Melting Heat Transfer in Magnetohydrodynamic Carreau Fluid over a Thermally Stratified Parabolic Surface

2018 ◽  
Vol 388 ◽  
pp. 246-264 ◽  
Author(s):  
G. Kumaran ◽  
Pallava Lakshminarayana ◽  
Bala Anki Reddy ◽  
N. Sandeep
Keyword(s):  
Heat Source ◽  
Sherwood Number ◽  
Weissenberg Number ◽  
Physical Parameters ◽  
Carreau Fluid ◽  
Dissipative Flow ◽  
Melting Surface ◽  
Source Sink ◽  
Power Law Index ◽  
Local Sherwood Number

In this paper, we theoretically analyzed the effects of non-uniform heat source/sink on the magnetohydrodynamic dissipative flow of a Carreau fluid towards a thermally stratified melting surface of the paraboloid of revolution. Exponential heat source along with the temperature dependent thermal conductivity and viscosity are taken into account. The representing differential conditions are changed into an arrangement of non-straight coupled ODE’s and solved by employing the R-K with shooting system. Numerical arrangements are obtained from the flow, temperature profiles of various parametric values and after that domino effect are exhibited graphically and also a friction factor and local Sherwood number of various physical parameters are demonstrated graphically and in tabular form. Boosting values of the Weissenberg number increase both the velocity and thermal profiles of Carreau fluid. Rising values of velocity power law index parameter depreciate both the flow and local Sherwood number.

scholarly journals Simultaneous impacts of Joule heating and variable heat source/sink on MHD 3D flow of Carreau-nanoliquids with temperature dependent viscosity

2019 ◽  
Vol 8 (1) ◽  
pp. 356-367 ◽  
Author(s):  
J. V. Ramana Reddy ◽  
V. Sugunamma ◽  
N. Sandeep
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Joule Heating ◽  
Uniform Space ◽  
Weissenberg Number ◽  
Physical Parameters ◽  
Temperature Dependent ◽  
3D Flow ◽  
Temperature Dependent Viscosity ◽  
Source Sink

Abstract The 3D flow of non-Newtonian nanoliquid flows past a bidirectional stretching sheet with heat transfer is investigated in the present study. It is assumed that viscosity of the liquid varies with temperature. Carreau non-Newtonain model, Tiwari and Das nanofluid model are used to formulate the problem. The impacts of Joule heating, nonlinear radiation and non-uniform (space and temperature dependent) heat source/sink are accounted. Al-Cu-CH3OH and Cu-CH3OH are considered as nanoliquids for the present study. The solution of the problem is attained by the application of shooting and R.K. numerical procedures. Graphical and tabular illustrations are incorporated with a view of understanding the influence of various physical parameters on the flow field. We eyed that using of Al-Cu alloy nanoparticles in the carrier liquid leads to superior heat transfer ability instead of using only Aluminum nanoparticles. Weissenberg number and viscosity parameter have inclination to exalt the thermal field.

Peristaltic transport of a MHD Carreau fluid in a tapered asymmetric channel with permeable walls

2015 ◽  
Vol 08 (04) ◽  
pp. 1550054 ◽  
Author(s):  
M. Kothandapani ◽  
J. Prakash ◽  
S. Srinivas
Keyword(s):  
Fluid Flow ◽  
Pressure Rise ◽  
Weissenberg Number ◽  
Physical Parameters ◽  
Asymmetric Channel ◽  
Carreau Fluid ◽  
Flow Equations ◽  
Axial Pressure Gradient ◽  
Significant Difference ◽  
Permeable Walls

The effect of permeable walls and magnetic field on the peristaltic flow of a Carreau fluid in a tapered asymmetric channel is studied. The tapered asymmetric channel is normally created due to the intra-uterine fluid flow induced by myometrial contractions and it was simulated by asymmetric peristaltic fluid flow in a two-dimensional infinite non-uniform channel. The analysis has been performed under long wavelength and low-Reynolds number assumptions to linearize the governing flow equations. A series solution in respect of a small Weissenberg number is obtained for the stream function, axial pressure gradient and shear stress. Time average of pressure rise and frictional force on the upper wall has also been computed using numerical integration. The results have been presented graphically for the various interested physical parameters. It is observed that for Carreau fluids the peristalsis works as a pump against a greater pressure rise compared with a Newtonian fluid, while there exists no significant difference in free pumping flux for Newtonian and Carreau fluids in the tapered asymmetric channel.

Mathematical modelling of classical Graetz–Nusselt problem for axisymmetric tube and flat channel using the Carreau fluid model: a numerical benchmark study

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Muhammad Waris Saeed Khan ◽  
Nasir Ali ◽  
Zeeshan Asghar
Keyword(s):  
New York ◽  
Eigenvalue Problem ◽  
Power Law ◽  
Fluid Model ◽  
Separation Of Variables ◽  
Solution Procedure ◽  
Weissenberg Number ◽  
Carreau Fluid ◽  
Constant Wall Temperature ◽  
Power Law Index

Abstract The thermal entrance problem (also known as the classical Graetz problem) is studied for the complex rheological Carreau fluid model. The solution of two-dimensional energy equation in the form of an infinite series is obtained by employing the separation of variables method. The ensuing eigenvalue problem (S–L problem) is solved for eigenvalues and corresponding eigenfunctions through MATLAB routine bvp5c. Numerical integration via Simpson’s rule is carried out to compute the coefficient of series solution. Current problem is also tackled by an alternative approach where numerical solution of eigenvalue problem is evaluated via the Runge–Kutta fourth order method. This problem is solved for both flat and circular confinements with two types of boundary conditions: (i) constant wall temperature and (ii) prescribed wall heat flux. The obtained results of both local and mean Nusselt numbers, fully developed temperature profile and average temperature are discussed for different values of Weissenberg number and power-law index through graphs and tables. This study is valid for typical range of Weissenberg number W e ≤ 1 $\left(We\le 1\right)$ and power-law index n < 1 $\left(n{< }1\right)$ for shear-thinning trend while n > 1 $\left(n{ >}1\right)$ for shear-thickening behaviour. The scope of the present study is broad in the context that the solution of the said problem is achieved by using two different approaches namely, the traditional Graetz approach and the solution procedure documented in M. D. Mikhailov and M. N. Ozisik, Unified Analysis and Solutions of Heat and Mass Diffusion, New York, Dover, 1994.

scholarly journals Magnetohydrodynamic Mixed Convection Stagnation-Point Flow of a Power-Law Non-Newtonian Nanofluid towards a Stretching Surface with Radiation and Heat Source/Sink

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Macha Madhu ◽  
Naikoti Kishan
Keyword(s):  
Heat Source ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Power Law ◽  
Volume Fraction ◽  
Nonlinear Differential Equations ◽  
Stagnation Point Flow ◽  
Physical Parameters ◽  
Stretching Surface ◽  
Source Sink

Two-dimensional MHD mixed convection boundary layer flow of heat and mass transfer stagnation-point flow of a non-Newtonian power-law nanofluid towards a stretching surface in the presence of thermal radiation and heat source/sink is investigated numerically. The non-Newtonian nanofluid model incorporates the effects of Brownian motion and thermophoresis. The basic transport equations are made dimensionless first and the complete nonlinear differential equations with associated boundary conditions are solved numerically by finite element method (FEM). The numerical calculations for velocity, temperature, and nanoparticles volume fraction profiles for different values of the physical parameters to display the interesting aspects of the solutions are presented graphically and discussed. The skin friction coefficient, the local Nusslet number and the Sherwood number are exhibited and examined. Our results are compatible with the existing results for a special case.

scholarly journals STEADY MHD MIXED CONVECTION NEWTONIAN FLUID FLOW ALONG A VERTICAL STRETCHING CYLINDER EMBEDDED IN POROUS MEDIUM

2021 ◽  
Vol 8 (7) ◽  
pp. 45-57
Author(s):  
Sharad Sinha ◽  
R. S. Yadav
Keyword(s):  
Porous Medium ◽  
Heat Source ◽  
Boundary Conditions ◽  
Mixed Convection ◽  
Fluid Velocity ◽  
Physical Parameters ◽  
Stretching Cylinder ◽  
Similarity Transformations ◽  
Mixed Convective Flow ◽  
Source Sink

A viscous electrically conducting fluid is considered and its steady mixed convective flow along a vertical stretching cylinder is investigated. It is assumed that the cylinder is embedded in a porous medium and, external magnetic field, heat source/sink are also taken into account. Suitable similarity transformations are used to reduce the governing equations and associated boundary conditions into a system of nonlinear ordinary differential equations. This system along with the boundary conditions is solved by fourth order Runge-Kutta method with shooting technique. Variations in fluid velocity and temperature due to various physical parameters such as heat source/sink parameter, mixed convection parameter, magnetic parameter are presented through graphs. Effect of these parameters on dimensionless shear stress and rate of heat transfer are discussed numerically through tables.

Effect of Radiation on MHD Free Convective Flow over a Stretching Sheet in the Presence of Heat Source/Sink

2017 ◽  
Vol 378 ◽  
pp. 1-15
Author(s):  
S. Baag ◽  
S.R. Mishra ◽  
B. Nayak ◽  
M.R. Acharya
Keyword(s):  
Differential Equations ◽  
Heat Source ◽  
Stretching Sheet ◽  
Physical Parameters ◽  
Linear Ordinary Differential Equations ◽  
Electrically Conducting ◽  
Flow Phenomena ◽  
Flow Heat ◽  
Layer Flow ◽  
Source Sink

In this analysis, effects of viscous dissipation and thermal radiation on an electrically conducting boundary layer flow, heat and mass transfer of a fluid through a porous medium over a stretching sheet in the presence of heat source/sink is considered. The symmetry groups admitted by the corresponding boundary value problem are obtained by using symmetric transformations. These transformations are used to convert the partial differential equations of the governing equations into self-similar non-linear ordinary differential equations. These transformed ODEs are solved by employing Runge-Kutta fourth order with shooting method. Numerical results obtained for different thermo-physical parameters characterizes the flow phenomena are drawn graphically and effects of various physical parameters on velocity, temperature and concentration profiles are discussed. Numerical computation for skin friction, Nusselt number and Sherwood number are also obtained and presented in Tables.

scholarly journals Impact of Temperature-Dependent Heat Source/Sink and Variable Species Diffusivity on Radiative Reiner–Philippoff Fluid

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
T. Sajid ◽  
M. Sagheer ◽  
S. Hussain
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Mass Transfer ◽  
Heat Source ◽  
Transfer Rate ◽  
Variable Thermal Conductivity ◽  
Physical Parameters ◽  
Molecular Diffusivity ◽  
Source Sink ◽  
The Impact

The principle aim of the current communication is to scrutinize the impact of distinguished effects like variable thermal conductivity and variable molecular diffusivity on non-Newtonian Reiner–Philippoff fluid moving over a stretchable surface. The process of heat transfer is carried out in the presence of nonlinear thermal radiation, variable thermal conductivity, and heat generation/absorption. Furthermore, the study of mass transfer phenomena is carried out in the existence of variable molecular diffusivity. The PDEs regarding our model are renovated into ODEs by utilizing similarity transformation. Furthermore, the dimensionless model is tackled with the help of the RK4 method in conjunction with the shooting technique. The effects of different physical parameters that emerged during the numerical simulation on mass transfer rate, heat transfer rate, and velocity field are portrayed in the form of tables and graphs. It is noteworthy that an elevation in the heat source/sink parameters causes a reduction in the temperature profile. Moreover, a positive variation in the species diffusivity parameter augments the mass fraction field. A variation in the fluid parameter is found to be significantly affecting the shear thinning and shear thickening behaviour of the fluid. Reliability of the numerical outcomes is judged by comparing the obtained outcomes with the already available literature. The article is unique in its sense that the heat and mass transfer analysis of Reiner–Philippoff fluid under the aforementioned effects has not been investigated yet.

scholarly journals Heat Transfer of Viscoelastic Fluid Flow due to Nonlinear Stretching Sheet with Internal Heat Source

2013 ◽  
Vol 18 (3) ◽  
pp. 739-760 ◽  
Author(s):  
M.M. Nandeppanavar ◽  
M.N. Siddalingappa ◽  
H. Jyoti
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Similarity Solutions ◽  
Physical Parameters ◽  
Local Skin ◽  
Source Sink

Abstract In the present paper, a viscoelastic boundary layer flow and heat transfer over an exponentially stretching continuous sheet in the presence of a heat source/sink has been examined. Loss of energy due to viscous dissipation of the non-Newtonian fluid has been taken into account in this study. Approximate analytical local similar solutions of the highly non-linear momentum equation are obtained for velocity distribution by transforming the equation into Riccati-type and then solving this sequentially. Accuracy of the zero-order analytical solutions for the stream function and velocity are verified by numerical solutions obtained by employing the Runge-Kutta fourth order method involving shooting. Similarity solutions of the temperature equation for non-isothermal boundary conditions are obtained in the form of confluent hypergeometric functions. The effect of various physical parameters on the local skin-friction coefficient and heat transfer characteristics are discussed in detail. It is seen that the rate of heat transfer from the stretching sheet to the fluid can be controlled by suitably choosing the values of the Prandtl number Pr and local Eckert number E, local viscioelastic parameter k*1 and local heat source/ sink parameter β*

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