A New Approach to Teaching Thermofluids Dimensional Analysis

2000 ◽  
Vol 28 (2) ◽  
pp. 174-184 ◽  
Author(s):  
Mark R. D. Davies ◽  
Tara M. Dalton
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Dimensional Analysis ◽  
New Approach ◽  
Flow And Heat Transfer ◽  
Single Method ◽  
Approach To Teaching ◽  
Simple Equations

A new method of dimensional analysis is presented by demonstrating its application to a range of problems in fluid flow and heat transfer. The technique is a development of a previously published and accepted method of inspectional analysis. This new technique is shown to give the correct results on both simple equations with solutions, and on more complex sets of partial differential equations without solutions. This development of a single method from the simple to the complex has obvious teaching advantages.

Unsteady separated stagnation-point flow and heat transfer past a stretching/shrinking sheet in a copper-water nanofluid

2019 ◽  
Vol 29 (8) ◽  
pp. 2588-2605 ◽  
Author(s):  
Natalia C. Roşca ◽  
Alin V. Roşca ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Stagnation Point ◽  
Design Methodology ◽  
Similarity Transformation ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Content Type ◽  
Flow And Heat Transfer

Purpose The purpose of this paper is to theoretically investigate the unsteady separated stagnation-point flow and heat transfer past an impermeable stretching/shrinking sheet in a copper (Cu)-water nanofluid using the mathematical nanofluid model proposed by Tiwari and Das. Design/methodology/approach A similarity transformation is used to reduce the governing partial differential equations to a set of nonlinear ordinary (similarity) differential equations which are then solved numerically using the function bvp4c from Matlab for different values of the governing parameters. Findings It is found that the solution is unique for stretching case; however, multiple (dual) solutions exist for the shrinking case. Originality/value The authors believe that all numerical results are new and original, and have not been published elsewhere.

Heat Transfer in an Upper Convected Maxwell Fluid with Fluid Particle Suspension

2015 ◽  
Vol 7 (3) ◽  
pp. 369-386 ◽  
Author(s):  
K. Vajravelu ◽  
K. V. Prasad ◽  
S. R. Santhi
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Differential Equations ◽  
Dust Particle ◽  
Maxwell Fluid ◽  
Fluid Temperature ◽  
Heat Transfer Characteristics ◽  
Flow And Heat Transfer ◽  
Ucm Fluid ◽  
Flow Phenomena

AbstractAn analysis is carried out to study the magnetohydrodynamic (MHD) flow and heat transfer characteristics of an electrically conducting dusty non-Newtonian fluid, namely, the upper convected Maxwell (UCM) fluid over a stretching sheet. The stretching velocity and the temperature at the surface are assumed to vary linearly with the distance from the origin. Using a similarity transformation, the governing nonlinear partial differential equations of the model problem are transformed into coupled non-linear ordinary differential equations and the equations are solved numerically by a second order finite difference implicit method known as the Keller-box method. Comparisons with the available results in the literature are presented as a special case. The effects of the physical parameters on the fluid velocity, the velocity of the dust particle, the density of the dust particle, the fluid temperature, the dust-phase temperature, the skin friction, and the wall-temperature gradient are presented through tables and graphs. It is observed that, Maxwell fluid reduces the wall-shear stress. Also, the fluid particle interaction reduces the fluid temperature in the boundary layer. Furthermore, the results obtained for the flow and heat transfer characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid flow phenomena, especially the dusty UCM fluid flow phenomena.

Viscous Dissipation Effect on Heat Transfer Through Nano Fluid in a Vertical Wavy Channel with Travelling Thermal Wave

2020 ◽  
Vol 28 ◽  
pp. 17-31
Author(s):  
Paladugu Venkata Ramana ◽  
Gosukonda Srinivas ◽  
G.V.P.N Srikanth
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Fluid Flow ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Thermal Wave ◽  
Transfer Rate ◽  
Wavy Channel ◽  
Nano Fluid ◽  
Flow And Heat Transfer

The effect of viscous dissipation on heat transfer through nano-fluid in a vertical wavy channel filled with porous media has been studied. The consequential differential equations are simplified by the R-K method of 6th order. The numerical obtained results are shown in the graphs. The significant results of fluid flow and heat transfer rate and its properties are shown graphically. Nusslet values are calculated a for varying the governing parameters φ Da, Gr, ε, Ec and the remaining parameters are to be constants.

Solving One-Dimensional Partial Differential Equations

2021 ◽  
pp. 191-215
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Material Properties ◽  
Final Part ◽  
Temperature Dependent ◽  
Partial Differential ◽  
One Dimensional

This chapter describes the pdepe command, which is used to solve spatially one-dimensional partial differential equations (PDEs). It begins with a description of the standard forms of PDEs and its initial and boundary conditions that the pdepe solver uses. It is shown how various PDEs and boundary conditions can be represented in standard forms. Applications to the mechanics are presented in the final part of the chapter. They illustrate how to solve: heat transfer PDE with temperature dependent material properties, startup velocities of the fluid flow in a pipe, Burger's PDE, and coupled FitzHugh-Nagumo PDE.

Analytical Investigation of Nusselt Number and Skin Friction of Fluid Flow Over a Stretching Sheet Using Optimal Homotopy Asymptotic Method

2020 ◽  
Vol 12 (5) ◽  
pp. 657-661
Author(s):  
Zohreh Aliannejadi
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Differential Equations ◽  
Skin Friction ◽  
Flow And Heat Transfer ◽  
Optimal Homotopy Asymptotic Method ◽  
The Magnetic Field

In many cases such as production of metal sheets, the behavior of fluid flow and heat transfer in the neighborhood of a hot plate is very important. The CFD simulation of fluid flow is a widespread study that reveals detail information about the fluid flow in the calculated domain. In this study, the flow and heat transfer of a specific fluid in the above area of a stretching plate is examined analytically to find the variation of skin friction and Nusselt number. For this purpose, the similarity transformations can be employed to achieve the ordinary differential equations from the governing partial differential equations. The optimal homotopy asymptotic method (OHAM) is used to solve the ordinary differential equations which is applicable in solving of nonlinear equations. The effects of magnetic field on the analytical results from solving the equations are evaluated in detail. It is found that the thickness of the flow boundary layer decreases and the thickness of the thermal boundary layer increases by increasing in the magnetic field. Moreover, the Nusselt number is lower and skin friction is higher for the higher values of the magnetic field.

A Quasi Method of Characteristics With Application to Fluid Lines With Frequency Dependent Wall Shear and Heat Transfer

1969 ◽  
Vol 91 (2) ◽  
pp. 217-226 ◽  
Author(s):  
F. T. Brown
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Method Of Characteristics ◽  
Hyperbolic Partial Differential Equations ◽  
Unsteady Fluid Flow ◽  
Wall Shear ◽  
Unsteady Fluid ◽  
Or History

The method of characteristics has been used in a variety of graphical, analytical, and numerical ways as a powerful tool in the solution of hyperbolic partial differential equations. The availability of digital computers permits the basic method to be applied to a greatly extended class of problems represented by semihyperbolic equations. This general extension is illustrated by problems of unsteady fluid flow in rigid tubes with the effects of frequency or history-dependent wall shear and heat transfer.

scholarly journals Heat transfer analysis in the time-dependent axisymmetric stagnation point flow over a lubricated surface

2018 ◽  
Vol 22 (6 Part A) ◽  
pp. 2483-2492 ◽  
Author(s):  
Khalid Mahmood ◽  
Muhammad Sajid ◽  
Nasir Ali ◽  
Tariq Javed
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Shear Stress ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Time Dependent ◽  
Surface Shear Stress ◽  
Partial Differential ◽  
Surface Shear ◽  
Flow And Heat Transfer

In this paper time-dependent, 2-D, axisymmetric flow and heat transfer of a viscous incompressible fluid impinging orthogonally on a disc is examined. The disc is lubricated with a thin layer of power-law fluid of variable thickness. It is assumed that surface temperature of the disc is time-dependent. Continuity of velocity and shear stress at the interface layer between the fluid and the lubricant has been imposed to obtain the solution of the governing partial differential equations. The set of partial differential equations is reduced into ordinary differential equations by suitable transformations and are solved numerically by using Keller-Box method. Solutions are presented in the form of graphs and tables in order to examine the influence of pertinent parameters on the flow and heat transfer characteristics. An increase in lubrication results in the reduction of surface shear stress and consequently viscous boundary layer becomes thin. However, the thermal boundary layer thickness increases by increasing lubrication. It is further observed that surface shear stress and heat transfer rate at the wall enhance due to unsteadiness. The results for the steady case are deduced from the present solutions and are found in good agreement with the existing results in the literature.

scholarly journals Analysis of the Physical Behavior of the Periodic Mixed-Convection Flow around a Nonconducting Horizontal Circular Cylinder Embedded in a Porous Medium

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Muhammad Ashraf ◽  
Zia Ullah ◽  
Saqib Zia ◽  
Sayer O. Alharbi ◽  
Dumitru Baleanu ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Fluid Flow ◽  
Partial Differential Equations ◽  
Circular Cylinder ◽  
Differential Equations ◽  
Mixed Convection ◽  
Skin Friction ◽  
Current Density ◽  
Horizontal Circular Cylinder

An oscillatory mixed-convection fluid flow mechanism across a nonconducting horizontal circular cylinder embedded in a porous medium has been computed. For this purpose, a model in the form of partial differential equations is formulated, and then, the governing equations of the dimensionless model are transformed into the primitive form for integration by using primitive variable formulation. The impact of emerging parameters such as porous medium parameter Ω , Richardson number λ , magnetic force parameter ξ , and Prandtl number Pr on skin friction, heat transfer, and current density is interpreted graphically. It is demonstrated that accurate numerical results can be obtained by the present method by treating nonoscillating and oscillating parts of coupled partial differential equations simultaneously. In this study, it is well established that the transient convective heat transfer, skin friction, and current density depend on amplitude and phase angle. One of the objects of the present study is to predict the mechanism of heat and fluid flow around different angles of a nonconducting horizontal circular cylinder embedded in a porous medium.

scholarly journals Thermal radiation effects on magneto hydro dynamic flow and heat transfer in a channel with porous walls of different permeability

2014 ◽  
Vol 18 (suppl.2) ◽  
pp. 563-572 ◽  
Author(s):  
Kishan Naikoti ◽  
Meenakshi Vadithya
Keyword(s):  
Heat Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Radiation Effects ◽  
Dynamic Flow ◽  
Partial Differential ◽  
Flow And Heat Transfer ◽  
Non Linear ◽  
Porous Walls

This paper deals with the problem of thermal radiation effects on magneto hydro dynamic flow and heat transfer in a channel with porous walls of different permeability. The equations governing the flow are coupled non-linear partial differential equations. By introducing the stream function, the governing partial differential equations are reduced to ordinary differential equations. The governing equations which are coupled and highly non-linear are first linearized by quasilinearization technique and obtained numerical solution by using implicit finite difference scheme. The effects of various parameters, namely, Reynolds number R, Permeability parameter K, Hartmann number S2, Prandtl number Pr, and Thermal radiation parameter F, entering into the problem on the velocity field and temperature distribution are shown graphically.

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