Low Knudsen Number Heat Transfer From Two Spheres in Contact

1974 ◽  
Vol 96 (4) ◽  
pp. 478-482 ◽  
Author(s):  
F. A. Morrison ◽  
L. D. Reed
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Knudsen Number ◽  
Peclet Number ◽  
Temperature Jump ◽  
Péclet Number

Heat transfer from an acrosol aggregate composed of two touching spheres is investigated analytically. In the range of interest, the Knudsen number is small and the Peclet number negligible. The Nusselt number of a sphere is found to be reduced by the presence of a neighbor and by temperature jump. Expressions for the Nusselt number are obtained.

Rarefaction, Temperature Jump, and Viscous Dissipation Effects on Heat Transfer in Rotating Micro Devices

2006 ◽  
Author(s):  
Latif M. Jiji
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Viscous Dissipation ◽  
Knudsen Number ◽  
Temperature Jump ◽  
Slip Flow ◽  
Fluid Temperature ◽  
Rotating Shaft ◽  
Number Range ◽  
Rotating Surface

This paper examines the effects of rarefaction and dissipation on flow and heat transfer characteristics in rotating micro devices. The housing is assumed to be at uniform temperature while the rotating surface is insulated. Thus heat generation and transfer are due to viscous dissipation only. An analytic solution is obtained for the velocity and temperature distribution in the gas filled concentric clearance between a rotating shaft and its stationary housing. The solution is valid in the slip flow and temperature jump domain defined by the Knudsen number range of Kn < 0.1. The Nusselt number was found to depend on three parameters: the Knudsen number Kn, ratio of housing to shaft radius ro / ri, and Prandtl number-specific heat ratio group γ/(γ + 1) Pr. Results indicate that curvature and Knudsen number have significant effect on the Nusselt number. However, fluid temperature rise due to dissipation is negligible.

scholarly journals Heat transfer from a moving fluid sphere with internal heat generation

2014 ◽  
Vol 18 (4) ◽  
pp. 1213-1222
Author(s):  
Silvia Alexandrova ◽  
Maria Karsheva ◽  
Abdellah Saboni ◽  
Christophe Gourdon
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Heat Generation ◽  
Peclet Number ◽  
Average Nusselt Number ◽  
Viscosity Ratio ◽  
Fluid Sphere ◽  
Péclet Number ◽  
Convection Equation

In this work, we solve numerically the unsteady conduction-convection equation including heat generation inside a fluid sphere. The results of a numerical study in which the Nusselt numbers from a spherical fluid volume were computed for different ranges of Reynolds number (0<Re<100), Peclet number (0<Pe<10000) and viscosity ratio (0<k<10), are presented. For a circulating drop with Re?0, steady creeping flow is assumed around and inside the sphere. In this case, the average temperatures computed from our numerical analysis are compared with those from literature and a very good agreement is found. For higher Reynolds number (0<Re<100), the Navier-Stokes equations are solved inside and outside the fluid sphere as well as the unsteady conduction-convection equation including heat generation inside the fluid sphere. It is proved that the viscosity ratio k (k = ?d/?c) influences significantly the heat transfer from the sphere. The average Nusselt number decreases with increasing k for a fixed Peclet number and a given Reynolds number. It is also observed that the average Nusselt number is increasing as Peclet number increases for a fixed Re and a fixed k.

Effect of Plate Characteristics on Axial Dispersion and Heat Transfer in Plate Heat Exchangers

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
K. Shaji ◽  
Sarit K. Das
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Exchangers ◽  
Peclet Number ◽  
Axial Dispersion ◽  
Outlet Temperature ◽  
Plate Heat ◽  
Péclet Number ◽  
Back Mixing ◽  
Two Fluid

A new mathematical model of single-blow transient testing technique is proposed for the determination of heat transfer and dispersion coefficients in plate heat exchangers (PHEs) in which the flow maldisrtibution effects are separated from the fluid back-mixing. The fluid axial dispersion is used to characterize the back-mixing and other deviations from plug flow. Single-blow experiments are carried out with different number of plates for various flow rates with three different plate geometries of 30 deg, 60 deg, and mixed (30 deg/60 deg) chevron angles. The outlet temperature response to an exponential inlet temperature variation is solved numerically using finite difference method. In the present work, the whole curve matching technique is used to determine the values of Nusselt number and dispersive Peclet number. Since the maldistribution effects are separated, these data are independent of test conditions and hence using a regression analysis, general correlations are developed for Nusselt number and Peclet number of the present plate heat exchangers. The applicability of the single-blow test data is validated using a two-fluid experiment. Two-fluid experiments are conducted on the same plate heat exchanger with smaller and larger number of plates and the results have been compared with its simulation which used the Nusselt number and Peclet number correlations developed by the new model of single-blow test as the inputs.

Heat transfer at high Péclet number from a small sphere freely rotating in a simple shear field

1971 ◽  
Vol 46 (2) ◽  
pp. 233-240 ◽  
Author(s):  
Andreas Acrivos
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Simple Shear ◽  
Peclet Number ◽  
Reynolds Numbers ◽  
Small Sphere ◽  
Péclet Number ◽  
Shear Field ◽  
Method Of Solution ◽  
Small Shear

The problem of heat transfer at high Péclet number Pe from a sphere freely rotating in a simple shear field is considered theoretically for the case of small shear Reynolds numbers. It is shown that the present problem is in many respects similar to that of heat transfer past a freely rotating cylinder which was recently solved by Frankel & Acrivos (1968). By taking advantage of the close analogy between these two problems, an approximate method of solution is developed according to which the asymptotic Nusselt number for Pe → ∞ is 9, i.e. 4½ times its value for pure conduction. As in the corresponding case of the cylinder, the fact that the asymptotic Nusselt number is independent of Pe results from the presence of a region of closed streamlines which completely surrounds the rotating sphere.

scholarly journals HEAT EXCHANGE IN A PLANE CHANNEL IN A TURBULENT FLOW REGIME IN THE CASE OF SMALL VALUES OF PRANDTL NUMBER ACCORDING TO DATA OF DIRECT NUMERICAL SIMULATION

2021 ◽  
Vol 56 ◽  
pp. 57-60
Author(s):  
Yurii G. Chesnokov ◽  
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Prandtl Number ◽  
Direct Numerical Simulation ◽  
Transfer Process ◽  
Peclet Number ◽  
Plane Channel ◽  
Heat Transfer Process ◽  
Flat Channel ◽  
Péclet Number

Using the results obtained by the method of direct numerical simulation of the heat transfer process in a flat channel by various authors, it is shown that at small values of Prandtl number quite a few characteristics of the heat transfer process in a flat channel depend not on Reynolds and Prandtl numbers separately, but on Peclet number. Peclet number is calculated from the so-called dynamic speed

scholarly journals A Non-Newtonian Magnetohydrodynamics (MHD) Nanofluid Flow and Heat Transfer with Nonlinear Slip and Temperature Jump

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1199 ◽  
Author(s):  
Jing Zhu ◽  
Yaxin Xu ◽  
Xiang Han
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Temperature Jump ◽  
Thin Sheet ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Slip Condition ◽  
Physical Parameters ◽  
Nanofluid Flow ◽  
Flow And Heat Transfer

The velocity and thermal slip impacts on the magnetohydrodynamics (MHD) nanofluid flow and heat transfer through a stretched thin sheet are discussed in the paper. The no slip condition is substituted for a new slip condition consisting of higher-order slip and constitutive equation. Similarity transformation and Lie point symmetry are adopted to convert the derived governed equations to ordinary differential equations. An approximate analytical solution is gained through the homotopy analysis method. The impacts of velocity slip, temperature jump, and other physical parameters on flow and heat transfer are illustrated. Results indicate that the first-order slip and nonlinear slip parameters reduce the velocity boundary layer thickness and Nusselt number, whereas the effect on shear stress is converse. The temperature jump parameter causes a rise in the temperature, but a decline in the Nusselt number. With the increase of the order, we can get that the error reaches 10 − 6 from residual error curve. In addition, the velocity contours and the change of skin friction coefficient are computed through Ansys Fluent.

Numerical Analysis of Heat Transfer Enhancement in a Micro-Channel Due to Mechanical Stirrers

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
M. Sreejith ◽  
S. Chetan ◽  
S. N. Khaderi
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Transfer Enhancement ◽  
Peclet Number ◽  
Periodic Case ◽  
Two Dimensional ◽  
Transfer Enhancement ◽  
Fluidic Channel ◽  
Enhancement Of Heat Transfer ◽  
Péclet Number

Abstract Using two-dimensional numerical simulations of the momentum, mass, and energy conservation equations, we investigate the enhancement of heat transfer in a rectangular micro-fluidic channel. The fluid inside the channel is assumed to be stationary initially and actuated by the motion imparted by mechanical stirrers, which are attached to the bottom of the channel. Based on the direction of the oscillation of the stirrers, the boundary conditions can be classified as either no-slip (when the oscillation is perpendicular to the length of the channel) or periodic (when the oscillation is along the length of the channel). The heat transfer enhancement due to the motion of the stirrers (with respect to the stationary stirrer situation) is analyzed in terms of the Reynolds number (ranging from 0.7 to 1000) and the Peclet number (ranging from 10 to 100). We find that the heat transfer first increases and then decreases with an increase in the Reynolds number for any given Peclet number. The heat transferred is maximum at a Reynolds number of 20 for the no-slip case and at a Reynolds number of 40 for the periodic case. For a given Peclet and Reynolds number, the heat flux for the periodic case is always larger than the no-slip case. We explain the reason for these trends using time-averaged flow velocity profiles induced by the oscillation of the mechanical stirrers.

Investigation of Heat Transfer Over a Rotating Disk in Case of Temperature and Velocity Jump Conditions by Using Differential Transform Method

2010 ◽  
Author(s):  
A. Y. Gunes ◽  
G. Komurgoz ◽  
A. Arikoglu ◽  
I. Ozkol
Keyword(s):  
Heat Transfer ◽  
Knudsen Number ◽  
Temperature Jump ◽  
Velocity Slip ◽  
Rotating Disk ◽  
Jump Conditions ◽  
Governing Equations ◽  
Transform Method ◽  
Differential Transform ◽  
Velocity Jump

The energy crisis in the last two decades has turned the attention of scientific and engineering communities to redesigned and developed heat-fluid interaction systems. All of the details in analyses are reconsidered to reduce energy consumption. The present work examines the effects of temperature and velocity jump conditions on heat transfer, fluid flow over a single rotating disk. The flow due to rotating disks is of great interest in thermal engineering as it appears in many industrial and engineering applications such as gas turbine engines and micropumps. The related equation of flow, which is nonlinear and coupled, and heat transfer governing equations are reduced to ordinary differential equations by applying the so-called classical approach which was first introduced by Von Karman. Instead of this approach, a pure numerical one, the recently developed popular semi numerical analytical technique differential transform method (DTM), with Benton transformation, is employed to solve the reduced governing equations under the assumptions of velocity-slip and temperature jump conditions on the disk surface. The solution is valid for continuum and slip-flow regime which has a Knudsen number smaller than 0.1. The results attained for various physical cases are interpreted by using non-dimensional parameters related to flow and temperature fields. Velocity and temperature profiles are presented graphically. The effect of various parameters such as the Knudsen Number (Kn), Reynolds Number (Re) and Nusselt Numbers (Nu) are examined. The observed physical consequences are the velocity slip and temperature jump at the wall becoming strongly dependant on the Knudsen number. It is also observed that the temperature jump and velocity jump conditions have nonlinear effects on slip; these effects are investigated with great details and presented graphically.

Effect of Rarefaction, Dissipation, and Accommodation Coefficients on Heat Transfer in Microcylindrical Couette Flow

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Latif M. Jiji
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Temperature Distribution ◽  
Couette Flow ◽  
Knudsen Number ◽  
Slip Flow ◽  
Accommodation Coefficient ◽  
Rotating Shaft ◽  
Number Range ◽  
Accommodation Coefficients

This paper examines the effects of rarefaction, dissipation, curvature, and accommodation coefficients on flow and heat transfer characteristics in rotating microdevices. The problem is modeled as a cylindrical Couette flow with a rotating shaft and stationary housing. The housing is maintained at uniform temperature while the rotating shaft is insulated. Thus, heat transfer is due to viscous dissipation only. An analytic solution is obtained for the temperature distribution in the gas filled concentric clearance between the rotating shaft and its stationary housing. The solution is valid in the slip flow and temperature jump domain defined by the Knudsen number range of 0.001<Kn<0.1. The important effect of the momentum accommodation coefficient on velocity reversal and its impact on heat transfer is determined. The Nusselt number was found to depend on four parameters: the momentum accommodation coefficient of the stationary surface σuo, Knudsen number Kn, ratio of housing to shaft radius ro∕ri, and the dimensionless group [γ∕(γ+1)](2σto−1)∕(σtoPr). Results indicate that curvature, Knudsen number, and the accommodation coefficients have significant effects on temperature distribution, heat transfer, and Nusselt number.

Heat Transfer From a Translating Droplet at High Peclet Numbers: Revisiting the Classic Solution of Kronig & Brink

2005 ◽  
Vol 128 (7) ◽  
pp. 648-652 ◽  
Author(s):  
Douglas L. Oliver ◽  
Adham W. Souccar
Keyword(s):  
Heat Transfer ◽  
Peclet Number ◽  
Numerical Techniques ◽  
Droplet Transfer ◽  
Péclet Number ◽  
Classic Solution ◽  
Droplet Phase

More than five decades ago Kronig and Brink published a classic analysis of transport from translating droplets. Their analysis assumed that the bulk of the resistance to transfer was in the droplet phase. It considered the limiting solution as the Peclet number became very large. Their work has been cited in many subsequent studies of droplet transfer. The present work revisits their solution using numerical techniques that were not then available. It was found that only the first mode of their solution is mathematically accurate. Hence, their solution is accurate only at large times.

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