scholarly journals Power Law Kernel Analysis of MHD Maxwell Fluid with Ramped Boundary Conditions: Transport Phenomena Solutions Based on Special Functions

2021 ◽  
Vol 5 (4) ◽  
pp. 248
Author(s):  
Muhammad Bilal Riaz ◽  
Aziz-Ur Rehman ◽  
Jan Awrejcewicz ◽  
Ali Akgül
Keyword(s):  
Power Law ◽  
Wall Temperature ◽  
Integral Transformation ◽  
Special Functions ◽  
Maxwell Fluid ◽  
Dimensionless Time ◽  
Constant Concentration ◽  
Fractional Models ◽  
Effects Of Radiation ◽  
Energy And Momentum

In this paper, a new approach to find exact solutions is carried out for a generalized unsteady magnetohydrodynamic transport of a rate-type fluid near an unbounded upright plate, which is analyzed for ramped-wall temperature and velocity with constant concentration. The vertical plate is suspended in a porous medium and encounters the effects of radiation. An innovative definition of the time-fractional operator in power-law-kernel form is implemented to hypothesize the constitutive mass, energy, and momentum equations. The Laplace integral transformation technique is applied on a dimensionless form of governing partial differential equations by introducing some non-dimensional suitable parameters to establish the exact expressions in terms of special functions for ramped velocity, temperature, and constant-concentration fields. In order to validate the problem, the absence of the mass Grashof parameter led to the investigated solutions obtaining good agreement in existing literature. Additionally, several system parameters were used, such as as magnetic value M, Prandtl value Pr, Maxwell parameter λ, dimensionless time τ, Schmidt number “Sc”, fractional parameter α, andMass and Thermal Grashof numbers Gm and Gr, respectively, to examine their impacts on velocity, wall temperature, and constant concentration. Results are also discussed in detail and demonstrated graphically via Mathcad-15 software. A comprehensive comparative study between fractional and non-fractional models describes that the fractional model elucidate the memory effects more efficiently.

scholarly journals Special functions-based solutions of unsteady convective flow of a MHD Maxwell fluid for ramped wall temperature and velocity with concentration

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Muhammad Bilal Riaz ◽  
Jan Awrejcewicz ◽  
Aziz Ur Rehman ◽  
Muhammad Abbas
Keyword(s):  
Wall Temperature ◽  
Radiation Effects ◽  
Integral Transform ◽  
Special Functions ◽  
Maxwell Fluid ◽  
Skin Friction Coefficient ◽  
Dimensionless Time ◽  
Constant Concentration ◽  
Special Cases ◽  
Physical Impact

AbstractIn this paper a new approach is taken to find the exact solutions for generalized unsteady magnetohydrodynamic transport of a rate-type fluid near an unbounded upright plate and is analyzed for ramped wall temperature and velocity with constant concentration. The vertical plate is suspended in a porous medium and encounters radiation effects. Solutions based on special functions are obtained using an integral transform for an unsteady MHD Maxwell fluid in the presence of ramped velocity, temperature and constant concentration. The relations for Nusselt number and skin-friction coefficient are efficiently computed to precisely estimate the rate of heat transfer at the boundary and the shear stress. Results are also discussed in detail and demonstrated graphically using software to comprehensively analyze the dynamics of the proposed problem, and the physical impact of several system parameters, such as magnetic field M, Prandtl number Pr, the relaxation time λ, dimensionless time τ, Schmidt number Sc, Mass and Thermal Grashof numbers Gm and Gr, respectively, is studied. Furthermore, solutions for some recently published work are compared with the current study that endorses the authenticity of our derived results and proves that those investigations are limiting or special cases of the current problem.

scholarly journals Influence of Thermal Radiation on Unsteady MHD Free Convection Flow of Jeffrey Fluid over a Vertical Plate with Ramped Wall Temperature

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Nor Athirah Mohd Zin ◽  
Ilyas Khan ◽  
Sharidan Shafie
Keyword(s):  
Free Convection ◽  
Thermal Radiation ◽  
Wall Temperature ◽  
Vertical Plate ◽  
Convection Flow ◽  
Jeffrey Fluid ◽  
Dimensionless Time ◽  
Free Convection Flow ◽  
Laplace Transform Technique ◽  
The Laplace Transform

Influence of thermal radiation on unsteady magnetohydrodynamic (MHD) free convection flow of Jeffrey fluid over a vertical plate with ramped wall temperature is studied. The Laplace transform technique is used to obtain the analytical solutions. Expressions for skin friction and Nusselt number are also obtained. Results of velocity and temperature distributions are shown graphically for embedded parameters such as Jeffrey fluid parameterλ, Prandtl numberPr, Grashof numberGr, Hartmann numberHa, radiation parameterRd, and dimensionless timeτ. It is observed that the amplitude of velocity and temperature profile for isothermal are always higher than ramped wall temperature.

scholarly journals Dufour Effect with Ramped Wall Temperature and Specie Concentration on Natural Convection Flow Through A Channel

Physics ◽  
2019 ◽  
Vol 1 (1) ◽  
pp. 111-130 ◽  
Author(s):  
Jha ◽  
Gambo
Keyword(s):  
Wall Temperature ◽  
Numerical Solutions ◽  
Vertical Channel ◽  
Convection Flow ◽  
Physical Situation ◽  
Dimensionless Time ◽  
Dufour Effect ◽  
Laplace Transform Technique ◽  
Flow Through ◽  
The Mathematical Model

In this paper, we have obtained an analytical solution to the problem of unsteady free convection and mass transfer flow of an incompressible fluid through a vertical channel in the presence of Dufour effect (or diffusion thermo). The bounding plates are assumed to have ramped wall temperature as well as specie concentration. The mathematical model responsible for the physical situation is presented in dimensionless form and solved analytically using the powerful Laplace Transform Technique (LTT) under relevant initial and boundary conditions. In order to cross check the accuracy of the analytical results, numerical solutions are obtained using PDEPE solver in MATLAB. The expressions for temperature, concentration, and velocity are obtained. The effects of Dufour parameter, Prandtl number (Pr), Schmidt number (Sc), and dimensionless time are described during the course of these discussions. The temperature, concentration, and velocity profiles are graphically presented for some realistic values of Pr=0.025, 0.71, 7.0, 11.62, 100.0 and Sc=0.22, 0.60, 1.00, 2.62, while the values of all other parameters are arbitrarily taken.

scholarly journals Maxwell Nanofluid Flow over an Infinite Vertical Plate with Ramped and Isothermal Wall Temperature and Concentration

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Naveed Khan ◽  
Farhad Ali ◽  
Muhammad Arif ◽  
Zubair Ahmad ◽  
Aamina Aamina ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Molybdenum Disulfide ◽  
Wall Temperature ◽  
Base Fluid ◽  
Vertical Plate ◽  
Maxwell Fluid ◽  
Engine Oil ◽  
Isothermal Wall ◽  
The Impact ◽  
Infinite Vertical Plate

The aim of this study is to investigate how heat and mass transfer impacts the unsteady incompressible flow of Maxwell fluid. An infinite vertical plate with ramped and isothermal wall temperature and concentration boundary conditions is considered with the Maxwell fluid. Furthermore, in this study, engine oil has been taken as a base fluid due to its enormous applications in modern science and technologies. To see the importance of nanofluids, we have suspended molybdenum disulfide in engine oil base fluid to enhance its heat transfer rate. To investigate the flow regime, the system of equations was derived in the form of partial differential equations. The exact solutions to the complex system are obtained using the Laplace transform technique. Graphically, the impact of different embedded parameters on velocity, temperature, and concentration distributions has been shown. Through using the graphical analysis, we were interested in comparing the velocity, temperature, and concentration profiles for ramped and isothermal wall temperature and concentration. The magnitude of velocity, temperature, and concentration distributions is greater for an isothermal wall and less for a ramped wall, according to our observations. We observed that adding molybdenum disulfide nanoparticles to the engine oil increased the heat transfer up to 12.899%. Finally, the corresponding skin friction, Nusselt number, and Sherwood number have been calculated and presented in a tabular form.

scholarly journals Conjugate Effects of Radiation Flux on Double Diffusive MHD Free Convection Flow of a Nanofluid over a Power Law Stretching Sheet

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Muhammad Imran Anwar ◽  
Sharidan Shafie ◽  
Ilyas Khan ◽  
Mohd Zuki Salleh
Keyword(s):  
Magnetic Field ◽  
Free Convection ◽  
Power Law ◽  
Radiation Flux ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Buoyancy Parameter ◽  
Effects Of Radiation

This study theoretically investigates the conjugate effects of radiation flux and magnetohydrodynamic (MHD) on free convection boundary layer flow of a nanofluid over a nonlinear stretching sheet. It is assumed that the magnetic Reynolds number is small enough and the sheet is stretched with a power law velocity under the effects of the magnetic field, the buoyancy parameter, and the solutal buoyancy parameter. The model used for the nanofluid incorporates the effects of Rosseland approximation, Brownian motion, and thermophoresis parameters. By using appropriate similarity transformations, the governing nonlinear partial differential equations are transformed into dimensionless form and numerically solved using an implicit finite difference scheme known as the Keller-box method. It is found that the variations of magnetic field, buoyancy parameter, solutal buoyancy parameter, and the power law velocity parameter have strong influence on the motion.

scholarly journals Role of Newtonian heating on a Maxwell fluid via special functions: memory impact of local and nonlocal kernels

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nazish Iftikhar ◽  
Fatima Javed ◽  
Muhammad Bilal Riaz ◽  
Muhammad Abbas ◽  
Abdullah M. Alsharif ◽  
...  
Keyword(s):  
Memory Effect ◽  
Fractional Derivatives ◽  
Special Functions ◽  
Maxwell Fluid ◽  
Laplace Transforms ◽  
Time Dependent ◽  
Abc Model ◽  
Newtonian Heating ◽  
The Impact

AbstractThe impact of Newtonian heating on a time-dependent fractional magnetohydrodynamic (MHD) Maxwell fluid over an unbounded upright plate is investigated. The equations for heat, mass and momentum are established in terms of Caputo (C), Caputo–Fabrizio (CF) and Atangana–Baleanu (ABC) fractional derivatives. The solutions are evaluated by employing Laplace transforms. The change in the momentum profile due to variability in the values of parameters is graphically illustrated for all three C, CF and ABC models. The ABC model has proficiently revealed a memory effect.

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