Laminar Boundary Layer Transfer over Rotating Bodies in Forced Flow

1978 ◽  
Vol 100 (3) ◽  
pp. 496-502 ◽  
Author(s):  
Min-Hsiun Lee ◽  
D. R. Jeng ◽  
K. J. De Witt
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Experimental Studies ◽  
Rotating Disk ◽  
Rotation Parameter ◽  
Forced Flow ◽  
Rotating Sphere ◽  
Prandtl Numbers ◽  
Special Case

A procedure is described for the calculation of momentum and heat transfer rates through laminar boundary layers over rotating axisymmetric bodies in forced flow. By applying appropriate coordinate transformations and Merk’s type of series, the governing momentum equations can be expressed as a set of coupled ordinary differential equations that depend on a wedge parameter and on a rotation parameter. For the energy equation, a set of ordinary differential equations is obtained which depend explicitly on the Prandtl number and implicitly on the aforementioned parameters. These equations are numerically integrated for a range of parameter values for the special case of a rotating sphere, and the local friction coefficient and the local Nusselt number are presented for values of the rotation parameter B = 1, 4, and 10 with Prandtl numbers of 1, 10, and 100. These results are then compared with previous theoretical results. It is also shown how the flow and heat transfer characteristics for a rotating disk can be readily obtained as a special case from the formulation for the rotating sphere. The disk results are also compared with previous theoretical and experimental studies.

Nonsimilar Boundary-Layer Heat Transfer of a Rotating Cone in Forced Flow

1967 ◽  
Vol 89 (2) ◽  
pp. 139-145 ◽  
Author(s):  
J. C. Y. Koh ◽  
J. F. Price
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Numerical Solutions ◽  
Cone Angle ◽  
Rotating Disk ◽  
Forced Flow ◽  
Degenerate Problem ◽  
Prandtl Numbers ◽  
Half Cone ◽  
Half Cone Angle

The nonsimilar boundary-layer flow and heat transfer of a cone rotating in a forced-flow field are investigated. Numerical solutions are shown for a half-cone angle of 53.5 deg with parameters (vw/ue)2 ranging from 0 to 20, and with Prandtl numbers from 0.2 to 10. With a half-cone angle of 90 deg (so that one has a rotating disk), the degenerate problem is solved in the same manner.

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.

Effects of Suction and Freestream Velocity on a Hydromagnetic Stagnation-Point Flow and Heat Transport in a Newtonian Fluid Toward a Stretching Sheet

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
P. G. Siddheshwar ◽  
N. Meenakshi
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Heat Transport ◽  
Newtonian Fluid ◽  
Stretching Sheet ◽  
Forced Flow ◽  
Stream Velocity ◽  
Freestream Velocity ◽  
Exponential Order ◽  
Order Surface

Forced flow of an electrically conducting Newtonian fluid due to an exponentially stretching sheet is studied numerically. Free stream velocity is present and so is suction at the sheet. The governing coupled, nonlinear, partial differential equations of flow and heat transfer are converted into coupled, nonlinear, ordinary differential equations by similarity transformation and are solved numerically using shooting method, and curve fitting on the data is done by differential transform method together with Padé approximation. Prescribed exponential order surface temperature (PEST) and prescribed exponential order surface heat flux are considered for investigation of heat transfer related quantities. The influence of Chandrasekhar number, suction/injection parameter, and freestream parameter on heat transport is presented and discussed. Coefficient of friction and heat transport is also evaluated in the study. The results are of interest in extrusions and such other processes.

scholarly journals Parametric analysis of the heat transfer behavior of the nano-particle ionic-liquid flow between concentric cylinders

2021 ◽  
Vol 13 (6) ◽  
pp. 168781402110240
Author(s):  
Rehan Ali Shah ◽  
Hidayat Ullah ◽  
Muhammad Sohail Khan ◽  
Aamir Khan
Keyword(s):  
Heat Transfer ◽  
Ionic Liquid ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Heat Source ◽  
Ordinary Differential Equations ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Concentric Cylinders

This paper investigates the enhanced viscous behavior and heat transfer phenomenon of an unsteady two di-mensional, incompressible ionic-nano-liquid squeezing flow between two infinite parallel concentric cylinders. To analyze heat transfer ability, three different type nanoparticles such as Copper, Aluminum [Formula: see text], and Titanium oxide [Formula: see text] of volume fraction ranging from 0.1 to 0.7 nm, are added to the ionic liquid in turns. The Brinkman model of viscosity and Maxwell-Garnets model of thermal conductivity for nano particles are adopted. Further, Heat source [Formula: see text], is applied between the concentric cylinders. The physical phenomenon is transformed into a system of partial differential equations by modified Navier-Stokes equation, Poisson equation, Nernst-Plank equation, and energy equation. The system of nonlinear partial differential equations, is converted to a system of coupled ordinary differential equations by opting suitable transformations. Solution of the system of coupled ordinary differential equations is carried out by parametric continuation (PC) and BVP4c matlab based numerical methods. Effects of squeeze number ( S), volume fraction [Formula: see text], Prandtle number (Pr), Schmidt number [Formula: see text], and heat source [Formula: see text] on nano-ionicliquid flow, ions concentration distribution, heat transfer rate and other physical quantities of interest are tabulated, graphed, and discussed. It is found that [Formula: see text] and Cu as nanosolid, show almost the same enhancement in heat transfer rate for Pr = 0.2, 0.4, 0.6.

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.

scholarly journals Implicit Finite Difference Simulation of Prandtl-Eyring Nanofluid over a Flat Plate with Variable Thermal Conductivity: A Tiwari and Das Model

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3153
Author(s):  
Nidal H. Abu-Hamdeh ◽  
Abdulmalik A. Aljinaidi ◽  
Mohamed A. Eltaher ◽  
Khalid H. Almitani ◽  
Khaled A. Alnefaie ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Finite Difference ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Variable Thermal Conductivity ◽  
Solid Particles ◽  
Engine Oil ◽  
Working Fluid ◽  
Implicit Finite Difference

The current article presents the entropy formation and heat transfer of the steady Prandtl-Eyring nanofluids (P-ENF). Heat transfer and flow of P-ENF are analyzed when nanofluid is passed to the hot and slippery surface. The study also investigates the effects of radiative heat flux, variable thermal conductivity, the material’s porosity, and the morphologies of nano-solid particles. Flow equations are defined utilizing partial differential equations (PDEs). Necessary transformations are employed to convert the formulae into ordinary differential equations. The implicit finite difference method (I-FDM) is used to find approximate solutions to ordinary differential equations. Two types of nano-solid particles, aluminium oxide (Al2O3) and copper (Cu), are examined using engine oil (EO) as working fluid. Graphical plots are used to depict the crucial outcomes regarding drag force, entropy measurement, temperature, Nusselt number, and flow. According to the study, there is a solid and aggressive increase in the heat transfer rate of P-ENF Cu-EO than Al2O3-EO. An increment in the size of nanoparticles resulted in enhancing the entropy of the model. The Prandtl-Eyring parameter and modified radiative flow show the same impact on the radiative field.

scholarly journals The Shape Effect of Gold Nanoparticles on Squeezing Nanofluid Flow and Heat Transfer between Parallel Plates

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Umair Rashid ◽  
Thabet Abdeljawad ◽  
Haiyi Liang ◽  
Azhar Iqbal ◽  
Muhammad Abbas ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Volume Fraction ◽  
Graphical Form ◽  
Shape Effect ◽  
Parallel Plates ◽  
Nanofluid Flow ◽  
Suction Parameter ◽  
Flow And Heat Transfer

The focus of the present paper is to analyze the shape effect of gold (Au) nanoparticles on squeezing nanofluid flow and heat transfer between parallel plates. The different shapes of nanoparticles, namely, column, sphere, hexahedron, tetrahedron, and lamina, have been examined using water as base fluid. The governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) by suitable transformations. As a result, nonlinear boundary value ordinary differential equations are tackled analytically using the homotopy analysis method (HAM) and convergence of the series solution is ensured. The effects of various parameters such as solid volume fraction, thermal radiation, Reynolds number, magnetic field, Eckert number, suction parameter, and shape factor on velocity and temperature profiles are plotted in graphical form. For various values of involved parameters, Nusselt number is analyzed in graphical form. The obtained results demonstrate that the rate of heat transfer is maximum for lamina shape nanoparticles and the sphere shape of nanoparticles has performed a considerable role in temperature distribution as compared to other shapes of nanoparticles.

scholarly journals On the solution of two-sided fractional ordinary differential equations of Caputo type

2016 ◽  
Vol 19 (6) ◽  
Author(s):  
Ma. Elena Hernández-Hernández ◽  
Vassili N. Kolokoltsov
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fractional Differential Equations ◽  
Well Posedness ◽  
Solutions To Equations ◽  
Fractional Differential ◽  
The Right ◽  
Stochastic Representations ◽  
Exit Problems ◽  
Special Case

AbstractThis paper provides well-posedness results and stochastic representations for the solutions to equations involving both the right- and the left-sided generalized operators of Caputo type. As a special case, these results show the interplay between two-sided fractional differential equations and two-sided exit problems for certain Lévy processes.

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.

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