scholarly journals Wall slip and non-integer order derivative effects on the heat transfer flow of Maxwell fluid over an oscillating vertical plate with new definition of fractional Caputo-Fabrizio derivatives

2017 ◽  
Vol 7 ◽  
pp. 1887-1898 ◽  
Author(s):  
Madeeha Tahir ◽  
M.A. Imran ◽  
N. Raza ◽  
M. Abdullah ◽  
Maryam Aleem
Keyword(s):  
Heat Transfer ◽  
Vertical Plate ◽  
Wall Slip ◽  
Maxwell Fluid ◽  
Order Derivative ◽  
Integer Order ◽  
Definition Of ◽  
Transfer Flow

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.

UNSTEADY HEAT TRANSFER FLOW OF A CASSON FLUID WITH NEWTONIAN HEATING AND THERMAL RADIATION

2016 ◽  
Vol 78 (4-4) ◽  
Author(s):  
Abid Hussanan ◽  
Mohd Zuki Salleh ◽  
Ilyas Khan ◽  
Razman Mat Tahar
Keyword(s):  
Heat Transfer ◽  
Thermal Radiation ◽  
Vertical Plate ◽  
Casson Fluid ◽  
Newtonian Heating ◽  
Governing Equations ◽  
Unsteady Heat Transfer ◽  
Laplace Transform Technique ◽  
Limiting Case ◽  
Transfer Flow

This study investigates the unsteady heat transfer flow of a non-Newtonian Casson fluid over an oscillating vertical plate with Newtonian heating on the wall under the effects of thermal radiation. With the help of non-dimensional variables, governing equations are written into dimensionless form and then solved analytically by Laplace transform technique to find the solutions of temperature and velocity. The corresponding solutions of Nusselt number and skin friction are also calculated. The solution in term of viscous fluid is recovered as a limiting case of this work. The effects of the pertinent parameters on temperature and velocity are presented graphically and discussed details in this paper.  

scholarly journals Effect of Local and Non-Local Kernels on Heat Transfer of Mixed Convection Flow of the Maxwell Fluid

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
M. B. Riaz ◽  
A. Atangana ◽  
Maryam Asgir ◽  
Muhammad Altaf Khan ◽  
Hafte Amsalu Kahsay
Keyword(s):  
Heat Transfer ◽  
Mixed Convection ◽  
Laplace Transform ◽  
Maxwell Fluid ◽  
Memory Effects ◽  
Inverse Laplace Transform ◽  
Order Derivative ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Hybrid Form

The heat transfer study of mixed convection flow of the Maxwell fluid is carried out here. The fluid flow is demonstrated by the system of coupled partial differential equations in the dimensionless form firstly. Then, its fractional form is developed by using the new definition of the noninteger-order derivative with the singular kernel (Caputo/C) and nonsingular kernels (Caputo–Fabrizio/CF and Atangana–Baleanu (nonlocal)/ABC). The hybrid-form solutions are obtained by applying the Laplace transform, and for the inverse Laplace transform, the problem is tackled by the numerical algorithms of Stehfest and Tzou. The C, CF, and ABC solution comparison under the effects of considered different parameters is depicted. The physical aspects of the considered problem are well explained by C, CF, and ABC in comparison to the integer-order derivative due to its memory effects. Furthermore, the best fit model to explain the memory effects of velocity is CF. The solutions for the Newtonian fluid and ordinary Maxwell fluid are considered as a special case and found in the literature.

Application of Atangana-Baleanu fractional derivative to convection flow of MHD Maxwell fluid in a porous medium over a vertical plate

2018 ◽  
Vol 13 (1) ◽  
pp. 1 ◽  
Author(s):  
K.A. Abro ◽  
I. Khan ◽  
A. Tassaddiq
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Porous Medium ◽  
Fractional Derivative ◽  
Vertical Plate ◽  
Transfer Problem ◽  
Maxwell Fluid ◽  
Convection Flow ◽  
Study Heat Transfer ◽  
Fractional Parameter

Atangana-Baleanu fractional derivative has been applied to study heat transfer problem of magnetohydrodynamic (MHD) Maxwell fluid over a vertical plate embedded in a porous medium. The analytical solutions have been obtained for temperature distribution and velocity field by employing Laplace transforms technique for both sine and cosine oscillations of the plate. The general solutions have been expressed in terms of Fox-H function satisfying imposed conditions. The results are plotted graphically and discussed for embedded parameters such as magnetic field, Maxwell parameter, porous medium, Prandtl number and fractional parameter.

scholarly journals A scientific report on heat transfer analysis in mixed convection flow of Maxwell fluid over an oscillating vertical plate

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Ilyas Khan ◽  
Nehad Ali Shah ◽  
L. C. C. Dennis
Keyword(s):  
Heat Transfer ◽  
Mixed Convection ◽  
Vertical Plate ◽  
Maxwell Fluid ◽  
Velocity Shear ◽  
Heat Transfer Analysis ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Constant Wall Temperature ◽  
Scientific Report

Abstract This scientific report investigates the heat transfer analysis in mixed convection flow of Maxwell fluid over an oscillating vertical plate with constant wall temperature. The problem is modelled in terms of coupled partial differential equations with initial and boundary conditions. Some suitable non-dimensional variables are introduced in order to transform the governing problem into dimensionless form. The resulting problem is solved via Laplace transform method and exact solutions for velocity, shear stress and temperature are obtained. These solutions are greatly influenced with the variation of embedded parameters which include the Prandtl number and Grashof number for various times. In the absence of free convection, the corresponding solutions representing the mechanical part of velocity reduced to the well known solutions in the literature. The total velocity is presented as a sum of both cosine and sine velocities. The unsteady velocity in each case is arranged in the form of transient and post transient parts. It is found that the post transient parts are independent of time. The solutions corresponding to Newtonian fluids are recovered as a special case and comparison between Newtonian fluid and Maxwell fluid is shown graphically.

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