Passive Heat Transfer in Solid-State Lighting: Relaxing the Boussinesq Approximation Analytically in the Vertical Channel

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Thomas D. Dreeben
Keyword(s):  
Heat Transfer ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Vertical Channel ◽  
Boussinesq Approximation ◽  
Solid State Lighting ◽  
Two Dimensional ◽  
Characteristic Velocity ◽  
Thermal Boundary Layer Thickness ◽  
Analytical Relations

Analytical relations between the heat flux, temperature rise, thermal boundary layer thickness, and characteristic velocity have been derived for the two-dimensional vertical channel, without use of the Boussinesq approximation. Results have been put into the context of well-established scaling behavior in the literature. In addition, useful implications of the analytical results have been described, including a criterion to determine the suitability of a heat-sink configuration to a particular application.

Significance of Prandtl Number on the Heat Transport and Flow Structure in Rotating Rayleigh–Bénard Convection

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Vishnu Venugopal T ◽  
Arnab Kumar De ◽  
Pankaj Kumar Mishra
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Flow Structure ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Thermal Boundary Layer Thickness ◽  
Rotation Rates ◽  
Conduction State ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Abstract A direct numerical simulation of rotating Rayleigh–Bénard convection (RBC) for different fluids (Pr=0.015,0.7,1,7,20, and 100) in a cylindrical cell of aspect ratio Γ=0.5 is carried out in this work. The effect of rotation on the heat transfer rate, flow structures, their associated dynamics, and influence on the boundary layers are investigated. The Rayleigh number is fixed to Ra=106 and the rotation rates are varied for a wide range, starting from no rotation (Ro→∞) to high rotation rates (Ro≈0.01). For all the Prandtl numbers (Pr=0.015–100), a reduction in heat transfer with increase in rotation is observed. However, for Pr=7 and 20, a marginal increase of the Nusselt number for low rotation rates is obtained, which is attributed to the change in the flow structure from quadrupolar to dipolar state. The change in flow structure is associated with the statistical behavior of the boundary layers. As the flow makes a transition from quadrupolar to dipolar state, a reduction in the thermal boundary layer thickness is observed. At higher rotation rates, the thermal boundary layer thickness shows a power law variation with the rotation rate. The power law exponent is close to unity for moderate Pr, while it reduces for both lower and higher Pr. At extremely high rotation rates, the flow makes a transition to the conduction state. The critical rotation rate (1/Roc) for which transition to the conduction state is observed depends on the Prandtl number according to 1/Roc∝Pr0.5.

Boundary Layer Closure and Heat Transfer in Constant Base Pressure and Simple Wave Guns

1978 ◽  
Vol 100 (4) ◽  
pp. 690-696 ◽  
Author(s):  
A. D. Anderson ◽  
T. J. Dahm
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Method Of Characteristics ◽  
Simple Wave ◽  
Momentum Equation ◽  
Base Pressure ◽  
Two Dimensional ◽  
The Method Of Characteristics

Solutions of the two-dimensional, unsteady integral momentum equation are obtained via the method of characteristics for two limiting modes of light gas launcher operation, the “constant base pressure gun” and the “simple wave gun”. Example predictions of boundary layer thickness and heat transfer are presented for a particular 1 in. hydrogen gun operated in each of these modes. Results for the constant base pressure gun are also presented in an approximate, more general form.

Conjugate Heat Transfer in a Rotor-Stator System With Through-Flow

2002 ◽  
Author(s):  
Reby Roy ◽  
B. V. S. S. S. Prasad ◽  
S. Srinivasa Murthy
Keyword(s):  
Heat Transfer ◽  
Boundary Layer Thickness ◽  
Conjugate Heat Transfer ◽  
Rotating Disk ◽  
Thermal Boundary Layer Thickness ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Nusselt Numbers ◽  
Commercial Code ◽  
Through Flow

The conjugate heat transfer in a stationary cylindrical cavity with a rotating disk and fluid through-flow is analysed at various rotational speeds ranging from 10000 to 50000 rpm by using a finite volume commercial code. The numerical model and code are validated for a problem, which involves rotation and fluid through-flow. A reduction of the thermal boundary layer thickness and increase in the heat transfer coefficients are observed with increase in the rotational speed. Marked differences are noticed between the Nusselt numbers obtained from the conjugate and constant temperature analyses.

scholarly journals Effects of Pressure Gradient on Convective Heat Transfer in a Boundary Layer Flow of a Maxwell Fluid Past a Stretching Sheet

2021 ◽  
Vol 26 (3) ◽  
pp. 104-118
Author(s):  
A.N. Kashif ◽  
F. Salah ◽  
D.S. Sankar ◽  
M.D.N. Izyan ◽  
K.K. Viswanathan
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Stretching Sheet ◽  
Maxwell Fluid ◽  
Gradient Term ◽  
Pressure Gradient Term ◽  
Layer Flow

Abstract The pressure gradient term plays a vital role in convective heat transfer in the boundary layer flow of a Maxwell fluid over a stretching sheet. The importance of the effects of the term can be monitored by developing Maxwell’s equation of momentum and energy with the pressure gradient term. To achieve this goal, an approximation technique, i.e. Homotopy Perturbation Method (HPM) is employed with an application of algorithms of Adams Method (AM) and Gear Method (GM). With this approximation method we can study the effects of the pressure gradient (m), Deborah number (β), the ratio of the free stream velocity parameter to the stretching sheet parameter (ɛ) and Prandtl number (Pr) on both the momentum and thermal boundary layer thicknesses. The results have been compared in the absence and presence of the pressure gradient term m . It has an impact of thinning of the momentum and boundary layer thickness for non-zero values of the pressure gradient. The convergence of the system has been taken into account for the stretching sheet parameter ɛ. The result of the system indicates the significant thinning of the momentum and thermal boundary layer thickness in velocity and temperature profiles. On the other hand, some results show negative values of f '(η) and θ (η) which indicates the case of fluid cooling.

Momentum and Thermal Boundary-layer Thickness in a Stagnation Flow Chemical Vapor Deposition Reactor

1997 ◽  
Vol 12 (4) ◽  
pp. 1112-1121 ◽  
Author(s):  
David S. Dandy ◽  
Jungheum Yun
Keyword(s):  
Boundary Layer ◽  
Chemical Vapor Deposition ◽  
Layer Thickness ◽  
Vapor Deposition ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Numerical Solutions ◽  
Chemical Vapor ◽  
Square Root ◽  
Thermal Boundary Layer Thickness

Explicit expressions have been derived for momentum and thermal boundary-layer thickness of the laminar, uniform stagnation flows characteristic of highly convective chemical vapor deposition pedestal reactors. Expressions for the velocity and temperature profiles within the boundary layers have also been obtained. The results indicate that, to leading order, the momentum boundary-layer thickness is inversely proportional to the square root of the Reynolds number, while the thermal boundary-layer thickness is inversely proportional to the square root of the Peclet number. Values computed using the approximate expressions are compared directly with numerical solutions of the equations of motion and thermal energy equation, for a specific set of conditions typical of diamond chemical vapor deposition. Because values of the Lewis number do not vary significantly from unity for many different chemical vapor deposition systems, the expression derived here for thermal boundary-layer thickness may be used directly as an approximate concentration boundary-layer thickness.

An integral approach to the calculation of skin friction and heat transfer in the laminar flow of a high-Prandtl-number power-law non-Newtonian fluid past a wedge

1991 ◽  
Vol 69 (2) ◽  
pp. 83-89 ◽  
Author(s):  
G. Ramamurty ◽  
K. Narasimha Rao ◽  
K. N. Seetharamu
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Skin Friction ◽  
Layer Thickness ◽  
Power Law ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Integral Approach ◽  
High Prandtl Number

An integral approach to the theoretical analysis for the skin friction of a non-Newtonian, power-law-fluid flow over a wedge is presented, when the inertia terms in the boundary-layer equations are small but need consideration. The method adopted for the solution of the equations considers an integrated average value of the inertia terms in the momentum equation. The values of the velocities and the boundary-layer thickness obtained from the hydrodynamic analysis are used for the calculation of the thermal-boundary-layer thickness. A linear velocity profile is assumed for the flow field within the thermal boundary layer as the fluids chosen for the analysis are high-Prandtl-number fluids. The results of the skin friction and the rates of the heat transfer are tabulated for a number of values of the flow behaviour index, n, varying from 0.05 to 5.0. This analysis is applicable to viscous polymer solutions having high Prandtl numbers.

On Natural Convective Heat Transfer in Vertical Channels With a Single Surface Mounted Heat-Flux Module

2003 ◽  
Vol 125 (4) ◽  
pp. 734-739 ◽  
Author(s):  
G. Desrayaud ◽  
A. Fichera
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Flow Characteristics ◽  
Vertical Channel ◽  
Numerical Data ◽  
Two Dimensional ◽  
Electronic Components ◽  
Adiabatic Wall ◽  
Numerical Predictions ◽  
Fluid Flow Characteristics

This paper presents the numerical predictions of heat transfer and fluid flow characteristics for natural convection in a vertical channel with two-dimensional protruding heat-flux module as applied to the cooling of electronic components. The investigation is for a configuration consisting of a single module mounted on a vertical adiabatic wall. An attempt was made to combine the temperature of the module for all the dimensions of the module into a single composite correlation, along with the numerical data.

Linear stability and energetics of rotating radial horizontal convection

2016 ◽  
Vol 795 ◽  
pp. 1-35 ◽  
Author(s):  
Gregory J. Sheard ◽  
Wisam K. Hussam ◽  
Tzekih Tsai
Keyword(s):  
Boundary Layer ◽  
Potential Energy ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Baroclinic Instability ◽  
Mean Flow ◽  
Thermal Boundary Layer Thickness ◽  
Available Potential Energy ◽  
Horizontal Convection ◽  
The Mean

The effect of rotation on horizontal convection in a cylindrical enclosure is investigated numerically. The thermal forcing is applied radially on the bottom boundary from the coincident axes of rotation and geometric symmetry of the enclosure. First, a spectral element method is used to obtain axisymmetric basic flow solutions to the time-dependent incompressible Navier–Stokes equations coupled via a Boussinesq approximation to a thermal transport equation for temperature. Solutions are obtained primarily at Rayleigh number $\mathit{Ra}=10^{9}$ and rotation parameters up to $Q=60$ (where $Q$ is a non-dimensional ratio between thermal boundary layer thickness and Ekman layer depth) at a fixed Prandtl number $\mathit{Pr}=6.14$ representative of water and enclosure height-to-radius ratio $H/R=0.4$. The axisymmetric solutions are consistently steady state at these parameters, and transition from a regime unaffected by rotation to an intermediate regime occurs at $Q\approx 1$ in which variation in thermal boundary layer thickness and Nusselt number are shown to be governed by a scaling proposed by Stern (1975, Ocean Circulation Physics. Academic). In this regime an increase in $Q$ sees the flow accumulate available potential energy and more strongly satisfy an inviscid change in potential energy criterion for baroclinic instability. At the strongest $Q$ the flow is dominated by rotation, accumulation of available potential energy ceases and horizontal convection is suppressed. A linear stability analysis reveals several instability mode branches, with dominant wavenumbers typically scaling with $Q$. Analysis of contributing terms of an azimuthally averaged perturbation kinetic energy equation applied to instability eigenmodes reveals that energy production by shear in the axisymmetric mean flow is negligible relative to that produced by conversion of available potential energy from the mean flow. An evolution equation for the quantity that facilitates this exchange, the vertical advective buoyancy flux, reveals that a baroclinic instability mechanism dominates over $5\lesssim Q\lesssim 30$, whereas stronger and weaker rotations are destabilised by vertical thermal gradients in the mean flow.

Time-Resolved Thermal Boundary-Layer Structure in a Pulsatile Reversing Channel Flow

2001 ◽  
Vol 123 (4) ◽  
pp. 655-664 ◽  
Author(s):  
Sean P. Kearney ◽  
Anthony M. Jacobi ◽  
Robert P. Lucht
Keyword(s):  
Boundary Layer ◽  
Channel Flow ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Layer Structure ◽  
Laminar Regime ◽  
Thermal Boundary Layer Thickness ◽  
Reversed Flow ◽  
Time Resolved ◽  
Primary Impact

In this paper, the results of an experimental study of the time-resolved structure of a thermal boundary layer in a pulsating channel flow are presented. The developing laminar regime is investigated. Two techniques were used for time-resolved temperature measurements: a nonintrusive, pure-rotational CARS method and cold-wire anemometry. Results are presented for differing degrees of flow reversal, and the data show that the primary impact of reversed flow is an increase in the instantaneous thermal boundary-layer thickness and a period of decreased instantaneous Nusselt number. For the developing laminar parameter space spanned by the experiments, time-averaged heat-transfer enhancements as high as a factor of two relative to steady flow are observed for nonreversing and partially reversed pulsating flows. It is concluded that reversal is not necessarily a requirement for enhancement.

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