Steady Temperature in a Rotating Cylinder Subject to Surface Heating and Convective Cooling

1984 ◽  
Vol 106 (1) ◽  
pp. 120-126 ◽  
Author(s):  
B. Gecim ◽  
W. O. Winer
Keyword(s):  
Heat Source ◽  
Peclet Number ◽  
High Speed ◽  
Integral Transform ◽  
The Body ◽  
Cooling Zone ◽  
Dimensionless Numbers ◽  
Péclet Number ◽  
Heating And Cooling ◽  
Simultaneous Heating

This study utilizes an integral transform technique in order to solve the heat conduction equation in cylindrical coordinates. The major assumption is the high speed (i.e., large Peclet number) assumption. The boundary value problem is governed by the parabolic form of the heat equation representing the quasi-stationary state. The boundary conditions are a combination of Neumann and mixed type due to simultaneous heating and cooling on the surface of the cylinder. The surface temperature reaches a peak value over the heat source and gradually decreases to a nearly constant level over the cooling zone. Thermal penetration in the radial direction is shown to be only a few percent of the radius, leaving the bulk of the body at a uniform temperature. The width of the heat source and the total heat input are shown to be effective on the level of temperature whereas the input distribution is shown to be unimportant. The dimensionless numbers involved are the Biot and the Peclet numbers where the solution is governed by the ratio of the Biot number to the square root of the Peclet number.

Temperature Rise at the Sliding Contact Interface for a Coated Semi-Infinite Body

1993 ◽  
Vol 115 (1) ◽  
pp. 1-9 ◽  
Author(s):  
X. Tian ◽  
F. E. Kennedy
Keyword(s):  
Surface Temperature ◽  
Temperature Rise ◽  
Peclet Number ◽  
Integral Transform ◽  
Sliding Contact ◽  
Contact Interface ◽  
Péclet Number ◽  
Maximum Surface ◽  
Semi Empirical ◽  
Maximum Surface Temperature

In this paper, a three-dimensional model of a semi-infinite layered body is used to predict steady-state maximum surface temperature rise at the sliding contact interface for the entire range of Peclet number. A set of semi-empirical solutions for maximum surface temperature problems of sliding layered bodies is obtained by using integral transform, finite element, heuristic and multivariable regression techniques. Two dimensionless parameters, A and Dp, which relate to coating thickness, contact size, sliding speed and thermal properties of both coating and substrate materials, are found to be the critical factors determining the effect of surface film on the surface temperature rise at a sliding contact interface. A semi-empirical solution for maximum surface temperature problems of homogeneous bodies, which covers the whole range of Peclet number, is also obtained.

Effect of a Surface Film on the Surface Temperature of a Rotating Cylinder

1986 ◽  
Vol 108 (1) ◽  
pp. 92-97 ◽  
Author(s):  
B. Gecim ◽  
W. O. Winer
Keyword(s):  
Thermal Properties ◽  
Heat Source ◽  
Film Thickness ◽  
Surface Temperature ◽  
Temperature Rise ◽  
High Speed ◽  
Integral Transform ◽  
Heat Conduction Problem ◽  
Surface Film ◽  
Layer Effect

Solution to the steady heat conduction problem of a rotating layered cylinder is presented. The governing differential equations (for the film and the substrate) are solved by using an integral transform technique. It is shown that the presence of a surface film measured in micrometers can substantially change the level of the surface temperature. The effect of the surface film on the surface temperature depends on: respective thermal properties of the film and the substrate; relative surface speed; heat source (contact) size; and surface film thickness. However, the range in which the effect of the film on the surface temperature is dependent on these parameters is limited. Outside this range (i.e., thin film/low speed or thick film/high speed) the surface temperature rise is determined by the thermal properties of the substrate, or by the properties of the film alone, respectively. Hence, outside this range, a further change in the film thickness does not influence the surface temperature rise. Dimensionless plots showing the change in surface temperature rise as a function of material thermal properties, surface speed, heat source size, and film thickness are presented. Behavior for specific material combinations are also presented. The present information can be utilized to predict the layer effect on the partition of heat between the layered cylinders.

Thermal Response of Rolling Components Under Mixed Boundary Conditions: An Analytical Approach

1993 ◽  
Vol 115 (4) ◽  
pp. 857-865 ◽  
Author(s):  
P. Ulysse ◽  
M. M. Khonsari
Keyword(s):  
Temperature Distribution ◽  
Peclet Number ◽  
Integral Transform ◽  
Mixed Boundary ◽  
Order Approximation ◽  
Thermal Response ◽  
Fourier Integral ◽  
Cylinder Surface ◽  
Péclet Number ◽  
Special Cases

An analytical solution for the steady-state temperature distribution in a cylinder undergoing uniform heating and nonuniform cooling is presented. The method of solution is a Fourier integral transform technique. The analysis shows that the Neumann series resulting from an integral equation can be well represented by a first-order approximation when the Peclet number is large. Furthermore, it is shown that the ratio of the Biot number to the square root of the Peclet number of the cooling zones is found to play an important role in governing the thermal response of the cylinder surface. The predicted results for the circumferential temperature distribution are compared to published experimental measurements for hot rolling and also existing analytical solutions for special cases. The agreement is found to be very good. By an appropriate superposition technique, the analysis presented may be easily extended to various heat sources and convective cooling zones at different locations of the cylinder surface.

Effect of Peclet Number in Thermo-Mechanical Cracking Due to High-Speed Friction Load

1988 ◽  
Vol 110 (2) ◽  
pp. 217-221 ◽  
Author(s):  
F. D. Ju ◽  
J. C. Liu
Keyword(s):  
Tensile Stress ◽  
Peclet Number ◽  
High Speed ◽  
Property Values ◽  
Critical Depth ◽  
Two Dimensional ◽  
Péclet Number ◽  
Parametric Effects ◽  
The Relationship ◽  
Thermal Tensile Stress

The present paper discussed the critical depth, i.e., the depth at which the thermal tensile stress reaches a maximum, caused by the frictional excitation of a fast moving asperity. In the study, the critical depth was computed directly by maximizing the thermal tensile stress with respect to positions under the asperity inside the material. The relationship between critical depth and Peclet number for all materials in the two-dimensional formulation may be simplified to satisfy the exponential form R(ηcr)2.275=20.4368. Stellite III was chosen as the indicator material. Other parametric effects including mechanical properties and thermal properties were tested with materials having diverse property values. These tests confirmed that for the two-dimensional formulation, the Peclet number is the only one which dominates the critical depth.

scholarly journals Energy Savings of Simultaneous Heating and Cooling System According to Indoor Set Temperature Changes in the Comfort Range

Energies ◽  
2021 ◽  
Vol 14 (22) ◽  
pp. 7691
Author(s):  
Dae-Uk Shin ◽  
Chang-Ho Jeong
Keyword(s):  
Heat Source ◽  
Energy Savings ◽  
Cooling System ◽  
Coefficient Of Performance ◽  
Energy Limit ◽  
Temperature Changes ◽  
Heating And Cooling ◽  
Small Load ◽  
Simultaneous Heating ◽  
Simultaneous Heating And Cooling

This study was conducted to derive the amount of energy savings when applying the method of making the load similar by changing the set temperature of the room in the building to which the simultaneous heating and cooling (SHC) system is applied. Energy savings were derived through theoretical analysis and comparisons through static simulations were performed to verify the proposed method. As a result, the energy savings are proportional to the energy limit that can be additionally input to the SHC and is proportional to the ratio of the coefficient of performance (COP) difference between the SHC and auxiliary heat source and the auxiliary heat source COP. That is, to increase the amount of energy savings, the maximum possible energy should be input for the SHC, or the SHC COP must be greater than the auxiliary heat source COP. In addition, comfort can be achieved stably by varying the set room temperature in a room with a small load. When a heat storage tank is installed or changing the indoor set temperature of both the hot and cold zones in real time by predicting the indoor load is possible, more energy can be saved.

Approximate solutions for developing shear dispersion with exchange between phases

1998 ◽  
Vol 374 ◽  
pp. 195-219 ◽  
Author(s):  
C. G. PHILLIPS ◽  
S. R. KAYE
Keyword(s):  
Peclet Number ◽  
Gaussian Approximation ◽  
Formal Solution ◽  
Fluid Phase ◽  
Approximate Solutions ◽  
Wall Layer ◽  
Dimensionless Numbers ◽  
Order Unity ◽  
Péclet Number ◽  
Shear Dispersion

We consider the transport of a tracer substance in Poiseuille flow through a pipe lined with a thin, fixed wall layer in which the tracer is soluble. A formal solution is given for the variation of concentration with time at a fixed downstream position following an initial release of tracer. Asymptotic approximations are derived assuming that: (i) the Péclet number is large; (ii) the time scale for diffusion across the wall layer is much larger than that for diffusion across the fluid phase and (iii) the dimensionless distance downstream of the point of release, z, is large. This means that the transverse concentration variation is small within the fluid phase, so that transport is dominated by the exchange of tracer between the phases and radial diffusion within the wall layer. The character of the concentration transient is found to be determined by two dimensionless numbers, an absorption parameter κ and an effective wall layer thickness ν (both rescaled to take account of the ratio of diffusivities in the two phases); by assumption (ii), ν is large. Several different regimes are possible, according to the values of κ, ν and z. At sufficiently large distances, a Gaussian approximation, analogous to Taylor's solution, is applicable. At intermediate distances, provided κ is not too large, a highly skewed transient is predicted. If κ is small, there exists another region further upstream where the effect of the wall is negligible, and Taylor's Gaussian approximation applies. More complicated behaviour occurs in the zones of transition between these three regions. The behaviour described is expected to be typical of a range of similar systems. In particular, it may be shown that the basic form of the skewed approximation is insensitive to the geometry of the system, and also applies when the Péclet number is of order unity.

Mixed Convection in a Liquid-Saturated Porous Medium

1988 ◽  
Vol 110 (1) ◽  
pp. 147-154 ◽  
Author(s):  
D. C. Reda
Keyword(s):  
Porous Medium ◽  
Heat Source ◽  
Mixed Convection ◽  
Peclet Number ◽  
Saturated Porous Medium ◽  
Fluid Motion ◽  
Power Input ◽  
Péclet Number ◽  
Thermal Fields ◽  
Pressure Driven

An experimental and numerical investigation of mixed convection phenomena about a finite-length, vertical, cylindrical heat source in a uniform, liquid-saturated, porous medium was conducted. Buoyancy-induced upflow about the heat source was systematically altered by the superposition of vertical, pressure-driven flows which opposed the buoyancy-induced fluid motion. The evolution of the mixed convection velocity and thermal fields with increasing magnitude of the imposed-flow Peclet number are reported. The ratio of the natural convection Rayleigh number Ra to the imposed-flow Peclet number Pe is shown to be the nondimensional parameter that characterizes the relative influence of buoyancy-induced to pressure-driven fluid motion. Using total disappearance of buoyancy-induced upflow as the criterion, the transition from mixed to forced convection, for opposing flows, is numerically predicted to occur for |Ra/Pe| ≈ 1/2, independent of the heat source length or power input.

A Parametric Study of the Quasi-Steady State Temperature Field by a Moving Heat Source for Surface Treating

2000 ◽  
Author(s):  
Nicola Bianco ◽  
Oronzio Manca
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Heat Source ◽  
Peclet Number ◽  
Three Dimensional ◽  
Laser Source ◽  
Quasi Steady State ◽  
Péclet Number ◽  
Spot Center ◽  
Laser Heat Source

Abstract A three dimensional numerical analysis of a solid irradiated by a moving laser heat source in a quasi-steady state is carried out. The thermophysical properties of the material are considered to be temperature dependent. The dependence of the solution on the radiative and convective heat losses, the latter due to an impinging jet on the upper surface, is highlighted; the dependence of the temperature distribution on the Reynolds number of the jet is also presented. Different thicknesses and widths are shown to have discrepant influences on the induced thermal fields for a Gaussian laser source. The parametric analysis shows the thermal profiles to be strongly dependent on the jet Reynolds number. The thermal field is almost symmetric with respect to the spot center for a Peclet number equal to 0.1. The thermal penetration decreases as the Peclet number increases.

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