Heat transport by laminar boundary layer flow with polymers

AbstractMotivated by recent experimental observations, we consider a steady-state boundary layer flow with polymers in forced convection above a heated plate and study how the heat transport might be affected by the polymers. We discuss how a set of equations can be derived for the problem and how these equations can be solved numerically by an iterative scheme. By carrying out such a scheme, we find that the effect of the polymers is equivalent to producing a space-dependent effective viscosity that first increases from the zero-shear value at the plate then decreases rapidly back to the zero-shear value far from the plate. We further show that such an effective viscosity leads to a decrease in the streamwise velocity near the plate, which in turn leads to a reduction in heat transport.

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Heat transport modification by finitely extensible polymers in laminar boundary layer flow

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.714 ◽

2016 ◽

Vol 788 ◽

pp. 337-357 ◽

Cited By ~ 5

Author(s):

Roberto Benzi ◽

Emily S. C. Ching ◽

Wilson C. K. Yu ◽

Yiqu Wang

Keyword(s):

Boundary Layer ◽

Heat Transport ◽

Laminar Boundary Layer ◽

Boundary Layer Flow ◽

Effective Viscosity ◽

Polymer Conformation ◽

Polymer Relaxation ◽

Layer Flow ◽

Conformation Tensor ◽

Nonlinear Elastic

We study how heat transport is affected by finitely extensible polymers in a laminar boundary layer flow within the framework of the Prandtl–Blasius–Pohlhausen theory. The polymers are described by the finitely extensible nonlinear elastic-Peterlin model with a parameter $b^{2}$, which is the ratio of the maximum to the equilibrium value of the trace of the polymer conformation tensor. For very large $b^{2}$, heat transport is reduced. When $b^{2}$ is small, heat transport is enhanced. We investigate the transition from heat reduction to heat enhancement as a function of the polymer relaxation time and concentration, and show that the transition can be explained in terms of the functional shape of the space-dependent effective viscosity due to the polymers.

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Turbulence statistics in smooth wall oscillatory boundary layer flow

Journal of Fluid Mechanics ◽

10.1017/jfm.2018.403 ◽

2018 ◽

Vol 849 ◽

pp. 192-230 ◽

Cited By ~ 6

Author(s):

Dominic A. van der A ◽

Pietro Scandura ◽

Tom O’Donoghue

Keyword(s):

Boundary Layer ◽

Normal Distribution ◽

Boundary Layer Flow ◽

Vertical Gradient ◽

Streamwise Velocity ◽

Normal Velocity ◽

Half Cycle ◽

Velocity Fluctuations ◽

Oscillatory Boundary Layer ◽

Layer Flow

Turbulence characteristics of an asymmetric oscillatory boundary layer flow are analysed through two-component laser-Doppler measurements carried out in a large oscillatory flow tunnel and direct numerical simulation (DNS). Five different Reynolds numbers, $R_{\unicode[STIX]{x1D6FF}}$, in the range 846–2057 have been investigated experimentally, where $R_{\unicode[STIX]{x1D6FF}}=\tilde{u} _{0max}\unicode[STIX]{x1D6FF}/\unicode[STIX]{x1D708}$ with $\tilde{u} _{0max}$ the maximum oscillatory velocity in the irrotational region, $\unicode[STIX]{x1D6FF}$ the Stokes length and $\unicode[STIX]{x1D708}$ the fluid kinematic viscosity. DNS has been carried out for the lowest three $R_{\unicode[STIX]{x1D6FF}}$ equal to 846, 1155 and 1475. Both experimental and numerical results show that the flow statistics increase during accelerating phases of the flow and especially at times of transition to turbulent flow. Once turbulence is fully developed, the near-wall statistics remain almost constant until the late half-cycle, with values close to those reported for steady wall-bounded flows. The higher-order statistics reach large values within a normalized wall distance of approximately $y/\unicode[STIX]{x1D6FF}=0.2$ at phases corresponding to the onset of low-speed streak breaking, because of the intermittency of the velocity fluctuations at these times. In particular, the flatness of the streamwise velocity fluctuations reaches values of the order of ten, while the flatness of the wall-normal velocity fluctuations reaches values of several hundreds. Far from the wall, at locations where the vertical gradient of the streamwise velocity is zero, the skewness is approximately zero and the flatness is approximately equal to 3, representative of a normal distribution. At lower elevations the distribution of the fluctuations deviate substantially from a normal distribution, but are found to be well described by other standard theoretical probability distributions.

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An instability in supersonic boundary-layer flow over a compression ramp

Journal of Fluid Mechanics ◽

10.1017/s0022112095003685 ◽

1995 ◽

Vol 300 ◽

pp. 265-285 ◽

Cited By ~ 25

Author(s):

K. W. Cassel ◽

A. I. Ruban ◽

J. D. A. Walker

Keyword(s):

Boundary Layer ◽

Boundary Layer Flow ◽

Streamwise Velocity ◽

Supersonic Boundary Layer ◽

Recirculation Region ◽

Hypersonic Boundary Layer ◽

Recirculating Flow ◽

Inflection Points ◽

Compression Ramp ◽

Layer Flow

Separation of a supersonic boundary layer (or equivalently a hypersonic boundary layer in a region of weak global interaction) near a compression ramp is considered for moderate wall temperatures. For small ramp angles, the flow in the vicinity of the ramp is described by the classical supersonic triple-deck structure governing a local viscous-inviscid interaction. The boundary layer is known to exhibit recirculating flow near the corner once the ramp angle exceeds a certain critical value. Here it is shown that above a second and larger critical ramp angle, the boundary-layer flow develops an instability. The instability appears to be associated with the occurrence of inflection points in the streamwise velocity profiles within the recirculation region and develops as a wave packet which remains stationary near the corner and grows in amplitude with time.

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MHD natural convection boundary-layer flow over a semi-infinite heated plate with arbitrary inclination

Discrete & Continuous Dynamical Systems - S ◽

10.3934/dcdss.2020059 ◽

2020 ◽

Vol 13 (3) ◽

pp. 1007-1015

Author(s):

Azhar Ali Zafar ◽

◽

Khurram Shabbir ◽

Asim Naseem ◽

Muhammad Waqas Ashraf

Keyword(s):

Boundary Layer ◽

Natural Convection ◽

Boundary Layer Flow ◽

Convection Boundary Layer ◽

Heated Plate ◽

Convection Boundary ◽

Layer Flow

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Transient Couple Stress Fluid Past a Vertical Cylinder With Bejan’s Heat and Mass Flow Visualization for Steady-State

Journal of Heat Transfer ◽

10.1115/1.4029085 ◽

2015 ◽

Vol 137 (3) ◽

Cited By ~ 14

Author(s):

H. P. Rani ◽

G. Janardhan Reddy ◽

Chang Nyung Kim ◽

Y. Rameshwar

Keyword(s):

Boundary Layer ◽

Steady State ◽

Flow Visualization ◽

Boundary Layer Flow ◽

Couple Stress ◽

Vertical Cylinder ◽

Couple Stress Fluid ◽

Layer Flow ◽

Flow Variables ◽

Mass Functions

In the present study, the transient, free convective, boundary layer flow of a couple stress fluid flowing over a vertical cylinder is investigated, and the heat and mass functions for the final steady-state of the present flow are developed. The solution of the time dependent nonlinear and coupled governing equations is obtained with the aid of an unconditionally stable Crank–Nicolson type of numerical scheme. Numerical results for the time histories of the skin-friction coefficient, Nusselt number, and Sherwood number as well as the steady-state velocity, temperature, and concentration are presented graphically and discussed. Also, it is observed that time required for the flow variables to reach the steady-state increases with the increasing values of Schmidt and Prandtl numbers, while the opposite trend is observed with respect to the buoyancy ratio parameter. To analyze the flow variables in the steady-state, the heatlines and masslines are used in addition to streamlines, isotherms, and isoconcentration lines. When the heat and mass functions are properly made dimensionless, its dimensionless values are related to the local and overall Nusselt and Sherwood numbers. Boundary layer flow visualization indicates that the heatlines and masslines are dense in the vicinity of the hot wall, especially near the leading edge.

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Vortex Instability in Buoyancy-Induced Flow over Inclined Heated Surfaces in Porous Media

Journal of Heat Transfer ◽

10.1115/1.3451053 ◽

1979 ◽

Vol 101 (4) ◽

pp. 660-665 ◽

Cited By ~ 40

Author(s):

C. T. Hsu ◽

Ping Cheng

Keyword(s):

Boundary Layer ◽

Inclination Angle ◽

Boundary Layer Flow ◽

Heated Surface ◽

Wave Number ◽

Heated Plate ◽

Local Similarity ◽

Linear Temperature ◽

Vortex Instability ◽

Layer Flow

A linear stability analysis is performed for the study of the onset of vortex instability in free convective flow over an inclined heated surface in a porous medium. The undisturbed state is assumed to be the steady two-dimensional buoyancy-induced boundary layer flow which is characterized by a non-linear temperature profile. By a scaling argument, it is shown that the length scales of disturbances are smaller than those for the undisturbed boundary layer flow, thus, confirming the so-called “bottling effects” whereby the disturbances are confined within the boundary layer. By neglecting the lowest order terms in the three-dimensional disturbances equations, the simplified equations are solved based on the local similarity approximations, wherein the disturbances are assumed to have a weak dependence in the streamwise direction. The resulting eigenvalue problem is solved numerically. The critical parameter and the critical wave number of disturbances at the onset of vortex instability are computed for different prescribed wall temperature distribution of the inclined surface. It is found that the larger the inclination angle with respect to the vertical, the more susceptible is the flow for the vortex mode of disturbances; and in the limit of zero inclination angle (i.e., a vertical heated plate) the flow is stable for this form of disturbances.

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Analytical solution of conjugate turbulent forced convection boundary layer flow over plates

Thermal Science ◽

10.2298/tsci140115062j ◽

2016 ◽

Vol 20 (5) ◽

pp. 1499-1507 ◽

Cited By ~ 1

Author(s):

Shariatzadeh Joneydi

Keyword(s):

Heat Transfer ◽

Boundary Layer ◽

Analytical Solution ◽

Forced Convection ◽

Boundary Layer Flow ◽

Finite Thickness ◽

Convection Boundary Layer ◽

Heated Plate ◽

Convection Boundary ◽

Layer Flow

A conjugate (coupled) forced convection heat transfer from a heated conducting plate under turbulent boundary layer flow is considered. A heated plate of finite thickness is cooled under turbulent forced convection boundary layer flow. Because the conduction and convection boundary layer flow is coupled (conjugated) in the problem, a semi-analytical solution based on Differential Transform Method (DTM) is presented for solving the non-linear integro-differential equation occurring in the problem. The main conclusion is that in the conjugate heat transfer case the temperature distribution of the plate is flatter than the one in the non-conjugate case. This feature is more pronounced under turbulent flow when compared with the laminar flow.

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