Axisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous Fluid on a Moving Cylinder With Time-Dependent Axial Velocity and Uniform Transpiration

2004 ◽  
Vol 126 (6) ◽  
pp. 997-1005 ◽  
Author(s):  
R. Saleh ◽  
A. B. Rahimi
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Axial Velocity ◽  
Time Dependent ◽  
Navier Stokes ◽  
Flow And Heat Transfer ◽  
Moving Cylinder ◽  
Self Similar ◽  
Suction Rate ◽  
Axial Speed

The unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite moving cylinder with time-dependent axial velocity and with uniform normal transpiration Uo are investigated. The impinging free stream is steady and with a constant strain rate k¯. An exact solution of the Navier–Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained by use of appropriate transformations for the most general case when the transpiration rate is also time-dependent but results are presented only for uniform values of this quantity. The general self-similar solution is obtained when the axial velocity of the cylinder and its wall temperature or its wall heat flux vary as specified time-dependent functions. In particular, the cylinder may move with constant speed, with exponentially increasing–decreasing axial velocity, with harmonically varying axial speed, or with accelerating–decelerating oscillatory axial speed. For self-similar flow, the surface temperature or its surface heat flux must have the same types of behavior as the cylinder motion. For completeness, sample semisimilar solutions of the unsteady Navier–Stokes and energy equations have been obtained numerically using a finite-difference scheme. Some of these solutions are presented for special cases when the time-dependent axial velocity of the cylinder is a step-function, and a ramp function. All the solutions above are presented for Reynolds numbers, Re=ka¯2/2υ, ranging from 0.1 to 100 for different values of dimensionless transpiration rate, S=Uo/ka¯, where a is cylinder radius and υ is kinematic viscosity of the fluid. Absolute value of the shear-stresses corresponding to all the cases increase with the increase of Reynolds number and suction rate. The maximum value of the shear- stress increases with increasing oscillation frequency and amplitude. An interesting result is obtained in which a cylinder moving with certain exponential axial velocity function at any particular value of Reynolds number and suction rate is axially stress-free. The heat transfer coefficient increases with the increasing suction rate, Reynolds number, Prandtl number, oscillation frequency and amplitude. Interesting means of cooling and heating processes of cylinder surface are obtained using different rates of transpiration. It is shown that a cylinder with certain type of exponential wall temperature exposed to a temperature difference has no heat transfer.

Axisymmetric Stagnation—Point Flow and Heat Transfer of a Viscous Fluid on a Rotating Cylinder With Time-Dependent Angular Velocity and Uniform Transpiration

2006 ◽  
Vol 129 (1) ◽  
pp. 106-115 ◽  
Author(s):  
A. B. Rahimi ◽  
R. Saleh
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Angular Velocity ◽  
Stokes Equations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow And Heat Transfer ◽  
Self Similar

The unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite rotating circular cylinder with transpiration U0 are investigated when the angular velocity and wall temperature or wall heat flux all vary arbitrarily with time. The free stream is steady and with a strain rate of Γ. An exact solution of the Navier-Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained by the use of appropriate transformations for the most general case when the transpiration rate is also time-dependent but results are presented only for uniform values of this quantity. The general self-similar solution is obtained when the angular velocity of the cylinder and its wall temperature or its wall heat flux vary as specified time-dependent functions. In particular, the cylinder may rotate with constant speed, with exponentially increasing/decreasing angular velocity, with harmonically varying rotation speed, or with accelerating/decelerating oscillatory angular speed. For self-similar flow, the surface temperature or its surface heat flux must have the same types of behavior as the cylinder motion. For completeness, sample semi-similar solutions of the unsteady Navier-Stokes equations have been obtained numerically using a finite-difference scheme. Some of these solutions are presented for special cases when the time-dependent rotation velocity of the cylinder is, for example, a step-function. All the solutions above are presented for Reynolds numbers, Re=Γa2∕2υ, ranging from 0.1 to 1000 for different values of Prandtl number and for selected values of dimensionless transpiration rate, S=U0∕Γa, where a is cylinder radius and υ is kinematic viscosity of the fluid. Dimensionless shear stresses corresponding to all the cases increase with the increase of Reynolds number and suction rate. The maximum value of the shear stress increases with increasing oscillation frequency and amplitude. An interesting result is obtained in which a cylinder rotating with certain exponential angular velocity function and at particular value of Reynolds number is azimuthally stress-free. Heat transfer is independent of cylinder rotation and its coefficient increases with the increasing suction rate, Reynolds number, and Prandtl number. Interesting means of cooling and heating processes of cylinder surface are obtained using different rates of transpiration.

Characteristics of Fully Developed Flow and Heat Transfer in Channels With Varying Wall Geometry

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Abhishek G. Ramgadia ◽  
Arun K. Saha
Keyword(s):  
Heat Transfer ◽  
Time Dependent ◽  
Navier Stokes ◽  
Fully Developed Flow ◽  
Flow And Heat Transfer ◽  
Collocated Grid ◽  
Wall Profile ◽  
Energy Equations ◽  
Volume Method ◽  
Wall Geometry

Present study focuses on numerical investigation of fully developed flow and heat transfer through three channels having sine-shaped, triangle-shaped, and arc-shaped wall profiles. All computations are performed at Reynolds number of 600. Finite volume method on collocated grid is used to solve the time-dependent Navier–Stokes and energy equations in primitive variable form. For all the geometries considered in the study, the ratios Hmin/Hmax and L/a are kept fixed to 0.4 and 8.0, respectively. The thermal performances of all the three wall configurations are assessed using integral parameters as well as instantaneous, time-averaged and fluctuating flow fields. The geometry with the sinusoidal-shaped wall profile is found to produce the best thermal properties as compared to the triangle-shaped and the arc-shaped profiles though the obtained heat transfer is the highest for the arc-shaped geometry.

scholarly journals Compressible, Turbulent, Viscous Flow Computations for Blade Aerodynamic and Heat Transfer

1996 ◽  
Author(s):  
A. A. Boretti
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Reynolds Number ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Viscous Flow ◽  
Three Dimensional ◽  
Time Dependent ◽  
Navier Stokes ◽  
Partial Differential

The paper presents a computer code for steady and unsteady, three-dimensional, compressible, turbulent, viscous flow simulations. The mathematical model is based on the Favre-averaged Navier-Stokes conservation equations, closed by a statistical model of turbulence. Turbulence effects are represented by using a low Reynolds number K-ω model. The numerical model makes use of a finite difference approximation in generalized coordinates for space discretization. The solution of time-dependent, three-dimensional, non-homogeneous, partial differential equations is obtained by solving, in a prescribed, symmetric pattern, three time-dependent, one-dimensional, homogeneous partial differential equations, representing convection and diffusion along each generalized coordinate direction, and one ordinary differential equation, representing generation and destruction. An explicit, multi-step, dissipative, Runge-Kutta scheme is finally adopted for time discretization. The code is applied to simulate the flow through a linear cascade of turbine rotor blades, where detailed experimental data are available. Blade aerodynamic and heat transfer are computed, at variable Reynolds and Mach numbers and turbulence levels, and compared with experimental data. While the aerodynamic prediction is relatively unaffected by the properties of both mathematical and numerical models, the heat transfer prediction proves to be extremely sensitive to models details. Low Reynolds number K-ω turbulence models theoretically reproduce laminar, turbulent and transitional boundary layers. However, their practical use in a Navier-Stokes code does not allow to entirely capture the effects of turbulence intensity and Mach and Reynolds numbers on blade heat transfer.

Optimization of Rib Shape and Inclination in a Square Duct with Response Surface Methodology

2021 ◽  
pp. 1-34
Author(s):  
Yigang Luan ◽  
Lanyi Yan ◽  
Yue Yin ◽  
Hao Fu
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Response Surface ◽  
Navier Stokes ◽  
Internal Cooling ◽  
Square Duct ◽  
Flow And Heat Transfer ◽  
Surface Method ◽  
Geometric Factors ◽  
Parameter Ranges

Abstract The paper conducts numerical investigation coupled with Reynolds-averaged Navier Stokes method on detailed flow field and heat transfer characteristics of ribbed channel with symmetric ribs mounted on two walls. The physical domain is modeled by reference to a practical turbine blade internal cooling channel. The effects of three selected geometric factors of ribs, i.e. rib inclination angle, dimensionless rib height and dimensionless rib pitch, on the flow and heat transfer are investigated by variable-controlled simulations with the Reynolds number ranges from 5,000 to 90,000. The parameter ranges are 30°≤a≤90°, 0.5≤e/w≤1.5 and 5≤P/w≤15 with the rib width w fixed at 1mm. It is newly found that the friction factor does not follow a monotonical trend with respect to the Reynolds number under certain rib configurations. In addition, three-level numerical calculations about three geometric factors as well as the Reynolds number are conducted with the response surface method (RSM). Quadratic regression model for the targeted response, TPF, is obtained. The optimal rib shape for the goal of maximizing the channel overall thermal performance turns out to be e/w=0.5, P/w=15, a=30° as Re is fixed at 30,000.

scholarly journals Numerical investigation of fluid flow and heat transfer characteristics in sine, triangular, and arc-shaped channels

2007 ◽  
Vol 11 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Zakir Hossain ◽  
Sadrul Islam
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Fluid Flow ◽  
Critical Reynolds Number ◽  
Navier Stokes ◽  
Heat Transfer Characteristics ◽  
Single Wave ◽  
Transfer Characteristics ◽  
Flow And Heat Transfer ◽  
Wavy Channels

Time dependent Navier-Stokes and energy equations have been solved to investigate the fluid flow and heat transfer characteristics in wavy channels. Three different types of two dimensional wavy geometries (e.g. sine-shaped, triangular, and arc-shaped) are considered. All of them are of single wave and have same geometric dimensions. Periodic boundary conditions are used to attain fully developed flow. The flow in the channels has been observed to be steady up to a critical Reynolds number, which depends on the geometric configuration. Beyond the critical Reynolds number a self-sustained oscillatory flow has been observed. As a result of this oscillation, there is increased mixing between core and the near-wall fluids, thereby increasing the heat transfer rate. For the same geometric dimensions, flow becomes unsteady at relatively lower Reynolds number in the arc-shaped channel. .

Flow and Heat Transfer in an Internally Ribbed Duct With Rotation: An Assessment of LES and URANS

2003 ◽  
Author(s):  
A. K. Saha ◽  
Sumanta Acharya
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Density Ratio ◽  
Navier Stokes ◽  
Flow And Heat Transfer ◽  
Number Ratio ◽  
Wide Range ◽  
Side Walls ◽  
Subgrid Stresses

Large Eddy Simulations (LES) and Unsteady Reynolds Averaged Navier-Stokes (URANS) simulations have been performed for flow and heat transfer in a rotating ribbed duct. The ribs are oriented normal to the flow and arranged in a staggered configuration on the leading and trailing surfaces. The LES results are based on a higher-order accurate finite difference scheme with a dynamic Smagorinsky model for the subgrid stresses. The URANS procedure utilizes a two equation k-ε model for the turbulent stresses. Both Coriolis and centrifugal buoyancy effects are included in the simulations. The URANS computations have been carried out for a wide range of Reynolds number (Re = 12,500–100,000), rotation number (Ro = 0–0.5) and density ratio (Δρ/ρ = 0–0.5), while LES results are reported for a single Reynolds number of 12,500 without and with rotation (Ro = 0.12, Δρ/ρ = 0.13). Comparison is made between the LES and URANS results, and the effects of various parameters on the flow field and surface heat transfer are explored. The LES results clearly reflect the importance of coherent structures in the flow, and the unsteady dynamics associated with these structures. The heat transfer results from both LES and URANS are found to be in reasonable agreement with measurements. LES is found to give higher heat transfer predictions (5–10% higher) than URANS. The Nusselt number ratio (Nu/Nu0) is found to decrease with increasing Reynolds number on all walls, while they increase with the density ratio along the leading and trailing walls. The Nusselt number ratio on the trailing and side walls also increases with rotation. However, the leading wall Nusselt number ratio shows an initial decrease with rotation (till Ro = 0.12) due to the stabilizing effect of rotation on the leading wall. However, beyond Ro = 0.12, the Nusselt number ratio increases with rotation due to the importance of centrifugal-buoyancy at high rotation.

Computation of Compressible Flow and Heat Transfer in a Rotating Duct With Inclined Ribs and a 180-Degree Bend

1997 ◽  
Author(s):  
M. A. Stephens ◽  
T. I-P. Shih
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Cross Sections ◽  
Three Dimensional ◽  
Side Wall ◽  
Secondary Flows ◽  
Navier Stokes ◽  
Outer Side ◽  
Flow And Heat Transfer ◽  
Density Ratios

Computations were performed to study the three-dimensional flow and heat transfer in a U-shaped duct of square cross section with and without ribs under rotating and staggered inclined ribs of rounded cross sections on the leading and trailing walls. Parameters investigated include: two rotation numbers (0, 0.24), two density ratios (0.13, 0.22), and smooth versus ribbed walls at a Reynolds number of 25,000 and an inlet Mach number of 0.05. For the conditions of the present study, rib-induced secondary flows were found to dominate over those induced by the Coriolis force in terms of flow pattern. This shifted tendency for flow separation induced by centrifugal buoyancy from the leading wall to the outer-side wall for radially outward flow. The secondary flows induced by the 180-degree bend were found to be comparable to that induced by the ribs, creating very complex interactions in flow and surface heat transfer characteristics. The computations are based on the ensemble-averaged conservation equations of mass, momentum (compressible Navier-Stokes), and energy closed by a low Reynolds number k-ω model of turbulence. Solutions were generated by using a cell-centered finite-volume method based on flux-difference splitting and a diagonalized alternating-direction implicit scheme with multigrid.

Numerical Computation of Fluid Flow and Heat Transfer in Microchannels

2005 ◽  
Author(s):  
Ningli Liu ◽  
Rene Chevray ◽  
Gerald A. Domoto ◽  
Elias Panides
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Energy Equation ◽  
Stokes Equations ◽  
Numerical Approach ◽  
Time Dependent ◽  
Navier Stokes ◽  
Temperature Profiles ◽  
Navier Stokes Equations ◽  
Flow And Heat Transfer

A finite difference numerical approach for solving slightly compressible, time-dependent, viscous laminar flow is presented in this study. Simplified system of Navier-Stokes equations and energy equation are employed in the study in order to perform more efficient numerical calculations. Fluid flow and heat transfer phenomena in two dimensional microchannels are illustrated numerically in this paper. This numerical approach provides a complete numerical simulation of the development of the fluid flow and the temperature profiles through multi-dimensional microchannels.

Flow and Heat Transfer in an Internally Ribbed Duct With Rotation: An Assessment of Large Eddy Simulations and Unsteady Reynolds-Averaged Navier-Stokes Simulations

2004 ◽  
Vol 127 (2) ◽  
pp. 306-320 ◽  
Author(s):  
A. K. Saha ◽  
Sumanta Acharya
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Density Ratio ◽  
Large Eddy Simulations ◽  
Navier Stokes ◽  
Flow And Heat Transfer ◽  
Number Ratio ◽  
Large Eddy ◽  
Reynolds Averaged Navier Stokes

Large eddy simulations (LES) and unsteady Reynolds averaged Navier-Stokes (URANS) simulations have been performed for flow and heat transfer in a rotating ribbed duct. The ribs are oriented normal to the flow and arranged in a staggered configuration on the leading and trailing surfaces. The LES results are based on a higher-order accurate finite difference scheme with a dynamic Smagorinsky model for the subgrid stresses. The URANS procedure utilizes a two equation k-ε model for the turbulent stresses. Both Coriolis and centrifugal buoyancy effects are included in the simulations. The URANS computations have been carried out for a wide range of Reynolds number (Re=12,500-100,000), rotation number (Ro=0-0.5) and density ratio (Δρ∕ρ=0-0.5), while LES results are reported for a single Reynolds number of 12,500 without and with rotation (Ro=0.12,Δρ∕ρ=0.13). Comparison is made between the LES and URANS results, and the effects of various parameters on the flow field and surface heat transfer are explored. The LES results clearly reflect the importance of coherent structures in the flow, and the unsteady dynamics associated with these structures. The heat transfer results from both LES and URANS are found to be in reasonable agreement with measurements. LES is found to give higher heat transfer predictions (5–10% higher) than URANS. The Nusselt number ratio (Nu∕Nu0) is found to decrease with increasing Reynolds number on all walls, while they increase with the density ratio along the leading and trailing walls. The Nusselt number ratio on the trailing and sidewalls also increases with rotation. However, the leading wall Nusselt number ratio shows an initial decrease with rotation (till Ro=0.12) due to the stabilizing effect of rotation on the leading wall. However, beyond Ro=0.12, the Nusselt number ratio increases with rotation due to the importance of centrifugal-buoyancy at high rotation.

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