scholarly journals MHD Flow and Heat Transfer in Sodium Alginate Fluid with Thermal Radiation and Porosity Effects: Fractional Model of Atangana–Baleanu Derivative of Non-Local and Non-Singular Kernel

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1295 ◽  
Author(s):  
Arshad Khan ◽  
Dolat Khan ◽  
Ilyas Khan ◽  
Muhammad Taj ◽  
Imran Ullah ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Temperature Profile ◽  
Sodium Alginate ◽  
Mhd Flow ◽  
Casson Fluid ◽  
Singular Kernel ◽  
Heat Transfer Analysis ◽  
Fractional Model ◽  
The Laplace Transform ◽  
Non Local

Heat transfer analysis in an unsteady magnetohydrodynamic (MHD) flow of generalized Casson fluid over a vertical plate is analyzed. The medium is porous, accepting Darcy’s resistance. The plate is oscillating in its plane with a cosine type of oscillation. Sodium alginate (SA–NaAlg) is taken as a specific example of Casson fluid. The fractional model of SA–NaAlg fluid using the Atangana–Baleanu fractional derivative (ABFD) of the non-local and non-singular kernel has been examined. The ABFD definition was based on the Mittag–Leffler function, and promises an improved description of the dynamics of the system with the memory effects. Exact solutions in the case of ABFD are obtained via the Laplace transform and compared graphically. The influence of embedded parameters on the velocity field is sketched and discussed. A comparison of the Atangana–Baleanu fractional model with an ordinary model is made. It is observed that the velocity and temperature profile for the Atangana–Baleanu fractional model are less than that of the ordinary model. The Atangana–Baleanu fractional model reduced the velocity profile up to 45.76% and temperature profile up to 13.74% compared to an ordinary model.

MHD FLOW AND HEAT TRANSFER IN A CASSON FLUID OVER A NONLINEARLY STRETCHING SHEET WITH NEWTONIAN HEATING

2018 ◽  
Vol 49 (12) ◽  
pp. 1185-1198 ◽  
Author(s):  
Abid Hussanan ◽  
Mohd Zuki Salleh ◽  
Hamzeh Taha Alkasasbeh ◽  
Ilyas Khan
Keyword(s):  
Heat Transfer ◽  
Stretching Sheet ◽  
Mhd Flow ◽  
Casson Fluid ◽  
Newtonian Heating ◽  
Flow And Heat Transfer ◽  
Nonlinearly Stretching Sheet

scholarly journals Fractional model for MHD flow of Casson fluid with cadmium telluride nanoparticles using the generalized Fourier’s law

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Nadeem Ahmad Sheikh ◽  
Dennis Ling Chuan Ching ◽  
Ilyas Khan ◽  
Hamzah Bin Sakidin ◽  
Muhammad Jamil ◽  
...  
Keyword(s):  
Energy Equation ◽  
Volume Fraction ◽  
Mhd Flow ◽  
Integral Transforms ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Fourier’S Law ◽  
Fractional Model ◽  
Laplace Transformations ◽  
Fourier's Law

AbstractThe present work used fractional model of Casson fluid by utilizing a generalized Fourier’s Law to construct Caputo Fractional model. A porous medium containing nanofluid flowing in a channel is considered with free convection and electrical conduction. A novel transformation is applied for energy equation and then solved by using integral transforms, combinedly, the Fourier and Laplace transformations. The results are shown in form of Mittag-Leffler function. The influence of physical parameters have been presented in graphs and values in tables are discussed in this work. The results reveal that heat transfer increases with increasing values of the volume fraction of nanoparticles, while the velocity of the nanofluid decreases with the increasing values of volume fraction of these particles.

Heat Transfer Analysis in Metal Foams With Low-Conductivity Fluids

2006 ◽  
Vol 128 (8) ◽  
pp. 784-792 ◽  
Author(s):  
Nihad Dukhan ◽  
Rubén Picón-Feliciano ◽  
Ángel R. Álvarez-Hernández
Keyword(s):  
Heat Transfer ◽  
Temperature Profile ◽  
Thermal Equilibrium ◽  
Metal Foam ◽  
Flow Direction ◽  
Reynolds Numbers ◽  
Heat Transfer Analysis ◽  
Local Thermal Equilibrium ◽  
Open Cell ◽  
Simplifying Assumptions

The use of open-cell metal foam in contemporary technologies is increasing rapidly. Certain simplifying assumptions for the combined conduction∕convection heat transfer analysis in metal foam have not been exploited. Solving the complete, and coupled, fluid flow and heat transfer governing equations numerically is time consuming. A simplified analytical model for the heat transfer in open-cell metal foam cooled by a low-conductivity fluid is presented. The model assumes local thermal equilibrium between the solid and fluid phases in the foam, and neglects the conduction in the fluid. The local thermal equilibrium assumption is supported by previous studies performed by other workers. The velocity profile in the foam is taken as non-Darcean slug flow. An approximate solution for the temperature profile in the foam is obtained using a similarity transform. The solution for the temperature profile is represented by the error function, which decays in what looks like an exponential fashion as the distance from the heat base increases. The model along with the simplifying assumptions were verified by direct experiment using air and several aluminum foam samples heated from below, for a range of Reynolds numbers and pore densities. The foam samples were either 5.08- or 20.32‐cm-thick in the flow direction. Reasonably good agreement was found between the analytical and the experimental results for a considerable range of Reynolds numbers, with the agreement being generally better for higher Reynolds numbers, and for foam with higher surface area density.

scholarly journals Heat Transfer Analysis for Non-Contacting Mechanical Face Seals Using the Variable-Order Derivative Approach

Energies ◽  
2021 ◽  
Vol 14 (17) ◽  
pp. 5512
Author(s):  
Slawomir Blasiak
Keyword(s):  
Heat Transfer ◽  
Classical Equation ◽  
Heat Transfer Analysis ◽  
Order Derivative ◽  
Variable Order ◽  
Fractional Model ◽  
Face Seals ◽  
Fractional Models ◽  
Characteristic Features ◽  
Variable Order Derivative

This article presents a variable-order derivative (VOD) time fractional model for describing heat transfer in the rotor or stator in non-contacting mechanical face seals. Most theoretical studies so far have been based on the classical equation of heat transfer. Recently, constant-order derivative (COD) time fractional models have also been used. The VOD time fractional model considered here is able to provide adequate information on the heat transfer phenomena occurring in non-contacting face seals, especially during the startup. The model was solved analytically, but the characteristic features of the model were determined through numerical simulations. The equation of heat transfer in this model was analyzed as a function of time. The phenomena observed in the seal include the conduction of heat from the fluid film in the gap to the rotor and the stator, followed by convection to the fluid surrounding them. In the calculations, it is assumed that the working medium is water. The major objective of the study was to compare the results of the classical equation of heat transfer with the results of the equations involving the use of the fractional-order derivative. The order of the derivative was assumed to be a function of time. The mathematical analysis based on the fractional differential equation is suitable to develop more detailed mathematical models describing physical phenomena.

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