A Numerical Study of Forced Convection Casson Nanofluid Flow Past a Wedge With Melting Process

2020 ◽  
Author(s):  
Mehari Fentahun Endalew ◽  
Subharthi Sarkar
Keyword(s):  
Differential Equations ◽  
Skin Friction ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Wedge Angle ◽  
Nanofluid Flow ◽  
Local Skin ◽  
Casson Nanofluid ◽  
Flow Past ◽  
Highly Nonlinear

Abstract A numerical investigation is carried out to analyze steady two dimensional Casson nanofluid flow past a wedge with melting. The partial differential equations that govern the nanofluid flow are transformed into highly nonlinear coupled ordinary differential equations by employing similarity transformation. Thereafter, numerical solutions of these governing equations are obtained by MATLAB routine bvp4c. A special case of the present study is compared with an existing solution in literature and is found to be in good agreement. The effects of pertinent physical entities on the nanofluid velocity, nanofluid temperature, and nanoparticle concentration are represented graphically, while skin friction, Nusselt number, and Sherwood number are recorded in tabular form. We observed that, with an increase of wedge angle parameter, nanofluid velocity and local skin friction increase. However, when the melting parameter increases, nanofluid temperature and heat transfer rate decrease. This study would be useful in unfurling novel applications of Casson nanofluids in cooling devices and heat sinks.

scholarly journals Dual Stratified Nanofluid Flow Past a Permeable Shrinking/Stretching Sheet Using a Non-Fourier Energy Model

2019 ◽  
Vol 9 (10) ◽  
pp. 2124 ◽  
Author(s):  
Najiyah Safwa Khashi’ie ◽  
Norihan Md Arifin ◽  
Ezad Hafidz Hafidzuddin ◽  
Nadihah Wahi
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Transfer Rate ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Thermal Relaxation ◽  
Physical Parameters ◽  
Nanofluid Flow ◽  
Local Skin ◽  
Flow Past

The present study emphasizes the combined effects of double stratification and buoyancy forces on nanofluid flow past a shrinking/stretching surface. A permeable sheet is used to give way for possible wall fluid suction while the magnetic field is imposed normal to the sheet. The governing boundary layer with non-Fourier energy equations (partial differential equations (PDEs)) are converted into a set of nonlinear ordinary differential equations (ODEs) using similarity transformations. The approximate relative error between present results (using the boundary value problem with fourth order accuracy (bvp4c) function) and previous studies in few limiting cases is sufficiently small (0% to 0.3694%). Numerical solutions are graphically displayed for several physical parameters namely suction, magnetic, thermal relaxation, thermal and solutal stratifications on the velocity, temperature and nanoparticles volume fraction profiles. The non-Fourier energy equation gives a different estimation of heat and mass transfer rates as compared to the classical energy equation. The heat transfer rate approximately elevates 5.83% to 12.13% when the thermal relaxation parameter is added for both shrinking and stretching cases. Adversely, the mass transfer rate declines within the range of 1.02% to 2.42%. It is also evident in the present work that the augmentation of suitable wall mass suction will generate dual solutions. The existence of two solutions (first and second) are noticed in all the profiles as well as the local skin friction, Nusselt number and Sherwood number graphs within the considerable range of parameters. The implementation of stability analysis asserts that the first solution is the real solution.

scholarly journals Aligned MHD Magnetic Nanofluid Flow Past a Static Wedge

2018 ◽  
Vol 7 (3.28) ◽  
pp. 28
Author(s):  
Mohd Rijal Ilias ◽  
Noraihan Afiqah Rawi ◽  
Noor Hidayah Mohd Zaki ◽  
Sharidan Shafie
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Magnetic Parameter ◽  
Fluid Velocity ◽  
Graphical Form ◽  
Nanofluid Flow ◽  
Local Skin ◽  
Magnetic Nanofluid ◽  
Flow Past ◽  
Special Cases

The problem of steady aligned MHD magnetic nanofluid flow past a static wedge is studied in this paper. The present aligned magnetic field along with constant temperature at the surface is considered. The governing partial differential equations, subject to boundary conditions are transformed into ordinary differential equations using similarity transformations. The transformed equations are then solved numerically by Keller-box method. To check the validity of the present method, numerical results for dimensionless local skin friction coefficient and rate of heat transfer are compared with results of available literature as special cases and revealed in good agreement. The influence of pertinent parameters on velocity, temperature profiles, as well as wall shear stress and heat transfer rate is displayed in graphical form and discussed. It is found that fluid velocity increases with the increase of inclined angle, magnetic parameter and thermal buoyancy parameters while decreasing for increasing in nanoparticle volume fraction.  It is also noticed that magnetic parameter influences fluid velocity and temperature significantly.   

scholarly journals Free Convective MHD Flow Past a Vertical Cone with Variable Heat and Mass Flux

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
J. Prakash ◽  
S. Gouse Mohiddin ◽  
S. Vijaya Kumar Varma
Keyword(s):  
Boundary Layer ◽  
Power Law ◽  
Mass Flux ◽  
Numerical Study ◽  
Convection Boundary Layer ◽  
Vertical Cone ◽  
Local Skin ◽  
Surface Mass ◽  
Flow Past ◽  
Power Law Exponent

A numerical study of buoyancy-driven unsteady natural convection boundary layer flow past a vertical cone embedded in a non-Darcian isotropic porous regime with transverse magnetic field applied normal to the surface is considered. The heat and mass flux at the surface of the cone is modeled as a power law according to qwx=xm and qw*(x)=xm, respectively, where x denotes the coordinate along the slant face of the cone. Both Darcian drag and Forchheimer quadratic porous impedance are incorporated into the two-dimensional viscous flow model. The transient boundary layer equations are then nondimensionalized and solved by the Crank-Nicolson implicit difference method. The velocity, temperature, and concentration fields have been studied for the effect of Grashof number, Darcy number, Forchheimer number, Prandtl number, surface heat flux power-law exponent (m), surface mass flux power-law exponent (n), Schmidt number, buoyancy ratio parameter, and semivertical angle of the cone. Present results for selected variables for the purely fluid regime are compared with the published results and are found to be in excellent agreement. The local skin friction, Nusselt number, and Sherwood number are also analyzed graphically. The study finds important applications in geophysical heat transfer, industrial manufacturing processes, and hybrid solar energy systems.

scholarly journals A generalized perspective of Fourier and Fick’s laws: Magnetized effects of Cattaneo-Christov models on transient nanofluid flow between two parallel plates with Brownian motion and thermophoresis

2020 ◽  
Vol 9 (1) ◽  
pp. 201-222 ◽  
Author(s):  
Usha Shankar ◽  
Neminath B. Naduvinamani ◽  
Hussain Basha
Keyword(s):  
Brownian Motion ◽  
Joule Heating ◽  
Concentration Field ◽  
Double Diffusion ◽  
Diffusion Models ◽  
Time Dependent ◽  
Parallel Plates ◽  
Nanofluid Flow ◽  
Casson Nanofluid ◽  
Highly Nonlinear

AbstractPresent research article reports the magnetized impacts of Cattaneo-Christov double diffusion models on heat and mass transfer behaviour of viscous incompressible, time-dependent, two-dimensional Casson nanofluid flow through the channel with Joule heating and viscous dissipation effects numerically. The classical transport models such as Fourier and Fick’s laws of heat and mass diffusions are generalized in terms of Cattaneo-Christov double diffusion models by accounting the thermal and concentration relaxation times. The present physical problem is examined in the presence of Lorentz forces to investigate the effects of magnetic field on double diffusion process along with Joule heating. The non-Newtonian Casson nanofluid flow between two parallel plates gives the system of time-dependent, highly nonlinear, coupled partial differential equations and is solved by utilizing RK-SM and bvp4c schemes. Present results show that, the temperature and concentration distributions are fewer in case of Cattaneo-Christov heat and mass flux models when compared to the Fourier’s and Fick’s laws of heat and mass diffusions. The concentration field is a diminishing function of thermophoresis parameter and it is an increasing function of Brownian motion parameter. Finally, an excellent comparison between the present solutions and previously published results show the accuracy of the results and methods used to achieve the objective of the present work.

Optimal Homotopic Exploration of features of Cattaneo-Christov model in Second Grade Nanofluid flow via Darcy-Forchheimer medium subject to Viscous Dissipation and Thermal Radiation

2021 ◽  
Vol 24 ◽  
Author(s):  
Ghulam Rasool ◽  
Anum Shafiq ◽  
Yu-Ming Chu ◽  
Muhammad Shoaib Bhutta ◽  
Amjad Ali
Keyword(s):  
Temperature Distribution ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Homotopy Analysis Method ◽  
Stream Velocity ◽  
Analysis Method ◽  
Nanofluid Flow ◽  
Optimal Homotopy Analysis Method ◽  
Homotopy Analysis

Introduction: In this article Optimal Homotopy analysis method (oHAM) is used for exploration of the features of Cattaneo-Christov model in viscous and chemically reactive nanofluid flow through a porous medium with stretching velocity at the solid/sheet surface and free stream velocity at the free surface. Methods: The two important aspects, Brownian motion and Thermophoresis are considered. Thermal radiation is also included in present model. Based on the heat and mass flux, the Cattaneo-Christov model is implemented on the Temperature and Concentration distributions. The governing Partial Differential Equations (PDEs) are converted into Ordinary Differential Equations (ODEs) using similarity transformations. The results are achieved using the optimal homotopy analysis method (oHAM). The optimal convergence and residual errors have been calculated to preserve the validity of the model. Results: The results are plotted graphically to see the variations in three main profiles i.e. momentum, temperature and concentration profile. Conclusion: The outcomes indicate that skin friction enhances due to implementation of Darcy medium. It is also noted that the relaxation time parameter results in enhancement of the temperature distribution. Thermal radiation enhances the temperature distribution and so is the case with skin friction.

Thermally and chemically reacted MHD Maxwell nanofluid flow past an inclined permeable stretching surface

2021 ◽  
pp. 095440892110507
Author(s):  
Amar B. Patil ◽  
Vishwambhar S. Patil ◽  
Pooja P. Humane ◽  
Nalini S. Patil ◽  
Govind R. Rajput
Keyword(s):  
Differential Equations ◽  
Energy Transport ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Linear Ordinary Differential Equations ◽  
Maxwell Nanofluid ◽  
Similarity Transformations ◽  
Flow Past ◽  
Chemically Reacting ◽  
The Impact

The present work deals with chemically reacting unsteady magnetohydrodynamic Maxwell nanofluid flow past an inclined permeable stretching surface embedded in a porous medium with thermal radiation. The formulated governing partial differential equations conveying the flow model of Maxwell with Buongiorno modeled nanofluid is transformed into the system of highly non-linear ordinary differential equations via suitable similarity transformations; those equations are transmuted into an initial value problem and then solved numerically by a shooting approach with Runge–-Kutta fourth-order schema. To obtain the physical insight of the flow situation, the influence of associated parameters on the velocity, temperature, and concentration profiles is sketched graphically with the aid of MATLAB software. Furthermore, engineering quantities of interest are interpreted graphically. The computed numerical results are compared to estimate the validity of the achieved results; it has been found out that the computed results are highly accurate. The impact of the Maxwell parameter and inclination angle of the sheet on the velocity field is observed in decaying. Both thermal and solutal energy transport are progressive in nature as the Maxwell parameter and thermophoresis parameter grows, and a reverse trend is observed for Prandtl number.

Numerical Solution for Boundary Layer Flow of a Dusty Micropolar Fluid Due to a Stretching Sheet with Constant Wall Temperature

2021 ◽  
Vol 87 (1) ◽  
pp. 30-40
Author(s):  
Anisah Dasman ◽  
Abdul Rahman Mohd Kasim ◽  
Iskandar Waini ◽  
Najiyah Safwa Khashi’ie
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Wall Temperature ◽  
Micropolar Fluid ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Particle Interaction ◽  
Dust Particles ◽  
Constant Wall Temperature

This paper aims to present the numerical study of a dusty micropolar fluid due to a stretching sheet with constant wall temperature. Using the suitable similarity transformation, the governing partial differential equations for two-phase flows of the fluid and the dust particles are reduced to the form of ordinary differential equations. The ordinary differential equations are then numerically analysed using the bvp4c function in the Matlab software. The validity of present numerical results was checked by comparing them with the previous study. The results graphically show the numerical solutions of velocity, temperature and microrotation distributions for several values of the material parameter K, fluid-particle interaction parameter and Prandtl number for both fluid and dust phase. The effect of microrotation is investigated and analysed as well. It is found that the distributions are significantly influenced by the investigated parameters for both phases.

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