Calorimetric Investigation for Thermal Plate of Casson Fluid via Fractional Derivative

2019 ◽  
Vol 8 (8) ◽  
pp. 1668-1675
Author(s):  
Muhammad Nawaz Mirbahar ◽  
Kashif Ali Abro ◽  
Abdul Wasim Shaikh
Keyword(s):  
Temperature Distribution ◽  
Velocity Profile ◽  
Mass Concentration ◽  
Special Functions ◽  
Integral Transforms ◽  
Casson Fluid ◽  
Collective Effects ◽  
Fractional Operator ◽  
Moving Plate ◽  
Fractional Solution

The manuscript reveals the collective effects of the moving plate of Casson fluid in which magnetic, porous outcomes are under consideration. Thermal stratification is investigated to disclose the hidden phenomenon of mass concentration and temperature distribution. Fractional operator has been applied on the fundamental equations of Casson fluid namely Caputo-Fabrizio fractional operator based on sufficient memory operator. For the exact analysis of basic fractional governing equations of velocity profile, temperature distribution and mass concentration the integral transforms have been employed. The solutions of the dimensionless equations have been described in terms special functions in convoluted form. For the sake of non-fractional solution of the basic equations of the Casson fluid X = 1 in the obtained solutions has been implemented for the four type's fluid models. Finally, thermal conductivity of the fluid has been analyzed by estimating various different parametric values which result the increment in velocity profile along with porous permeability but reverse in transvers magnetic field on the flow.

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.

Nusselt Numbers in Rectangular Ducts With Laminar Viscous Dissipation

1999 ◽  
Vol 121 (4) ◽  
pp. 1083-1087 ◽  
Author(s):  
G. L. Morini ◽  
M. Spiga
Keyword(s):  
Boundary Condition ◽  
Temperature Distribution ◽  
Viscous Dissipation ◽  
Integral Transforms ◽  
Navier Stokes ◽  
Brinkman Number ◽  
Balance Equations ◽  
Nusselt Numbers ◽  
Finite Integral ◽  
Axial Heat

In this paper, the steady temperature distribution and the Nusselt numbers are analytically determined for a Newtonian incompressible fluid in a rectangular duct, in fully developed laminar flow with viscous dissipation, for any combination of heated and adiabatic sides of the duct, in H1 boundary condition, and neglecting the axial heat conduction in the fluid. The Navier-Stokes and the energy balance equations are solved using the technique of the finite integral transforms. For a duct with four uniformly heated sides (4 version), the temperature distribution and the Nusselt numbers are obtained as a function of the aspect ratio and of the Brinkman number and presented in graphs and tables. Finally it is proved that the temperature field in a fully developed T boundary condition can be obtained as a particular case of the H1 problem and that the corresponding Nusselt numbers do not depend on the Brinkman number.

Recent Developments in Calculation Methods for Turbulent Boundary Layers With Pressure Gradients and Heat Transfer

1966 ◽  
Vol 33 (2) ◽  
pp. 429-437 ◽  
Author(s):  
J. C. Rotta
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Temperature Distribution ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Calculation Methods ◽  
Recent Developments ◽  
Incompressible Boundary

A review is given of the recent development in turbulent boundary layers. At first, for the case of incompressible flow, the variation of the shape of velocity profile with the pressure gradient is discussed; also the temperature distribution and heat transfer in incompressible boundary layers are treated. Finally, problems of the turbulent boundary layer in compressible flow are considered.

scholarly journals Certain Integral Transform and Fractional Integral Formulas for the Generalized Gauss Hypergeometric Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Junesang Choi ◽  
Praveen Agarwal
Keyword(s):  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Integral Transform ◽  
Special Functions ◽  
Integral Transforms ◽  
Integral Formulas ◽  
Special Cases

A remarkably large number of integral transforms and fractional integral formulas involving various special functions have been investigated by many authors. Very recently, Agarwal gave some integral transforms and fractional integral formulas involving theFp(α,β)(·). In this sequel, using the same technique, we establish certain integral transforms and fractional integral formulas for the generalized Gauss hypergeometric functionsFp(α,β,m)(·). Some interesting special cases of our main results are also considered.

Thermally stratified stagnation point flow of Casson fluid with slip conditions

2015 ◽  
Vol 25 (4) ◽  
pp. 724-748 ◽  
Author(s):  
Tasawar Hayat ◽  
Muhammad Farooq ◽  
A. Alsaedi
Keyword(s):  
Velocity Profile ◽  
Stagnation Point ◽  
Design Methodology ◽  
Casson Fluid ◽  
Series Solutions ◽  
Analysis Method ◽  
Governing Equations ◽  
Content Type ◽  
Slip Effects ◽  
Homotopy Analysis

Purpose – The purpose of this paper is to focus on the stratified phenomenon through vertical stretching cylinder in the region of stagnation point with slip effects. Design/methodology/approach – Homotopy analysis method is used to find the series solutions of the governing equations. Findings – Velocity profile decreases with an increase in stratified parameters due to temperature and concentration. Velocity and thermal slips cause a reduction in the velocity profile. Thermally stratified and thermal slip parameters reduce the temperature field. Originality/value – The present analysis has not been existed in the literature yet.

scholarly journals Influence of Radiation and Mass Concentration on MHD Flow over a Moving Plate

2013 ◽  
Vol 5 (2) ◽  
pp. 18-23
Author(s):  
Godpower Onwugbuta ◽  
Yehuwdah E. Chad-Umoren ◽  
Chigozie Israel-Cookey
Keyword(s):  
Mass Concentration ◽  
Mhd Flow ◽  
Moving Plate

Unsteady Chemically Reacting Casson Fluid Flow in an Irregular Channel with Convective Boundary

2015 ◽  
Vol 70 (8) ◽  
pp. 583-591
Author(s):  
Muhammad Nasir ◽  
Adnan Saeed Butt ◽  
Asif Ali
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Mass Concentration ◽  
Perturbation Technique ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Wavy Wall ◽  
Convective Boundary ◽  
Grashof Number ◽  
Chemically Reacting

AbstractA mathematical model has been performed for momentum, temperature, and mass concentration of a time-dependent Casson fluid flow between a long vertical wavy wall and a parallel wavy wall subject to convective boundary conditions. Perturbation technique is used to convert the coupled partial differential equations for velocity, temperature, and mass concentration to systems of ordinary differential equations. Analytical results for these differential equations are computed. The effects of various physical parameters such as thermal conductivity, thermal Grashof number, solutal Grashof number, heat absorption parameter, and Biot number are analysed graphically.

On a family of the incomplete H-functions and associated integral transforms

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Manish Kumar Bansal ◽  
Devendra Kumar
Keyword(s):  
Integral Transform ◽  
Special Functions ◽  
Natural Extension ◽  
Integral Transforms ◽  
Legendre Transform ◽  
Physical Sciences ◽  
Special Cases ◽  
Improper Integrals ◽  
Jacobi Transform ◽  
Math Phys

Abstract Recently, Srivastava, Saxena and Parmar [H. M. Srivastava, R. K. Saxena and R. K. Parmar, Some families of the incomplete H-functions and the incomplete H ¯ {\overline{H}} -functions and associated integral transforms and operators of fractional calculus with applications, Russ. J. Math. Phys. 25 2018, 1, 116–138] suggested incomplete H-functions (IHF) that paved the way to a natural extension and decomposition of H-function and other connected functions as well as to some important closed-form portrayals of definite and improper integrals of different kinds of special functions of physical sciences. In this article, our key aim is to present some new integral transform (Jacobi transform, Gegenbauer transform, Legendre transform and 𝖯 δ {\mathsf{P}_{\delta}} -transform) of this family of incomplete H-functions. Further, we give several interesting new and known results which are special cases our key results.

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