem were illustrated graphically. The effect of the material parameters (α1 α2), Darcy number Da, Forchheimer number Fs, Magnetic Pressure number RH, Magnetic Prandtl number Pm, Prandtl number Pr, Radiation parameter Rn, Dufour number Nd, Brownian motion parameter Nb, Thermophoresis parameter Nt, Heat generation Q, Lewis number Le, and Sort number Ld on those formula were discussed specially in the case of pure Coutte flow (U0 = 1, d <inline-formula> <mml:math display="block"> <mml:mrow> <mml:mover accent="true"> <mml:mi>P</mml:mi> <mml:mo stretchy="true">^</mml:mo> </mml:mover> </mml:mrow> </mml:math> </inline-formula> /dx = 0). Also, an estimation of the global error for the numerical values of the solutions is calculated by using Zadunaisky technique.

scholarly journals THEORETICAL STUDY OF MHD MAXWELL FLUID WITH COMBINED EFFECT OF HEAT AND MASS TRANSFER VIA LOCAL AND NONLOCAL TIME DERIVATIVES

Fractals ◽  
2021 ◽  
pp. 2240010
Author(s):  
MUHAMMAD BILAL RIAZ ◽  
FAHD JARAD ◽  
DUMITRU BALEANU ◽  
MARYAM ASGIR
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Integral Transform ◽  
Previous History ◽  
Maxwell Fluid ◽  
Rate Of Change ◽  
Combined Effect ◽  
Inversion Algorithm ◽  
Previous State ◽  
Definition Of

This study highlights the combined effect of heat and mass transfer on MHD Maxwell fluid under time-dependent generalized boundary conditions for velocity, temperature, and concentration. The classical calculus due to the fact that it is assumed as the instant rate of change of the output when the input level changes. Therefore, it is not able to include the previous state of the system called the memory effect. But in the fractional calculus (FC), the rate of change is affected by all points of the considered interval, so it can incorporate the previous history/memory effects of any system. Due to this reason, we applied the modern definition of fractional derivatives (local and nonlocals kernels). Here, the order of fractional derivative will be treated as an index of memory. The exact and semi-analytical solutions are obtained using the integral transform and inversion algorithm. Several important properties of different parameters are analyzed by graphs. Interesting results are revealed by this investigation due to their vast applications in engineering and applied sciences.

Thermophoretic and Nonlinear Convection in Non-Darcy Porous Medium

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
P. K. Kameswaran ◽  
P. Sibanda ◽  
M. K. Partha ◽  
P. V. S. N. Murthy
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Heat And Mass Transfer ◽  
Fluid Velocity ◽  
Solute Concentration ◽  
Fluid Temperature ◽  
Nonlinear Convection ◽  
Transfer Rates ◽  
Special Cases ◽  
Layer Flow

In this paper, we study the effects of nonlinear convection and thermophoresis in steady boundary layer flow over a vertical impermeable wall in a non-Darcy porous medium. Both the fluid temperature and the solute concentration are assumed to be nonlinear while at the wall, both the temperature and concentration are maintained at a constant value. A similarity transformation was used to obtain a system of nonlinear ordinary differential equations, which were then solved numerically using the Matlab bvp4c solver. A comparison of the numerical results with previously published results for special cases shows a good agreement. The effects of the nonlinear temperature and concentration parameters on the velocity and heat and mass transfer are shown graphically. A representative sample of the results is presented showing the effects of thermophoresis on the fluid velocity and heat and mass transfer rates. It is found among other results, that the concentration profiles decreased with increasing values of the thermophoretic parameter.

scholarly journals A fractional study of generalized Oldroyd-B fluid with ramped conditions via local & non-local kernels

2021 ◽  
Vol 10 (1) ◽  
pp. 177-186
Author(s):  
Syed Tauseef Saeed ◽  
Muhammad Bilal Riaz ◽  
Dumitru Baleanu
Keyword(s):  
Mass Transfer ◽  
Prandtl Number ◽  
Heat And Mass Transfer ◽  
Convective Flow ◽  
Integral Transform ◽  
Mass Transfer Process ◽  
Rate Of Change ◽  
Physical Parameters ◽  
Inversion Algorithm ◽  
Definition Of

Abstract Convective flow is a self-sustained flow with the effect of the temperature gradient. The density is nonuniform 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 Oldroyd-B fluid in the presence of ramped conditions. The new governing equations of MHD Oldroyd-B fluid have been fractionalized by means of singular and non-singular differentiable operators. In order to have an accurate physical significance of imposed conditions on the geometry of Oldroyd-B fluid, the ramped temperature, concentration and velocity are considered. The fractional solutions of temperature, concentration and velocity have been investigated by means of integral transform and inversion algorithm. The influence of physical parameters and flow is analyzed graphically via computational software (MATHCAD-15). The velocity profile decreases by increasing the Prandtl number. The existence of a Prandtl number may reflect the control of the thickness and enlargement of the thermal effect. The classical calculus is assumed as the instant rate of change of the output when the input level changes. Therefore it is not able to include the previous state of the system called the memory effect. Due to this reason, we applied the modern definition of fractional derivatives. Obtained generalized results are very important due to their vast applications in the field of engineering and applied sciences.

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