Convective transport of thermal and solutal energy in unsteady MHD Oldroyd-B nanofluid flow

2021 ◽  
Author(s):  
Muhammad Yasir ◽  
Masood Khan ◽  
Awais Ahmed ◽  
Malik Zaka Ullah
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Heat Generation ◽  
Axisymmetric Flow ◽  
Convective Transport ◽  
Buongiorno’S Model ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

Abstract In this work, an analysis is presented for the unsteady axisymmetric flow of Oldroyd-B nanofluid generated by an impermeable stretching cylinder with heat and mass transport under the influence of heat generation/absorption, thermal radiation and first-order chemical reaction. Additionally, thermal and solutal performances of nanofluid are studied using an interpretation of the well-known Buongiorno's model, which helps us to determine the attractive characteristics of Brownian motion and thermophoretic diffusion. Firstly, the governing unsteady boundary layer equation's (PDEs) are established and then converted into highly non-linear ordinary differential equations (ODEs) by using the suitable similarity transformations. For the governing non-linear ordinary differential equations, numerical integration in domain [0, ∞) is carried out using the BVP Midrich scheme in Maple software. For the velocity, temperature and concentration distributions, reliable results are prepared for different physical flow constraints. According to the results, for increasing values of Deborah numbers, the temperature and concentration distribution are higher in terms of relaxation time while these are decline in terms of retardation time. Moreover, thermal radiation and heat generation/absorption are increased the temperature distribution and corresponding boundary layer thickness. With previously stated numerical values, the acquired solutions have an excellent accuracy.

scholarly journals MHD boundary layer slip flow of a casson fluid over an exponentially stretching surface in the presence of thermal radiation and chemical reaction

2016 ◽  
Vol 13 (2) ◽  
pp. 165-177 ◽  
Author(s):  
P. Bala Anki Reddy
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Casson Fluid ◽  
Stretching Surface ◽  
Linear Ordinary Differential Equations ◽  
Non Linear ◽  
Exponentially Stretching Surface ◽  
Exponentially Stretching

An analysis is carried out to investigate the steady two-dimensional magnetohydrodynamic boundary layer flow of a Casson fluid over an exponentially stretching surface in the presence of thermal radiation and chemical reaction. Velocity, thermal and solutal slips are considered instead of no-slip conditions at the boundary. Stretching velocity, wall temperature and wall concentration are considered in the exponential forms. The non-linear partial differential equations are converted into a system of non-linear ordinary differential equations by similarity transformations. The resultant non-linear ordinary differential equations are solved numerically by fourth order Runge-Kutta method along with shooting technique. The influence of various parameters on the fluid velocity, temperature, concentration, wall skin friction coefficient, the heat transfer coefficient and the Sherwood number have been computed and the results are presented graphically and discussed quantitatively. Comparisons with previously published works are performed on various special cases and are found to be in excellent agreement.  

Radiative Unsteady Rarefied Gaseous Flow Over a Stretching Sheet with Velocity Slip and Temperature Jump Effects

2020 ◽  
Vol 87 (3-4) ◽  
pp. 261
Author(s):  
Ram Prakash Sharma ◽  
N. Indumathi ◽  
S. Saranya ◽  
B. Ganga ◽  
A. K. Abdul Hakeem
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Stretching Sheet ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Gaseous Flow ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In this study a mathematical analysis has been carried out to scrutinize the unsteady boundary layer flow of an incompressible, rarefied gaseous flow over a vertical stretching sheet with velocity slip and thermal jump boundary conditions in the presence of thermal radiation. Using boundary layer approach and suitable similarity transformations, the governing partial differential equations with the boundary conditions are reduced to a system of non-linear ordinary differential equations. The resulting non-linear ordinary differential equations are solved with the help of fourth order Runge-Kutta method with shooting technique. The results obtained for the velocity profile, temperature profile, skin friction coefficient and the reduced Nusselt number are described through graphs. It is predicted that the velocity and temperature profiles are lower for unsteady flow and has an opposite effect for steady flow.

scholarly journals Effect of Thermal Radiation on Magneto-Convection of a Micropolar Nanoliquid towards a Non-Linear Stretching Surface with Convective Boundary

2018 ◽  
Vol 7 (4.10) ◽  
pp. 417
Author(s):  
K. Jagan ◽  
S. Sivasankaran ◽  
M. Bhuvaneswari ◽  
S. Rajan
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Convective Boundary Condition ◽  
Convection Flow ◽  
Stretching Surface ◽  
Convective Boundary ◽  
Linear Ordinary Differential Equations ◽  
Boundary Parameter ◽  
Non Linear

The objective of this paper is to analyze the effect of thermal radiation on MHD mixed convection flow of a micropolar nanoliquid   towards a non-linear stretching surface with convective boundary condition. The governing equations are converted into non-linear    ordinary differential equations by using suitable similarity transformations. The homotopy analysis method is used for solving the non-linear ordinary differential equations. The temperature profiles increase due to increase in thermal radiation parameter. The microrotation   profile increases when boundary parameter is increased. Also, the skin friction coefficient and local Nusselt are plotted for various    parameters.  

Stokes’ first problem for MHD flow of Casson nanofluid

2017 ◽  
Vol 13 (1) ◽  
pp. 2-10
Author(s):  
Syed Tauseef Mohyud-din ◽  
Umar Khan ◽  
Naveed Ahmed ◽  
M.M. Rashidi
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Mhd Flow ◽  
Governing Equations ◽  
Content Type ◽  
Buongiorno’S Model ◽  
Linear Ordinary Differential Equations ◽  
Flux Condition ◽  
Non Linear ◽  
Flow Heat

Purpose The purpose of this paper is to present investigation of the flow, heat and mass transfer of a nanofluid over a suddenly moved flat plate using Buongiorno’s model. This study is different from some of the previous studies as the effects of Brownian motion and thermophoresis on nanoparticle fraction are passively controlled on the boundary rather than actively. Design/methodology/approach The partial differential equations governing the flow are reduced to a system of non-linear ordinary differential equations. Viable similarity transforms are used for this purpose. A well-known numerical scheme called Runge-Kutta-Fehlberg method coupled with shooting procedure has been used to find the solution of resulting system of equations. Discussions on the effects of different emerging parameters are provided using graphical aid. A table is also given that provides the results of different parameters on local Nusselt and Sherwood numbers. Findings A revised model for Stokes’ first problem in nanofluids is presented in this paper. This model considers a zero flux condition at the boundary. Governing equations after implementing the similarity transforms get converted into a system of non-linear ordinary differential equations. Numerical solution using RK-Fehlberg method is also carried out. Emerging parameters are analyzed graphically. Figures indicate a quite significant change in concentration profile due to zero flux condition at the wall. Originality/value This work can be extended for other problems involving nanofluids for the better understanding of different properties of nanofluids.

scholarly journals DTM-PADE APPROACH TO MHD SLIP FLOW AND HEAT TRANSFER OVER A RADIALLY STRETCHING SHEET WITH THERMAL RADIATION

2020 ◽  
Vol 50 (3) ◽  
pp. 175-184
Author(s):  
Shoeb Rashid Sayyed ◽  
Brijbhan Singh ◽  
Oluwole Makinde ◽  
Nasreen Bano Muslim Shaikh
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Fluid Velocity ◽  
Slip Flow ◽  
Fluid Temperature ◽  
Linear Ordinary Differential Equations ◽  
Flow And Heat Transfer ◽  
Non Linear

The present paper deals with the boundary layer flow and heat transfer of an electrically conducting magnetohydrodynamic viscous fluid over a radially stretching power-law sheet with suction/injection within a porous medium by considering the effects of momentum and thermal slips and thermal radiation. The governing non-linear partial boundary layer differential equations are reduced to a  system of coupled non-linear ordinary differential equations (ODEs) with the aid of appropriate similarity transformations. These transformed ODEs are then solved by employing a semi-analytic technique known as differential transformation method (DTM) in combination with Pade approximation. The numerical values of skin friction and local Nusselt number are tabulated and validated by comparing them with the corresponding values available in the literature. Our results have been found in precise agreement  with the results published earlier. The effects of different governing parameters on velocity and temperature distributions are analyzed graphically. It has been found that with an increase in the velocity slip parameter the fluid velocity decreases whereas the temperature of the fluid increases. Also, the fluid temperature gets enhanced with an increase in the radiation parameter, but it decreases with an increase in thermal slip.

MHD STAGNATION POINT FLOW OF HYPERBOLIC TANGENT FLUID WITH VISCOUS DISSIPATION AND CHEMICAL REACTION

2021 ◽  
Vol 21 (2) ◽  
pp. 569-588
Author(s):  
KINZA ARSHAD ◽  
MUHAMMAD ASHRAF
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stagnation Point ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Normal Velocity ◽  
Hyperbolic Tangent ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In the present work, two dimensional flow of a hyperbolic tangent fluid with chemical reaction and viscous dissipation near a stagnation point is discussed numerically. The analysis is performed in the presence of magnetic field. The governing partial differential equations are converted into non-linear ordinary differential equations by using appropriate transformation. The resulting higher order non-linear ordinary differential equations are discretized by finite difference method and then solved by SOR (Successive over Relaxation parameter) method. The impact of the relevant parameters is scrutinized by plotting graphs and discussed in details. The main conclusion is that the large value of magnetic field parameter and wiessenberg numbers decrease the streamwise and normal velocity while increase the temperature distribution. Also higher value of the Eckert number Ec results in increases in temperature profile.

Unsteady Flow and Heat Transfer of a MHD Micropolar Fluid Over a Porous Stretching Sheet in the Presence of Thermal Radiation

2013 ◽  
Vol 29 (3) ◽  
pp. 559-568 ◽  
Author(s):  
G. C. Shit ◽  
R. Haldar ◽  
A. Sinha
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Boundary Layer Flow ◽  
Micropolar Fluid ◽  
Stretching Sheet ◽  
Flow And Heat Transfer ◽  
Non Linear ◽  
Layer Flow

AbstractA non-linear analysis has been made to study the unsteady hydromagnetic boundary layer flow and heat transfer of a micropolar fluid over a stretching sheet embedded in a porous medium. The effects of thermal radiation in the boundary layer flow over a stretching sheet have also been investigated. The system of governing partial differential equations in the boundary layer have reduced to a system of non-linear ordinary differential equations using a suitable similarity transformation. The resulting non-linear coupled ordinary differential equations are solved numerically by using an implicit finite difference scheme. The numerical results concern with the axial velocity, micro-rotation component and temperature profiles as well as local skin-friction coefficient and the rate of heat transfer at the sheet. The study reveals that the unsteady parameter S has an increasing effect on the flow and heat transfer characteristics.

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