Steady Laminar Convective Flow with Variable Properties Due to a Porous Rotating Disk

2005 ◽  
Vol 127 (12) ◽  
pp. 1406-1409 ◽  
Author(s):  
Kh. Abdul Maleque ◽  
Md. Abdus Sattar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rotating Disk ◽  
Polar Coordinates ◽  
Shooting Methods ◽  
Variable Properties ◽  
Relative Temperature ◽  
Flow And Heat Transfer ◽  
Steady Laminar

The present paper investigates the effects of variable properties (density (ρ), viscosity (μ), and thermal conductivity (κ)) on steady laminar flow and heat transfer for a viscous fluid due to an impulsively started rotating porous infinite disk. These properties ρ, μ and κ are taken to be the functions of temperature. The system of axisymmetric nonlinear partial differential equations governing the steady flow and heat transfer are written in cylindrical polar coordinates and are reduced to nonlinear ordinary differential equations by introducing suitable similarity parameters. The resulting steady equations are solved numerically by using Runge-Kutta and Shooting methods, and the effects of the relative temperature difference and suction/injection parameters are examined.

scholarly journals Dynamics of water conveying zinc oxide through divergent-convergent channels with the effect of nanoparticles shape when Joule dissipation are significant

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0245208
Author(s):  
Umair Rashid ◽  
Azhar Iqbal ◽  
Haiyi Liang ◽  
Waris Khan ◽  
Muhammad Waqar Ashraf
Keyword(s):  
Heat Transfer ◽  
Zinc Oxide ◽  
Differential Equations ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Joule Dissipation ◽  
Flow And Heat Transfer ◽  
Shape Effects ◽  
The Magnetic Field

Aim of study The shape effects of nanoparticles are very significant in fluid flow and heat transfer. In this paper, we discuss the effects of nanoparticles shape in nanofluid flow between divergent-convergent channels theoretically. In this present study, various shapes of nanoparticles, namely sphere, column and lamina in zinc oxide-water nanofluid are used. The effect of the magnetic field and joule dissipation are also considered. Research methodology The system of nonlinear partial differential equations (PDEs) is converted into ordinary differential equations (ODES). The analytical solutions are successfully obtained and compared with numerical solutions. The Homotopy perturbation method and NDsolve method are used to compare analytical and numerical results respectively. Conclusion The results show that the lamina shape nanoparticles have higher performance in temperature disturbance and rate of heat transfer as compared to other shapes of nanoparticles.

MHD Flow of Shear-Thinning Fluid over a Rotating Disk with Heat Transfer

2011 ◽  
Vol 130-134 ◽  
pp. 3599-3602
Author(s):  
Chun Ying Ming ◽  
Lian Cun Zheng ◽  
Xin Xin Zhang
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Power Law ◽  
Swirling Flow ◽  
Mhd Flow ◽  
Rotating Disk ◽  
Electrically Conducting ◽  
Flow And Heat Transfer ◽  
Power Law Index ◽  
Shear Thinning Fluid

This paper studied the Magneto hydrodynamic (MHD) flow and heat transfer of an electrically conducting non-Newtonian fluid over a rotating disk in the presence of a uniform magnetic field. The steady, laminar and axial-symmetric flow is driven solely by the rotating disk, and the incompressible fluid obeys the inelastic Ostwald de-Waele power-law model. The governing differential equations were reduced to a set of ordinary differential equations by utilizing the generalized Karman similarity transformation. The nonlinear two-point boundary value problem is solved by multi-shooting method. Numerical results show that the magnetic parameter and the power-law index have significant effects on the swirling flow and heat transfer.

scholarly journals IMPACT OF SUCTION/INJECTION AND HEAT TRANSFER ON UNSTEADY MHD FLOW OVER A STRETCHABLE ROTATING DISK

2020 ◽  
Vol 50 (3) ◽  
pp. 159-165
Author(s):  
K. V. Prasad ◽  
Hanumesh Vaidya ◽  
O D Makinde ◽  
Kuppalapalle Vajravelu ◽  
V Ramajini
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Mhd Flow ◽  
Rotating Disk ◽  
Skin Friction Coefficient ◽  
Convective Boundary ◽  
Optimal Homotopy Analysis Method ◽  
Similarity Transformations

In this article, the unsteady magnetohydrodynamic two-dimensional boundary layer flow and heat transfer over a stretchable rotating disk with mass suction/injection is investigated. Temperature-dependent physical properties and convective boundary conditions are taken into account. The governing coupled nonlinear partial differential equations are transformed into a system of ordinary differential equations by adopting the well-known similarity transformations. Further, the solutions are obtained through the semi-analytical method called an Optimal Homotopy Analysis Method (OHAM). The obtained results are discussed graphically to predict the features of the involved key parameters which are monitoring the flow model. The skin friction coefficient and Nusselt number are also examined. The validation of the present work is verified with the earlier published results and is found to be in excellent agreement. It is noticed that an increase in the viscosity parameter leads to decay in momentum boundary layer thickness, and the inverse trend is observed in the case of the temperature profile.

scholarly journals Nanofluid Flow over a Rotating Disk with Prescribed Heat Flux

2012 ◽  
Vol 11 (3) ◽  
pp. 77-92
Author(s):  
Julie Andrews ◽  
S P Anjali Devi
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Prandtl Number ◽  
Skin Friction ◽  
Rotating Disk ◽  
Skin Friction Coefficient ◽  
Copper Water ◽  
Flow And Heat Transfer

An analysis is carried out to study the problem of the steady flow and heat transfer over a rotating disk with a prescribed heat flux in nanofluid. Nanofluid considered is Copper (Cu) with water as the base fluid. The governing partial differential equations are transformed into a set of nonlinear ordinary differential equations using similarity transformation, which are then solved using the Nachtsheim-Swigert Shooting iteration technique along with the fourth order Runga Kutta method. The features of the flow and heat transfer characteristics are analyzed and discussed. The radial velocity, tangential velocity and the axial velocity for copper-water nanofluid are calculated and are represented graphically. Numerical results for dimensionless temperature, the radial skin friction coefficient and the tangential skin friction coefficient of the nanofluid flows are obtained and computations are carried out for the various values of Prandtl number. It is found that for the prescribed heat flux case (PHF case), the effect of Prandtl number is to reduce the temperature as it increases for copper-water nanofluid.

scholarly journals Impact of autocatalytic chemical reaction in an Ostwald-de-Waele nanofluid flow past a rotating disk with heterogeneous catalysis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bai Yu ◽  
Muhammad Ramzan ◽  
Saima Riasat ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Power Law ◽  
Variable Thickness ◽  
Rotating Disk ◽  
Thermal Profile ◽  
Nanofluid Flow ◽  
Power Law Index

AbstractThe nanofluids owing to their alluring attributes like enhanced thermal conductivity and better heat transfer characteristics have a vast variety of applications ranging from space technology to nuclear reactors etc. The present study highlights the Ostwald-de-Waele nanofluid flow past a rotating disk of variable thickness in a porous medium with a melting heat transfer phenomenon. The surface catalyzed reaction is added to the homogeneous-heterogeneous reaction that triggers the rate of the chemical reaction. The added feature of the variable thermal conductivity and the viscosity instead of their constant values also boosts the novelty of the undertaken problem. The modeled problem is erected in the form of a system of partial differential equations. Engaging similarity transformation, the set of ordinary differential equations are obtained. The coupled equations are numerically solved by using the bvp4c built-in MATLAB function. The drag coefficient and Nusselt number are plotted for arising parameters. The results revealed that increasing surface catalyzed parameter causes a decline in thermal profile more efficiently. Further, the power-law index is more influential than the variable thickness disk index. The numerical results show that variations in dimensionless thickness coefficient do not make any effect. However, increasing power-law index causing an upsurge in radial, axial, tangential, velocities, and thermal profile.

scholarly journals Construction of Analytic Solution to Axisymmetric Flow and Heat Transfer on a Moving Cylinder

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1335
Author(s):  
Vasile Marinca ◽  
Nicolae Herisanu
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stokes Equations ◽  
Nonlinear Differential Equations ◽  
Axisymmetric Flow ◽  
Control Parameters ◽  
Auxiliary Functions ◽  
Flow And Heat Transfer ◽  
Moving Cylinder ◽  
Convergence Control

Based on a new kind of analytical approach, namely the Optimal Auxiliary Functions Method (OAFM), a new analytical procedure is proposed to solve the problem of the annular axisymmetric stagnation flow and heat transfer on a moving cylinder with finite radius. As a novelty, explicit analytical solutions were obtained for the considered complex problem. First, the Navier–Stokes equations were simplified by means of similarity transformations that depended on different parameters and some combinations of these parameters, and the problem under study was reduced to six nonlinear ordinary differential equations with six unknowns. The OAFM proves to be a powerful tool for finding an accurate analytical solution for nonlinear problems, ensuring a fast convergence after the first iteration, even if the small or large parameters are absent, since the determination of the convergence-control parameters is independent of the magnitude of the coefficients that appear in the nonlinear differential equations. Concerning the main novelties of the proposed approach, it is worth mentioning the presence of some auxiliary functions, the involvement of the convergence-control parameters, the construction of the first iteration and much freedom to select the procedure for determining the optimal values of the convergence-control parameters.

Magnetohydrodynamic flow and heat transfer impact on ZnO-SAE50 nanolubricant flow over an inclined rotating disk

2019 ◽  
Vol 26 (5) ◽  
pp. 1146-1160 ◽  
Author(s):  
M. K. Nayak ◽  
Rashid Mehmood ◽  
O. D. Makinde ◽  
O. Mahian ◽  
Ali J. Chamkha
Keyword(s):  
Heat Transfer ◽  
Rotating Disk ◽  
Magnetohydrodynamic Flow ◽  
Flow And Heat Transfer

Numerical solutions of non-alignment stagnation-point flow and heat transfer over a stretching/shrinking surface in a nanofluid

2016 ◽  
Vol 26 (6) ◽  
pp. 1747-1767 ◽  
Author(s):  
Ioan Pop ◽  
Kohi Naganthran ◽  
Roslinda Nazar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Content Type ◽  
Boundary Layer Equations ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

Purpose – The purpose of this paper is to analyse numerically the steady stagnation-point flow of a viscous and incompressible fluid over continuously non-aligned stretching or shrinking surface in its own plane in a water-based nanofluid which contains three different types of nanoparticles, namely, Cu, Al2O3 and TiO2. Design/methodology/approach – Similarity transformation is used to convert the system of boundary layer equations which are in the form of partial differential equations into a system of ordinary differential equations. The system of similarity governing equations is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in Matlab software. Findings – Unique solution exists when the surface is stretched and dual solutions exist as the surface shrunk. For the dual solutions, stability analysis has revealed that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable. The effect of non-alignment is huge for the shrinking surface which is in contrast with the stretching surface. Practical implications – The results obtained can be used to explain the characteristics and applications of nanofluids, which are widely used as coolants, lubricants, heat exchangers and micro-channel heat sinks. This problem also applies to some situations such as materials which are manufactured by extrusion, production of glass-fibre and shrinking balloon. In this kind of circumstance, the rate of cooling and the stretching/shrinking process play an important role in moulding the final product according to preferable features. Originality/value – The present results are original and new for the study of fluid flow and heat transfer over a stretching/shrinking surface for the problem considered by Wang (2008) in a viscous fluid and extends to nanofluid by using the Tiwari and Das (2007) model.

Heat transfer of three-dimensional micropolar fluid on a Riga plate

2020 ◽  
Vol 98 (1) ◽  
pp. 32-38 ◽  
Author(s):  
S. Nadeem ◽  
M.Y. Malik ◽  
Nadeem Abbas
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Differential Equations ◽  
Surface Temperature ◽  
Ordinary Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Nonlinear Ordinary Differential Equations ◽  
Exponential Order ◽  
Riga Plate

In this article, we deal with prescribed exponential surface temperature and prescribed exponential heat flux due to micropolar fluids flow on a Riga plate. The flow is induced through an exponentially stretching surface within the time-dependent thermal conductivity. Analysis is performed inside the heat transfer. In our study, two cases are discussed here, namely prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux (PEHF). The governing systems of the nonlinear partial differential equations are converted into nonlinear ordinary differential equations using appropriate similarity transformations and boundary layer approach. The reduced systems of nonlinear ordinary differential equations are solved numerically with the help of bvp4c. The significant results are shown in tables and graphs. The variation due to modified Hartman number M is observed in θ (PEST) and [Formula: see text] (PEHF). θ and [Formula: see text] are also reduced for higher values of the radiation parameter Tr. Obtained results are compared with results from the literature.

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