Heat transfer in nano fluid from a stretching (shrinking), porous and heated sheet of variable thickness

2021 ◽  
pp. 095440622199070
Author(s):  
Azhar Ali ◽  
Dil Nawaz Khan Marwat ◽  
Aftab Alam
Keyword(s):  
Heat Transfer ◽  
Brownian Motion ◽  
Variable Thickness ◽  
Lewis Number ◽  
Physical Parameters ◽  
Boundary Layer Equations ◽  
Nano Fluid ◽  
Special Cases ◽  
Classical Models ◽  
New Variables

Heat transfer in Nano fluid from a stretching (shrinking) and porous sheet of variable thickness is investigated in this paper. A set of unseen transformations is generated and the new variables are consequently used for the solution of partial differential equations under consideration. The classical models of heat transfer in Nano fluids from rigid/porous and stretching/shrinking sheets with Brownian motion and thermophoresis effects will be the special case of current study. The set of generalized similarity variables is introduced into the systems of boundary layer equations and boundary conditions and a system of coupled and non-linear ODE’s is formed. The final ODE’s are characterized by several dimensionless parameters and their effects are examined on field quantities. The governing parameters are: suction (injection), stretching (shrinking) parameters, Brownian motion number ( Nb), Thermophoresis number ( Nt) and Lewis number ( Le). The numerical observations are shown in different graphs and tables, whereas, effects of physical parameters are seen on the rate of heat transfer [Formula: see text] and mass transfer [Formula: see text], defined at the surface of the sheet. Moreover, the new results are presented in the respective sections. The remarkable aspects of the present simulations are scrutinized, however, special cases of current simulations give the previous problems, which are highlighted in the consequent sections.

Impact of Velocity Slip and Temperature Jump of Nanofluid in the Flow over a Stretching Sheet with Variable Thickness

2016 ◽  
Vol 71 (5) ◽  
pp. 413-425 ◽  
Author(s):  
Chengjie Guo ◽  
Liancun Zheng ◽  
Chaoli Zhang ◽  
Xuehui Chen ◽  
Xinxin Zhang
Keyword(s):  
Brownian Motion ◽  
Variable Thickness ◽  
Stretching Sheet ◽  
Temperature Jump ◽  
Industrial Process ◽  
Lewis Number ◽  
Velocity Slip ◽  
Solid Boundary ◽  
Physical Parameters ◽  
Homotopy Analysis

AbstractIn this study, the generalised velocity slip and the generalised temperature jump of nanofluid in the flow over a stretching sheet with variable thickness are investigated. Because of the non-adherence of the fluid to a solid boundary, the velocity slip and the temperature jump between fluid and moving sheet may happen in industrial process, so taking velocity slip and temperature jump into account is indispensable. It is worth mentioning that the analysis of the velocity v, which has not been seen in the previous references related to the variable thickness sheet, is presented. The thermophoresis and the Brownian motion, which are the two very important physical parameters, are fully studied. The governing equations are simplified into ordinary differential equations by the proper transformations. The homotopy analysis method (HAM) is applied to solve the reduced equations for general conditions. In addition, the effects of involved parameters such as velocity slip parameter, temperature jump parameter, Prandtl number, magnetic field parameter, permeable parameter, Lewis number, thermophoresis parameter, and Brownian motion parameter are investigated and analysed graphically.

scholarly journals Modelling of Applied Magnetic Field and Thermal Radiations Due to the Stretching of Cylinder

Processes ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 1077
Author(s):  
Muhammad Tamoor ◽  
Muhammad Kamran ◽  
Sadique Rehman ◽  
Aamir Farooq ◽  
Rewayat Khan ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Boundary Layer Equations ◽  
Convective Parameter ◽  
Momentum And Heat Transfer ◽  
Dimensional Boundary

In this study, a numerical approach was adopted in order to explore the analysis of magneto fluid in the presence of thermal radiation combined with mixed convective and slip conditions. Using the similarity transformation, the axisymmetric three-dimensional boundary layer equations were reduced to a self-similar form. The shooting technique, combined with the Range–Kutta–Fehlberg method, was used to solve the resulting coupled nonlinear momentum and heat transfer equations numerically. When physically interpreting the data, some important observations were made. The novelty of the present study lies in finding help to control the rate of heat transfer and fluid velocity in any industrial manufacturing processes (such as the cooling of metallic plates). The numerical results revealed that the Nusselt number decrease for larger Prandtl number, curvature, and convective parameters. At the same time, the skin friction coefficient was enhanced with an increase in both slip velocity and convective parameter. The effect of emerging physical parameters on velocity and temperature profiles for a nonlinear stretching cylinder has been thoroughly studied and analyzed using plotted graphs and tables.

scholarly journals Analysis of a Chemically Reactive Mhd Flow With Heat and Mass Transfer Over a Permeable Surface

2019 ◽  
Vol 24 (1) ◽  
pp. 53-66
Author(s):  
O.J. Fenuga ◽  
S.J. Aroloye ◽  
A.O. Popoola
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Mhd Flow ◽  
Skin Friction Coefficient ◽  
Permeable Surface ◽  
Physical Parameters ◽  
Boundary Layer Equations ◽  
Special Cases ◽  
Momentum Boundary Layer

Abstract This paper investigates a chemically reactive Magnetohydrodynamics fluid flow with heat and mass transfer over a permeable surface taking into consideration the buoyancy force, injection/suction, heat source/sink and thermal radiation. The governing momentum, energy and concentration balance equations are transformed into a set of ordinary differential equations by method of similarity transformation and solved numerically by Runge- Kutta method based on Shooting technique. The influence of various pertinent parameters on the velocity, temperature, concentration fields are discussed graphically. Comparison of this work with previously published works on special cases of the problem was carried out and the results are in excellent agreement. Results also show that the thermo physical parameters in the momentum boundary layer equations increase the skin friction coefficient but decrease the momentum boundary layer. Fluid suction/injection and Prandtl number increase the rate of heat transfer. The order of chemical reaction is quite significant and there is a faster rate of mass transfer when the reaction rate and Schmidt number are increased.

Flow and Heat Transfer of Bingham Plastic Fluid over a Rotating Disk with Variable Thickness

2016 ◽  
Vol 71 (11) ◽  
pp. 1003-1015 ◽  
Author(s):  
Chunyan Liu ◽  
Mingyang Pan ◽  
Liancun Zheng ◽  
Chunying Ming ◽  
Xinxin Zhang
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Variable Thickness ◽  
Shape Parameter ◽  
Rotating Disk ◽  
Physical Parameters ◽  
Bingham Plastic ◽  
Flow And Heat Transfer ◽  
Approximate Analytical Solutions ◽  
Plastic Fluid

AbstractThis paper studies the steady flow and heat transfer of Bingham plastic fluid over a rotating disk of finite radius with variable thickness radially in boundary layer. The boundary layer flow is caused by the rotating disk when the extra stress is greater than the yield stress of the Bingham fluid. The analyses of the velocity and temperature field related to the variable thickness disk have not been investigated in current literatures. The governing equations are first simplified into ordinary differential equations owing to the generalized von Kármán transformation for seeking solutions easily. Then semi-similarity approximate analytical solutions are obtained by using the homotopy analysis method for different physical parameters. It is found that the Bingham number clearly influences the velocity field distribution, and the skin friction coefficientCfris nonlinear growth with respect to the shape parameterm. Additionally, the effects of the involved parameters (i.e. shape parameterm, variable thickness parameterβ, Reynolds number Rev, and Prandtl number Pr) on velocity and temperature distribution are investigated and analyzed in detail.

scholarly journals UNSTEADY BOUNDARY LAYERS: CONVECTIVE HEAT TRANSFER OVER A VERTICAL FLAT PLATE

2009 ◽  
Vol 50 (4) ◽  
pp. 541-549 ◽  
Author(s):  
ROBERT A. VAN GORDER ◽  
K. VAJRAVELU
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Shear Thinning ◽  
Momentum Equation ◽  
Physical Parameters ◽  
Flow And Heat Transfer ◽  
Special Cases ◽  
Layer Flow

AbstractIn this paper, we extend the results in the literature for boundary layer flow over a horizontal plate, by considering the buoyancy force term in the momentum equation. Using a similarity transformation, we transform the partial differential equations of the problem into coupled nonlinear ordinary differential equations. We first analyse several special cases dealing with the properties of the exact and approximate solutions. Then, for the general problem, we construct series solutions for arbitrary values of the physical parameters. Furthermore, we obtain numerical solutions for several sets of values of the parameters. The numerical results thus obtained are presented through graphs and tables and the effects of the physical parameters on the flow and heat transfer characteristics are discussed. The results obtained reveal many interesting behaviours that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

scholarly journals The new analytical study for boundary-layer slip flow and heat transfer of nanofluid over a stretching sheet

2017 ◽  
Vol 21 (1 Part A) ◽  
pp. 289-301 ◽  
Author(s):  
Fazle Mabood ◽  
Waqar Khan ◽  
Muhammad Rashidi
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Brownian Motion ◽  
Prandtl Number ◽  
Stretching Sheet ◽  
Lewis Number ◽  
Partial Slip ◽  
Surface Shear Stress ◽  
Slip Parameter ◽  
Slip Factor

In this article, the semi-analytical/numerical technique known as the homotopy analysis method (HAM) is employed to derive solutions for partial slip effects on the heat transfer of nanofluids over a stretching sheet. An accurate analytical solution is presented which depends on the Prandtl number, slip factor, Lewis number, Brownian motion number, and thermophoresis number. The variation of the reduced Nusselt and reduced Sherwood numbers with Brownian motion number, and thermophoresis number for various values Prandtl number, slip factor, Lewis number is presented in tabular and graphical forms. The results of the present article show the flow velocity and the surface shear stress on the stretching sheet and also reduced Nusselt number and reduced Sherwood number are strongly influenced by the slip parameter. It is found that hydrodynamic boundary layer decreases and thermal boundary layer increases with slip parameter. Comparison of the present analysis is made with the previously existing literature and an appreciable agreement in the values is observed for the limiting case.

scholarly journals Assisting and Opposing Stagnation Point Pseudoplastic Nano Liquid Flow towards a Flexible Riga Sheet: A Computational Approach

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Aysha Rehman ◽  
Azad Hussain ◽  
Sohail Nadeem
Keyword(s):  
Brownian Motion ◽  
Mixed Convection ◽  
Hartmann Number ◽  
Lewis Number ◽  
Weissenberg Number ◽  
Physical Parameters ◽  
Nanofluid Flow ◽  
Diverse Range ◽  
Flow Equations ◽  
Buongiorno Model

Nanofluids are used as coolants in heat transport devices like heat exchangers, radiators, and electronic cooling systems (like a flat plate) because of their improved thermal properties. The preeminent perspective of this study is to highlight the influence of combined convection on heat transfer and pseudoplastic non-Newtonian nanofluid flow towards an extendable Riga surface. Buongiorno model is incorporated in the present study to tackle a diverse range of Reynolds numbers and to analyze the behavior of the pseudoplastic nanofluid flow. Nanofluid features are scrutinized through Brownian motion and thermophoresis diffusion. By the use of the boundary layer principle, the compact form of flow equations is transformed into component forms. The modeled system is numerically simulated. The effects of various physical parameters on skin friction, mass transfer, and thermal energy are numerically computed. Fluctuations of velocity increased when modified Hartmann number and mixed convection parameter are boosted, where it collapses for Weissenberg number and width parameter. It can be revealed that the temperature curve gets down if modified Hartmann number, mixed convection, and buoyancy ratio parameters upgrade. Concentration patterns diminish when there is an incline in width parameter and Lewis number; on the other hand, it went upward for Brownian motion parameter, modified Hartmann, and Prandtl number.

scholarly journals Variable thickness flow over a rotating disk under the influence of variable magnetic field: An application to parametric continuation method

2020 ◽  
Vol 12 (6) ◽  
pp. 168781402093638 ◽  
Author(s):  
Muhammad Shuaib ◽  
Rehan Ali Shah ◽  
Muhammad Bilal
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Variable Thickness ◽  
Numerical Scheme ◽  
Continuation Method ◽  
Finite Difference Methods ◽  
Rotating Disk ◽  
Variable Magnetic Field ◽  
Physical Parameters ◽  
Parametric Continuation

The present work explores the behavior of three-dimensional incompressible viscous fluid flow and heat transfer over the surface of a non-flat stretchable rotating disk. A variable thickness fluid is subjected under the influence of an external variable magnetic field and heat transfer. Navier–Stokes equation is coupled with Maxwell equations to examine the hydrothermal properties of fluid. The basic governing equations of motion are diminished to a system of nonlinear ordinary differential equations using appropriate similarity framework, which are further treated with numerical scheme known as parametric continuation method. The parametric continuation method has combined interesting characteristics of both shooting and implicit finite difference methods. For validity of the present numerical scheme, a comparison with the published work is performed and it is found that the results are in excellent agreement with each other. Numerical and graphical results for the velocity, temperature, and magnetic strength profiles as well as skin fractions and Nusselt number are presented and discussed in detail for various physical parameters. The heat transfer process is reduced with positive increment of no-flatness parameter [Formula: see text], while Prandtl number increases the heat transfer rate at the surface of the disk.

Gyrotactic Microorganism Effects on Mixed Convective Nanofluid Flow Past a Vertical Cylinder

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
Palani Sudhagar ◽  
Peri K. Kameswaran ◽  
B. Rushi Kumar
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Saturated Porous Medium ◽  
Vertical Cylinder ◽  
Lewis Number ◽  
Convection Boundary Layer ◽  
Physical Parameters ◽  
Transfer Rates ◽  
Layer Analysis ◽  
Gyrotactic Microorganism

The transient mixed convection boundary layer analysis of incompressible flow over an isothermal vertical cylinder is embedded in a saturated porous medium in the vicinity for Gyrotactic microorganism effects. The mathematical model used for the bioconvective nanofluid incorporates the effects of Brownian motion, thermophoresis, and gyrotactic microorganisms. Moreover, the resulting governing nonsimilarity equations are changed into partial differential equations and solved numerically. The results are explained graphically for various physical parameters. It is determined that bioconvection parameter boosts the heat transfer rates and the thickness of the motile microorganism reduces the mass transfer rates. Expanding bioconvection Lewis number leads to decrease in heat transfer rates and the density of the motile microorganism, whereas the mass transfer rates decelerate the flow field. The investigation is pertinent to the nanobiopolymer manufacturing processes.

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