Dual solutions of a micropolar nanofluid flow with radiative heat mass transfer over stretching/shrinking sheet using spectral quasilinearization method

2019 ◽  
Vol 16 (2) ◽  
pp. 238-255 ◽  
Author(s):  
Mangwiro Magodora ◽  
Hiranmoy Mondal ◽  
Precious Sibanda
Keyword(s):  
Brownian Motion ◽  
Error Analysis ◽  
Micropolar Fluid ◽  
Numerical Solutions ◽  
Surface Radiation ◽  
Shrinking Sheet ◽  
Quasilinearization Method ◽  
Spectral Collocation ◽  
Content Type ◽  
Micropolar Nanofluid

Purpose The purpose of this paper is to focus on the application of Chebyshev spectral collocation methodology with Gauss Lobatto grid points to micropolar fluid over a stretching or shrinking surface. Radiation, thermophoresis and nanoparticle Brownian motion are considered. The results have attainable scientific and technological applications in systems involving stretchable materials. Design/methodology/approach The model equations governing the flow are transformed into non-linear ordinary differential equations which are then reworked into linear form using the Newton-based quasilinearization method (SQLM). Spectral collocation is then used to solve the resulting linearised system of equations. Findings The validity of the model is established using error analysis. The velocity, temperature, micro-rotation, skin friction and couple stress parameters are conferred diagrammatically and analysed in detail. Originality/value The study obtains numerical explanations for rapidly convergent solutions using the spectral quasilinearization method. Convergence of the numerical solutions was monitored using the residual error analysis. The influence of radiation, heat and mass parameters on the flow are depicted graphically and analysed. The study is an extension on the work by Zheng et al. (2012) and therefore the novelty is that the authors tend to take into account nanoparticles, Brownian motion and thermophoresis in the flow of a micropolar fluid.

scholarly journals Analysis of Chemical Reaction on MHD Micropolar Fluid Flow over a Shrinking Sheet near Stagnation Point with Nanoparticles and External Heat

2021 ◽  
Vol 39 (1) ◽  
pp. 262-268
Author(s):  
Krishnandan Verma ◽  
Debozani Borgohain ◽  
Bishwaram Sharma
Keyword(s):  
Stagnation Point ◽  
Chemical Reaction ◽  
Micropolar Fluid ◽  
Numerical Data ◽  
Mhd Flow ◽  
Heat Transfer Process ◽  
External Heat ◽  
Shrinking Sheet ◽  
Similarity Transformations ◽  
Micropolar Nanofluid

The present study investigates numerically MHD flow near the stagnation point of micropolar fluid through a shrinking sheet containing nanoparticles under the influence of chemical reaction and external heat. The study is an attempt to investigate the flow behaviour of micropolar nanofluid because of its importance in heat transfer process in industries as well as cooling systems. The governing equations are converted to nonlinear ordinary differential equations by implementing similarity transformations. Numerical results are investigated in the form of figures and tables by using MATLAB built in solver bvp4c for various dimensionless parameters. The impacts of external heat parameter on temperature and chemical reaction factor on concentration of the nanofluid are illustrated in the form of graphs. It is observed that the temperature of the nanofluid and nanoparticle volume distributions increase when Biot number attain larger values. Rise in Thermophoretic parameter increases the nanoparticles concentration in the boundary layer. Numerical data are presented for Nusselt number and Sherwood number.

scholarly journals The Effects of Activation Energy and Thermophoretic Diffusion of Nanoparticles on Steady Micropolar Fluid along with Brownian Motion

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Zulqurnain Sabir ◽  
Assad Ayub ◽  
Juan L. G. Guirao ◽  
Saira Bhatti ◽  
Syed Zahir Hussain Shah
Keyword(s):  
Activation Energy ◽  
Brownian Motion ◽  
Differential Equations ◽  
Concentration Profile ◽  
Micropolar Fluid ◽  
Numerical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Local Skin ◽  
Arrhenius Function ◽  
Local Skin Friction

The present study is related to the effects of activation energy and thermophoretic diffusion on steady micropolar fluid along with Brownian motion. The activation energy and thermal conductivity of steady micropolar fluid are also discussed. The equation of motion, angular momentum, temperature, concentration, and their boundary conditions are presented for the micropolar fluid. The detail of geometry reveals the effects of several parameters on the parts of the system. The nonlinear partial differential equations are converted into nonlinear ordinary differential equations, and a famous shooting scheme is used to present the numerical solutions. The comparison of the obtained results by the shooting technique and the numerical bvp4c technique is presented. The behavior of local skin friction numbers and couple stress number is tabulated for different parameters, and some figures are plotted to present the different parameters. For uplifting the values of AE for parameter λA, the concentration profile is increased because of the Arrhenius function, and AE increases with the reduction of this function. The increasing values of the parameter of rotation G show the decrement in velocity because of the rotation of the particle of the fluid, so the linear motion decreases. Thermophoresis is responsible for shifting the molecules within the fluid, and due to this, an increment in boundary layer thickness is found, so by a greater value of Nt, the concentration profile decreases and temperature profile goes down.

Shifted Legendre spectral collocation technique for solving stochastic Volterra–Fredholm integral equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohamed A. Abdelkawy
Keyword(s):  
Brownian Motion ◽  
Error Analysis ◽  
Integral Equations ◽  
Lagrange Interpolation ◽  
Fredholm Integral Equations ◽  
Algebraic Equations ◽  
Spectral Collocation ◽  
Numerical Examples ◽  
Collocation Technique

Abstract This paper addresses a spectral collocation technique to treat the stochastic Volterra–Fredholm integral equations (SVF-IEs). The shifted Legendre–Gauss–Radau collocation (SL-GR-C) method is developed for approximating the FSV-IDEs. The principal target in our technique is to transform the SVF-IEs to a system of algebraic equations. For computational purposes, the Brownian motion W(x) is discretized by Lagrange interpolation. While the integral terms are interpolated by Legendre–Gauss–Lobatto quadrature. Some numerical examples are given to test the accuracy and applicability of our technique. Also, an error analysis is introduced for the proposed method.

Numerical study of surface radiation and combined natural convection heat transfer in a solar cavity receiver

2017 ◽  
Vol 27 (10) ◽  
pp. 2385-2399 ◽  
Author(s):  
Kamel Milani Shirvan ◽  
Mojtaba Mamourian ◽  
Soroush Mirzakhanlari ◽  
A.B. Rahimi ◽  
R. Ellahi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Numerical Solutions ◽  
Convection Heat Transfer ◽  
Surface Radiation ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Surface Emissivity ◽  
Content Type

Purpose The purpose of this paper is to present the numerical solutions of surface radiation and combined natural convection heat transfer in a solar cavity receiver. The paper aims to discuss sundry issues that take place in the said model. Design/methodology/approach The numerical solutions are developed by means of second-order upwind scheme using the SIMPLE algorithm. Findings The effects of physical factors such as Rayleigh number (104 ≤ Ra ≤ 106), inclination angels of insulated walls (0º ≤ θ ≤ 10º) and the wall surface emissivity (0 ≤ ε ≤ 1) on natural convection-surface radiation heat transfer rate are analyzed. Impact of sundry parameters on flow quantities are discussed and displayed via graphs and tables. Stream lines and isothermal lines have also been drawn in the region of cavity. The numerical results reveal that increasing the Rayleigh number, wall surface emissivity and inclination angels of insulated walls in an open cavity enhances the mean total Nusselt number. The variations of the surface radiation and natural convection heat transfer mean Nusselt numbers are very small to the inclination angle of θ, while a significant change is noted for the case of Rayleigh number and emissivity. Originality/value To the best of authors’ knowledge, this model is reported for the first time.

Oblique stagnation-point flow of a nanofluid past a shrinking sheet

2016 ◽  
Vol 26 (1) ◽  
pp. 189-213 ◽  
Author(s):  
M M Rahman ◽  
Teodor Grosan ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Brownian Motion ◽  
Differential Equations ◽  
Strain Rate ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Flow Behavior ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Content Type

Purpose – The laminar two-dimensional stagnation-point flow and heat transfer of a viscous incompressible nanofluid obliquely impinging on a shrinking surface is formulated as a similarity solution of the Navier-Stokes, energy and concentration equations. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The effect of the dimensionless strain rate, shrinking parameter, Brownian motion parameter and thermophoresis parameter on the flow, temperature and nanoparticle volume fraction is investigated in details. The paper aims to discuss these issues. Design/methodology/approach – The transformed system of ordinary differential equations was solved using the function bvp4c from Matlab. The relative tolerance was set to 10−10. Findings – It is found that dimensionless strain rate and shrinking parameter causes a shift in the position of the point of zero skin friction along the stretching sheet. Obliquity of the flow toward the surface increases as the strain rate intensifies. The results indicate that dual solutions exist for the opposing flow case. Research limitations/implications – The problem is formulated for an incompressible nanofluid with no chemical reactions, dilute mixture, negligible viscous dissipation and negligible radiative heat transfer assuming nanoparticles and base fluid are locally in thermal equilibrium. Beyond the critical point λ c to obtain further solutions, the full basic partial differential equations have to be solved. Originality/value – The present results are original and new for the oblique stagnation-point flow of a nanofluid past a shrinking sheet. Therefore, this study would be important for the researchers working in the relatively new area of nanofluids in order to become familiar with the flow behavior and properties of such nanofluids.

Axisymmetric flow of hybrid nanofluid due to a permeable non-linearly stretching/shrinking sheet with radiation effect

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Natalia C. Roşca ◽  
Alin V. Roşca ◽  
Ioan Pop
Keyword(s):  
Design Methodology ◽  
Radiation Effect ◽  
Numerical Solutions ◽  
Axisymmetric Flow ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Hybrid Nanofluids ◽  
Shrinking Surface

Purpose This paper aims to report theoretical and numerical results for the problem of laminar axisymmetric flow of hybrid nanofluid over a permeable non-linearly stretching/shrinking sheet with radiation effect. Design/methodology/approach The numerical solutions of the arising boundary value problem are obtained using the function bvp4c from MATLAB for different values of the governing parameters. Findings It is found that the solutions of the ordinary (similarity) differential equations have two branches, upper and lower branch solutions, in a certain range of the stretching/shrinking and suction parameters. To establish which of these solutions are stable and which are not, a stability analysis has been performed. Originality/value To the best of the authors’ knowledge, present results are original and new for the study of fluid flow and heat transfer over a stretching/shrinking surface, as they successfully extend the problem considered by Mustafa et al. (2015) to the case of hybrid nanofluids.

scholarly journals MHD Flow and Heat Transfer of Double Stratified Micropolar Fluid over a Vertical Permeable Shrinking/Stretching Sheet with Chemical Reaction and Heat Source

2020 ◽  
Vol 21 (1) ◽  
pp. 1-14
Author(s):  
Ansab Azam Khan ◽  
Suliadi Firdaus Sufahani ◽  
Khairy Zaimi ◽  
Mohammad Ferdows
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Heat Source ◽  
Chemical Reaction ◽  
Sherwood Number ◽  
Micropolar Fluid ◽  
Numerical Solutions ◽  
Mhd Flow ◽  
Shrinking Sheet ◽  
Local Sherwood Number

The present study analyses the magnetohydrodynamic (MHD) flow of a double stratified micropolar fluid across a vertical stretching/shrinking sheet in the presence of suction, chemical reaction, and heat source effects. The governing equations in the form of partial differential equations are transitioned into coupled nonlinear ordinary differential equations by means of similarity transformation. The numerical solutions are obtained with the aid of the boundary value problem bvp4c solver in the MATLAB software. Numerical results have been confirmed with the previous results for a certain case and the comparison is found to be in an excellent agreement. Results for related profiles and heat transfer characteristics are displayed through plots and tabulated for the governing parameters involved. It is found that the reduced skin friction coefficient and the local Nusselt number increase with the increasing chemical reaction and heat source parameters. The rising values of the chemical reaction parameter have increased the magnitude of the local Sherwood number. In contrary, the heat source parameter has the tendency to decrease the magnitude of the local Sherwood number.

scholarly journals Numerical Solutions of Micropolar Nanofluid over an Inclined Surface Using Keller Box Analysis

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Khuram Rafique ◽  
Hammad Alotaibi ◽  
Taher A. Nofal ◽  
Muhammad Imran Anwar ◽  
Masnita Misiran ◽  
...  
Keyword(s):  
Brownian Motion ◽  
Skin Friction ◽  
Transfer Rate ◽  
Numerical Solutions ◽  
Practical Interest ◽  
Energy Transfer Rate ◽  
Buongiorno’S Model ◽  
Micropolar Nanofluid ◽  
Inclined Surface ◽  
Physical Quantities

The Brownian motion and thermophoretic impacts attained a noticeable intention of the recent researchers because these factors trigger the thermal conductivity of the nanofluid. In this study, we focus on radiation and Soret effects on a slanted stretchable sheet. Buongiorno’s model is taken into account with Brownian motion and thermophoretic effects. Compatible transformations are implemented to attain the nonlinear differential equation from the boundary value PDE’s. The physical quantities of practical interest are treated by graphically as well as numerically. For numerical results, the Keller box technique is applied. The numerical outcomes through tabulated magnitudes performed a good settlement with already existing results. Energy transfer rate against involved factor exhibited via graphs. Energy and mass transport rates enhance against increment in Soret factor while skin friction diminishes. Moreover, Nusselt number and Sherwood number decrease on improving inclination while skin friction increases.

MHD flow and heat transfer over a permeable stretching/shrinking sheet in a hybrid nanofluid with a convective boundary condition

2019 ◽  
Vol 29 (9) ◽  
pp. 3012-3038 ◽  
Author(s):  
Emad H. Aly ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Mhd Flow ◽  
Convective Boundary Condition ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Convective Boundary ◽  
Content Type ◽  
Flow And Heat Transfer

Purpose The purpose of this study is to present both effective analytic and numerical solutions to MHD flow and heat transfer past a permeable stretching/shrinking sheet in a hybrid nanofluid with suction/injection and convective boundary conditions. Water (base fluid) nanoparticles of alumina and copper were considered as a hybrid nanofluid. Design/methodology/approach Proper-similarity variables were applied to transform the system of partial differential equations into a system of ordinary (similarity) differential equations. Exact analytical solutions were then presented for the dimensionless stream and temperature functions. Further, the authors introduce a very nice analytic and numerical solutions for both small and large values of the magnetic parameter. Findings It was found that no/unique/two equal/dual physical solutions exist for the investigated boundary value problem. The physically realizable practice of these solutions depends on the range of the governing parameters. For a stretching/shrinking sheet, it was deduced that a hybrid nanofluid works as a cooler on increasing some of the investigated parameters. Moreover, in the case of a shrinking sheet, the first solutions of hybrid nanofluid are stable and physically realizable rather than the nanofluid, while those of the second solutions are not for both hybrid nanofluid and nanofluid. Originality/value The present results for the hybrid nanofluids are new and original, as they successfully extend (generalize) the problems previously considered by different authors for the case of nanofluids.

scholarly journals Flow and heat transfer past a permeable stretching/shrinking sheet in Cu−Al2O3/water hybrid nanofluid

2019 ◽  
Vol 30 (3) ◽  
pp. 1197-1222 ◽  
Author(s):  
Rusya Iryanti Yahaya ◽  
Norihan M. Arifin ◽  
Roslinda Nazar ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Skin Friction Coefficient ◽  
The Other ◽  
Shrinking Sheet ◽  
Physical Parameters ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Flow And Heat Transfer

Purpose The purpose of this paper is to study the flow and heat transfer of a hybrid nanofluid, Cu–Al2O3/water, past a permeable stretching/shrinking sheet. The effects of Brownian motion and thermophoresis are considered here. Design/methodology/approach Similarity transformations are used to reduce the governing partial differential equations to a system of ordinary (similarity) differential equations. A MATLAB solver called the bvp4c is then used to compute the numerical solutions of equations (12) to (14) subject to the boundary conditions of equation (15). Then, the effects of various physical parameters on the flow and thermal fields of the hybrid nanofluid are analyzed. Findings Multiple (dual) solutions are found for the basic boundary layer equations. A stability analysis is performed to see which solutions are stable and, therefore, applicable in practice and which are not stable. Besides that, a comparison is made between the hybrid nanofluid and a traditional nanofluid, Cu/water. The skin friction coefficient and Nusselt number of the hybrid nanofluid are found to be greater than that of the other nanofluid. Thus, the hybrid nanofluid has a higher heat transfer rate than the other nanofluid. However, the increase in the shrinking parameter reduces the velocity of the hybrid nanofluid. Originality/value The present results are original and new for the study of the flow and heat transfer past a permeable stretching/shrinking sheet in Cu–Al2O3/water hybrid nanofluid.

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