scholarly journals Energy transport analysis in flow of Carreau nanofluid inspired by variable thermal conductivity and zero mass flux conditions

2021 ◽  
Vol 13 (2) ◽  
pp. 168781402199496
Author(s):  
Zahoor Iqbal ◽  
Masood Khan ◽  
Aamir Hamid ◽  
Awais Ahmed
Keyword(s):  
Thermal Conductivity ◽  
Activation Energy ◽  
Mass Flux ◽  
Numerical Technique ◽  
Variable Thermal Conductivity ◽  
Convection Flow ◽  
Physical Constraints ◽  
The Core ◽  
Zero Mass ◽  
Carreau Nanofluid

The presence of nanometric particles in the base fluids lead to form nanofluids. Nanofluids are prominent due to their astonishing features in thermally conducting flows and in the development of electronic and mechanical devices. Based on these motivations, we have designed our article to investigate the thermal conduction features in the free and forced convection flow of unsteady Carreau nanofluid due to stretching cylinder with the effects of variable magnetic field. Moreover, the transport of thermal energy in the flow is properly examined by including the impacts of variable thermal conductivity and nonuniform heat rise/fall. Furthermore, the transport of solutal energy in the flow of nanofluid is encountered under the influences of activation energy and binary chemical reactions. A momentous feature of this study is to employ the zero-mass flux condition at the wall of the cylinder. A section of this study is proposed for mathematical modelling of the current problem. Moreover, the impacts of involved physical constraints are explored by employing an efficient numerical technique namely bvp4c. The features of all physical constraints on flow, thermal and solutal curves are illustrated in the form of graphs and discussed with reasonable physical arguments in discussion section of the article. The core findings of this study are mentioned in the section of closing remarks. The core upshot of the current study is that the nanoparticles concentration rate of nanofluid depicts ascending trend for escalating values of activation energy constraint. A significant upsurge in the coefficients of skin friction and Nusselt number is detected with an escalation in the constraints of buoyancy and thermophoresis forces, respectively. The references regarding this article are also provided at the end.

scholarly journals MHD stagnation point flow of micro nanofluid towards a shrinking sheet with convective and zero mass flux conditions

2017 ◽  
Vol 65 (2) ◽  
pp. 155-162 ◽  
Author(s):  
A. Rauf ◽  
S. A. Shehzad ◽  
T. Hayat ◽  
M. A. Meraj ◽  
A. Alsaedi
Keyword(s):  
Stagnation Point ◽  
Mass Flux ◽  
Numerical Technique ◽  
Convective Boundary Condition ◽  
Momentum Equation ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Convective Boundary ◽  
Electrically Conducting ◽  
Zero Mass

AbstractIn this article the stagnation point flow of electrically conducting micro nanofluid towards a shrinking sheet, considering a chemical reaction of first order is investigated. Involvement of magnetic field occurs in the momentum equation, whereas the energy and concentrations equations incorporated the influence of thermophoresis and Brownian motion. Convective boundary condition on temperature and zero mass flux condition on concentration are implemented. Partial differential equations are converted into the ordinary ones using suitable variables. The numerical technique is utilized to discuss the results for velocity, microrotation, temperature, and concentration fields.

Effects of Energy Dissipation and Variable Thermal Conductivity on Entropy Generation Rate in Mixed Convection Flow

2018 ◽  
Vol 10 (4) ◽  
Author(s):  
Muhammad Qasim ◽  
Muhammad Idrees Afridi
Keyword(s):  
Thermal Conductivity ◽  
Energy Dissipation ◽  
Mixed Convection ◽  
Entropy Generation ◽  
Variable Thermal Conductivity ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Entropy Generation Number ◽  
Similarity Transformations ◽  
Generation Number

Analysis of entropy generation in mixed convection flow over a vertically stretching sheet has been carried out in the presence of variable thermal conductivity and energy dissipation. Governing equations are reduced to self-similar ordinary differential equations via similarity transformations and are solved numerically by applying shooting and fourth-order Runge–Kutta techniques. The expressions for entropy generation number and Bejan number are also obtained by using similarity transformations. The influence of embedding physical parameters on quantities of interest is discussed through graphical illustrations. The results reveal that entropy generation number increases significantly in the vicinity of stretching surface and gradually dies out as one move away from the sheet. Also, the entropy generation number decreases with an increase in temperature difference parameter. Moreover, entropy generation number enhances with an enhancement in the Eckert number, Prandtl number, and variable thermal conductivity parameter.

Zero Mass Flux Effects on Time Dependent Flow of an Eyring Powell with Activation Energy

2020 ◽  
Vol 9 (3) ◽  
pp. 216-229
Author(s):  
Hussan Zeb ◽  
Hafiz Abdul Wahab ◽  
Umar Khan
Keyword(s):  
Activation Energy ◽  
Mass Flux ◽  
Slip Boundary Condition ◽  
Time Dependent ◽  
Physical Parameters ◽  
Detailed Result ◽  
Discussion Section ◽  
Nonlinear Odes ◽  
Zero Mass ◽  
The Impact

In this work we demonstrated the impacts of zero mass flux in Powell-Eyring fluid over time dependent stretching sheet. We analyzed the Arrhenius activation energy in heat transfer with momentum and thermal slip boundary condition. The governing model is very complex to solve it directly therefore we transform these governed model into a coupled nonlinear ODEs via similarity transformation. After that, we solve these ODEs by using numerica method so calledshooting technique with RK-technique. The characteristics of different beneficial physical parameters on momentum, energy and concentration fields are represented through graphs. We concluded in this work the arising or reducing in the velocity, temperature and concentration fields for the existence of physical parameters. The impact of physical quantities namely skin fraction (Cf), Nusselt (Nux) and Sherwood (Shx) numbers are calculated numerically via tables. In this paper we concluded that the decreases occurring in velocity field for higher values of (M) (H) and (β). Moreover the characteristics of concentration Φ(ζ), temperature θ(ζ) and velocity f′(ζ) gradients are presented for important physical parameters see in detailed Result and discussion section.

Zero Mass Flux Dependent on Radiative Magnetohydrodynamics Carreau Nanofluid Over a Radially Surface with Temperature Jump and Slip Flow: A Hybrid Nanofluid Analysis

2021 ◽  
Vol 10 (1) ◽  
pp. 118-127
Author(s):  
Amit Parmar ◽  
Rakesh Choudhary ◽  
Krishna Agrawal
Keyword(s):  
Mass Flux ◽  
Temperature Jump ◽  
Slip Flow ◽  
Velocity Slip ◽  
Concentration Profiles ◽  
Fluid Temperature ◽  
Slip Parameter ◽  
First Order ◽  
Zero Mass ◽  
Carreau Nanofluid

The present study explores the slip flow and heat transfer induced by a radially surface with MHD Carreau nanofluid. In addition, the effects of temperature jump, non-linear radiation and the dependent zero mass flux also taken into account. This study also considers the cross-diffusion effect on temperature and concentration governing profiles. Appropriate transformations are engaged in order to acquire nonlinear differential equations (ODEs) from the partial differential system, their solutions are obtained by Runge-Kutta 4th order with shooting scheme in MATLAB. The impact of pertinent flow parameters such as first and second order velocity slip parameter, temperature jump, magnetic parameter, heat source, radiation parameter, melting surface parameter, temperature ratio parameter on dimensionless velocity, temperature and concentration profiles achieved graphically as well as local skin friction, Nusselt number and Sherwood number are demonstrated in the form of Table. first order velocity slip parameter (slip1) on f′, Θ and Φ profile fields. With an increment in the velocity slip first order parameter (slip1) we have perceived a fall in the momentum boundary layer and concentration profiles and a growth in the fluid temperature field.

scholarly journals Unsteady/Steady Hydromagnetic Convective Flow between Two Vertical Walls in the Presence of Variable Thermal Conductivity

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
M. M. Hamza ◽  
I. G. Usman ◽  
A. Sule
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Skin Friction ◽  
Numerical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Vertical Channel ◽  
Approximate Solutions ◽  
Variable Thermal Conductivity ◽  
Convection Flow

Unsteady as well as steady natural convection flow in a vertical channel in the presence of uniform magnetic field applied normal to the flow region and temperature dependent variable thermal conductivity is studied. The nonlinear partial differential equations governing the flow have been solved numerically using unconditionally stable and convergent semi-implicit finite difference scheme. For steady case, approximate solutions have been derived for velocity, temperature, skin friction, and the rate of heat transfer using perturbation series method. Results of the computations for velocity, temperature, skin friction, and the rate of heat transfer are presented graphically and discussed quantitatively for various parameters embedded in the problem. An excellent agreement was found during the numerical computations between the steady-state approximate solutions and unsteady numerical solutions at steady-state time. In addition, comparison with previously published work is performed and the results agree well.

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