scholarly journals Computational Modelling of Couette Flow of Nanofluids with Viscous Heating and Convective Cooling

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Oluwole Daniel Makinde ◽  
Ahmada Omar ◽  
M. Samuel Tshehla
Keyword(s):  
Couette Flow ◽  
Computational Modelling ◽  
Navier Stokes ◽  
Viscous Heating ◽  
Parallel Plates ◽  
Regular Perturbation ◽  
Convective Cooling ◽  
Friction Pressure Drop ◽  
Water Base ◽  
Energy Equations

The combined effect of viscous heating and convective cooling on Couette flow and heat transfer characteristics of water base nanofluids containing Copper Oxide (CuO) and Alumina (Al2O3) as nanoparticles is investigated. It is assumed that the nanofluid flows in a channel between two parallel plates with the channel’s upper plate accelerating and exchange heat with the ambient surrounding following the Newton’s law of cooling, while the lower plate is stationary and maintained at a constant temperature. Using appropriate similarity transformation, the governing Navier-Stokes and the energy equations are reduced to a set of nonlinear ordinary differential equations. These equations are solved analytically by regular perturbation method with series improvement technique and numerically by an efficient Runge-Kutta-Fehlberg integration technique coupled with shooting method. The effects of the governing parameters on the dimensionless velocity, temperature, skin friction, pressure drop and Nusselt number are presented graphically, and discussed quantitatively.

scholarly journals Analysis of Heat Transfer in Berman Flow of Nanofluids with Navier Slip, Viscous Dissipation, and Convective Cooling

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
O. D. Makinde ◽  
S. Khamis ◽  
M. S. Tshehla ◽  
O. Franks
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Perturbation Methods ◽  
Regular Perturbation ◽  
Convective Cooling ◽  
Navier Slip ◽  
Nusselt Numbers ◽  
Similarity Transformations ◽  
Friction Pressure Drop

Heat transfer characteristics of a Berman flow of water based nanofluids containing copper (Cu) and alumina (Al2O3) as nanoparticles in a porous channel with Navier slip, viscous dissipation, and convective cooling are investigated. It is assumed that the exchange of heat with the ambient surrounding takes place at the channel walls following Newton’s law of cooling. The governing partial differential equations and boundary conditions are converted into a set of nonlinear ordinary differential equations using appropriate similarity transformations. These equations are solved analytically by regular perturbation methods with series improvement technique and numerically using an efficient Runge-Kutta Fehlberg integration technique coupled with shooting scheme. The effects of the governing parameters on the dimensionless velocity, temperature, skin friction, pressure drop, and Nusselt numbers are presented graphically and discussed quantitatively.

Thermally Developing 3D Cross Flow Between Cross Corrugated Parallel Plates in Evaporative Coolers

2010 ◽  
Author(s):  
Ehsan Tavakoli ◽  
Reza Hosseini
Keyword(s):  
Pressure Drop ◽  
Flow Direction ◽  
Cross Flow ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Main Emphasis ◽  
Saturation Efficiency ◽  
Finite Difference Discretization ◽  
Corrugated Plates ◽  
Energy Equations

The 3D cross flow between parallel corrugated plates with perpendicular directions of corrugation is numerically modeled as a laminar, incompressible, steady flow. The present work tries to investigate the thermally developing characteristics of the flow in this type of geometry, in the case of constant temperature on walls. The main emphasis is on introducing correlations for saturation efficiency and simply modeling the evaporation process within evaporative coolers with such geometries. The applied numerical method is the Chorin’s artificial incompressibility method and finite difference discretization is used to model the Navier-Stokes and energy equations in a structured mesh. The results show that saturation efficiency decreases with increase in Reynolds number. This also depends on the depth of evaporative media along the flow direction. Increasing the number of waves along the flow direction, results higher saturation efficiencies and also more pressure drop. For a specific saturation efficiency, the overall pressure drop decreases at higher amplitude to wavelength ratios. Also the overall pressure drop grows as the depth of the domain increases. The same trend is observed for experimental data of commercial evaporative pads.

The stability of plane Couette flow with viscous heating

1973 ◽  
Vol 57 (4) ◽  
pp. 651-670 ◽  
Author(s):  
Peter C. Sukanek ◽  
Charles A. Goldstein ◽  
Robert L. Laurence
Keyword(s):  
Couette Flow ◽  
Maximum Shear Stress ◽  
Negative Real Part ◽  
Navier Stokes ◽  
Exponential Dependence ◽  
Viscous Heating ◽  
Thermal Mode ◽  
Neutral Stability ◽  
Plane Couette Flow ◽  
The Stability

An investigation of the stability of plane Couette flow with viscous heating of a Navier–Stokes–Pourier fluid with an exponential dependence of viscosity upon temperature is presented. Using classical small perturbation theory, the stability of the flow can be described by a sixth-order set of coupled ordinary differential equations. Using Galerkin's method, these equations are reduced to an algebraic eigenvalue problem. An eigenvalue with a negative real part means that the flow is unstable.Neutral stability curves are determined at Brinkman numbers of 15, 19, 25, 30,40,80 and 600 for Prandtl numbers of 1, s and 50. A Brinkman number of 19 corresponds approximately to the maximum shear stress which can be applied to the system.The results indicate that four different modes of instability occur: one termed an inviscid mode, arising from an inflexion point in the primary flow; a viscous mode, due to the stratification of viscosity in the flow field and an associated diffusive mechanism; a coupling mode, resulting from the convective and viscous dissipation terms in the energy equation; and finally a purely thermal mode.

Numerical Investigation of the Natural Convection Flows for Low-Prandtl Fluids in Vertical Parallel-Plates Channels

2005 ◽  
Vol 73 (1) ◽  
pp. 96-107 ◽  
Author(s):  
Antonio Campo ◽  
Oronzio Manca ◽  
Biagio Morrone
Keyword(s):  
Natural Convection ◽  
Computational Procedure ◽  
Navier Stokes ◽  
Computational Domain ◽  
Parallel Plates ◽  
Nusselt Numbers ◽  
Aspect Ratios ◽  
Rate Maximum ◽  
Induced Flow ◽  
Energy Equations

Laminar natural convection of metallic fluids (Pr⪡1) between vertical parallel plate channels with isoflux heating is investigated numerically in this work. The full elliptic Navier-Stokes and energy equations have been solved with the combination of the stream function and vorticity method and the finite-volume technique. An enlarged computational domain is employed to take into account the flow and thermal diffusion effects. Results are presented in terms of velocity and temperature profiles. The investigation also focuses on the flow and thermal development inside the channel; the outcomes show that fully developed flow is attained up to Ra=103, whereas the thermal fully developed condition is attained up to Ra=104. Further, correlation equations for the dimensionless induced flow rate, maximum dimensionless wall temperatures, and average Nusselt numbers as functions of the descriptive geometrical and thermal parameters covering the collection of channel Grashof numbers 1.32×103⩽Gr∕A⩽5.0×106 and aspect ratios 5⩽A⩽15. Comparison with experimental measurements has been presented to assess the validity of the numerical computational procedure.

Transient Analysis of Natural Convection in a Horizontal Open Ended Cavity

2002 ◽  
Author(s):  
Assunta Andreozi ◽  
Oronzio Manca ◽  
Yogesh Jaluria
Keyword(s):  
Natural Convection ◽  
Stokes Equations ◽  
Chemical Vapor ◽  
Navier Stokes ◽  
Uniform Heat Flux ◽  
Temperature Profiles ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Penetration Length ◽  
Energy Equations

The configuration of two horizontal parallel walls can be found in many applications, such as the cooling of electronic components, solar energy systems and chemical vapor deposition systems (CVD). In the present investigation a transient numerical analysis for laminar natural convection in air between two horizontal parallel plates, with the upper plate heated at uniform heat flux and the lower one unheated, is carried out by means of the finite volume method. The model was assumed to be two-dimensional. The full two-dimensional Navier-Stokes equations together with the continuity and energy equations are solved by a numerical scheme derived from a SIMPLE-like algorithm in an H-shaped domain. Results are presented in terms of velocity and temperature profiles, wall temperature profiles and the temporal behavior of several significant variables, such as the penetration length, is reported for different Rayleigh numbers and aspect ratio values.

Numerical Performances Study of Curved Photovoltaic Panel Integrated with Phase Change Material

2020 ◽  
Vol 22 (4) ◽  
pp. 1439-1452
Author(s):  
Mohamed L. Benlekkam ◽  
Driss Nehari ◽  
Habib Y. Madani
Keyword(s):  
Phase Change ◽  
Phase Change Material ◽  
Numerical Study ◽  
Numerical Data ◽  
Navier Stokes ◽  
Photovoltaic Panel ◽  
Pv Panel ◽  
Energy Equations ◽  
Solid Liquid ◽  
Change Material

AbstractThe temperature rise of photovoltaic’s cells deteriorates its conversion efficiency. The use of a phase change material (PCM) layer linked to a curved photovoltaic PV panel so-called PV-mirror to control its temperature elevation has been numerically studied. This numerical study was carried out to explore the effect of inner fins length on the thermal and electrical improvement of curved PV panel. So a numerical model of heat transfer with solid-liquid phase change has been developed to solve the Navier–Stokes and energy equations. The predicted results are validated with an available experimental and numerical data. Results shows that the use of fins improve the thermal load distribution presented on the upper front of PV/PCM system and maintained it under 42°C compared with another without fins and enhance the PV cells efficiency by more than 2%.

Internal laminar flow

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Poiseuille Flow ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Concentric Cylinder ◽  
Navier Stokes Equations ◽  
Concentric Cylinders ◽  
Constant Viscosity ◽  
Pressure Driven Flow

In this chapter it is shown that solutions to the Navier-Stokes equations can be derived for steady, fully developed flow of a constant-viscosity Newtonian fluid through a cylindrical duct. Such a flow is known as a Poiseuille flow. For a pipe of circular cross section, the term Hagen-Poiseuille flow is used. Solutions are also derived for shear-driven flow within the annular space between two concentric cylinders or in the space between two parallel plates when there is relative tangential movement between the wetted surfaces, termed Couette flows. The concepts of wetted perimeter and hydraulic diameter are introduced. It is shown how the viscometer equations result from the concentric-cylinder solutions. The pressure-driven flow of generalised Newtonian fluids is also discussed.

Numerical Study of the Effect of Inlet Constriction on Bubble Growth During Flow Boiling in Microchannels

2005 ◽  
Author(s):  
Abhijit Mukherjee ◽  
Satish G. Kandlikar
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Flow Boiling ◽  
Navier Stokes ◽  
Channel Cross Section ◽  
Vapor Bubbles ◽  
Reversed Flow ◽  
Cross Sectional ◽  
Parallel Microchannels ◽  
Energy Equations

Flow boiling through microchannels is characterized by nucleation of vapor bubbles on the channel walls and their rapid growth as they fill the entire channel cross-section. In parallel microchannels connected through a common header, formation of vapor bubbles often results in flow maldistribution that leads to reversed flow in certain channels. The reversed flow is detrimental to the heat transfer and leads to early CHF condition. One way of eliminating the reversed flow is to incorporate flow restrictions at the channel inlet. In the present numerical study, a nucleating vapor bubble placed near the restricted end of a microchannel is numerically simulated. The complete Navier-Stokes equations along with continuity and energy equations are solved using the SIMPLER method. The liquid-vapor interface is captured using the level set technique. The results show that with no restriction the bubble moves towards the nearest channel outlet, whereas in the presence of a restriction, the bubble moves towards the distant but unrestricted end. It is proposed that channels with increasing cross-sectional area may be used to promote unidirectional growth of the vapor plugs and prevent reversed flow.

Prediction and Analysis of the Bubble Formation in Film Boiling

2004 ◽  
Author(s):  
A. Agrawal ◽  
G. Biswas ◽  
S. W. J. Welch ◽  
F. Durst
Keyword(s):  
Complete Solution ◽  
Bubble Formation ◽  
Transport Coefficients ◽  
Quantitative Information ◽  
Horizontal Surface ◽  
Film Boiling ◽  
Navier Stokes ◽  
Interface Tracking ◽  
Energy Equations ◽  
Interface Mass Transfer

The bubble formation and heat transfer on a horizontal surface have been numerically analyzed using a volume of fluid (VOF) based interface tracking method incorporated into a complete solution of the Navier-Stokes and the thermal energy equations. The numerical method took into account the effects of surface tension, the interface mass transfer and the corresponding latent heat. The computations demonstrated capability of the algorithm in generating quantitative information on unsteady periodic bubble release patterns and on the spatially and temporally varying film thickness. The computations also predict the transport coefficients on the horizontal surface.

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