Shape Change of an Initially Vertical Wall Undergoing Condensation-Driven Melting

1983 ◽  
Vol 105 (2) ◽  
pp. 235-240 ◽  
Author(s):  
K. Taghavi-Tafreshi ◽  
V. K. Dhir
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Numerical Solutions ◽  
Shape Change ◽  
Vertical Wall ◽  
Melting Rate ◽  
Vertical Surface ◽  
Saturated Steam ◽  
Atmosphere Pressure ◽  
The One

Condensation-driven melting of an initially vertical wall is studied both analytically and experimentally. It is shown that a vertical surface undergoing simultaneous melting-condensation will not stay vertical and will go through a series of transient shapes before attaining a steady-state shape. Numerical solutions are obtained both for the transient shapes of the wall and the heat transfer. The steady-state shape of the wall is found to be the one which yields a constant melting rate along the wall. The total melting rate is shown to increase during the time the shape change occurs such that the steady-state shape yields about 35 percent more melting rate than the initial vertical wall. Experiments are conducted at one atmosphere pressure by condensing saturated steam on vertical surfaces of slabs made of naphthalene, biphenyl, and stearic acid. The heat transfer and shape change data are found to compare well with the predictions.

Verification of Finite Volume Computations on Steady-State Fluid Flow and Heat Transfer

2001 ◽  
Vol 124 (1) ◽  
pp. 11-21 ◽  
Author(s):  
J. Cadafalch ◽  
C. D. Pe´rez-Segarra ◽  
R. Co`nsul ◽  
A. Oliva
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Steady State ◽  
Finite Volume ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Independent Solution ◽  
Post Processing ◽  
Square Duct ◽  
Flow And Heat Transfer

This work presents a post-processing tool for the verification of steady-state fluid flow and heat transfer finite volume computations. It is based both on the generalized Richardson extrapolation and the Grid Convergence Index GCI. The observed order of accuracy and a error band where the grid independent solution is expected to be contained are estimated. The results corresponding to the following two and three-dimensional steady-state simulations are post-processed: a flow inside a cavity with moving top wall, an axisymmetric turbulent flow through a compressor valve, a premixed methane/air laminar flat flame on a perforated burner, and the heat transfer from an isothermal cylinder enclosed by a square duct. Discussion is carried out about the certainty of the estimators obtained with the post-processing procedure. They have been shown to be useful parameters in order to assess credibility and quality to the reported numerical solutions.

Analysis of a Transient Asymmetrically Heated/Cooled Open Thermosyphon

1993 ◽  
Vol 115 (3) ◽  
pp. 621-630 ◽  
Author(s):  
G. F. Jones ◽  
J. Cai
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Vertical Plate ◽  
Numerical Study ◽  
Vertical Wall ◽  
Constant Heat Flux ◽  
Closed Form Expression ◽  
Transient Temperature ◽  
Large Reservoir ◽  
One Dimensional

We present a numerical study of transient natural convection in a rectangular open thermosyphon having asymmetric thermal boundary conditions. One vertical wall of the thermosyphon is either heated by constant heat flux (“warmup”) or cooled by convection to the surroundings (“cooldown”). The top of the thermosyphon is open to a large reservoir of fluid at constant temperature. The vorticity, energy, and stream-function equations are solved by finite differences on graded mesh. The ADI method and iteration with overrelaxation are used. We find that the thermosyphon performs quite differently during cooldown compared with warmup. In cooldown, flows are mainly confined to the thermosyphon with little momentum and heat exchange with the reservoir. For warmup, the circulation resembles that for a symmetrically heated thermosyphon where there is a large exchange with the reservoir. The difference is explained by the temperature distributions. For cooldown, the fluid becomes stratified and the resulting stability reduces motion. In contrast, the transient temperature for warmup does not become stratified but generally exhibits the behavior of a uniformly heated vertical plate. For cooldown and Ra > 104, time-dependent heat transfer is predicted by a closed-form expression for one-dimensional conduction, which shows that Nu → Bi1/2/A in the steady-state limit. For warmup, transient heat transfer behaves as one-dimensional conduction for early times and at steady state and for Ra* ≥ 105, can be approximated as that for a uniformly heated vertical plate.

scholarly journals Unsteady/Steady Hydromagnetic Convective Flow between Two Vertical Walls in the Presence of Variable Thermal Conductivity

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
M. M. Hamza ◽  
I. G. Usman ◽  
A. Sule
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Skin Friction ◽  
Numerical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Vertical Channel ◽  
Approximate Solutions ◽  
Variable Thermal Conductivity ◽  
Convection Flow

Unsteady as well as steady natural convection flow in a vertical channel in the presence of uniform magnetic field applied normal to the flow region and temperature dependent variable thermal conductivity is studied. The nonlinear partial differential equations governing the flow have been solved numerically using unconditionally stable and convergent semi-implicit finite difference scheme. For steady case, approximate solutions have been derived for velocity, temperature, skin friction, and the rate of heat transfer using perturbation series method. Results of the computations for velocity, temperature, skin friction, and the rate of heat transfer are presented graphically and discussed quantitatively for various parameters embedded in the problem. An excellent agreement was found during the numerical computations between the steady-state approximate solutions and unsteady numerical solutions at steady-state time. In addition, comparison with previously published work is performed and the results agree well.

scholarly journals A Simplified Technique for Thermal Analysis of a Fenestration system with a Venetian Blind

2021 ◽  
Author(s):  
Hidayat Ullah Shahid
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Thermal Performance ◽  
Approximate Model ◽  
Vertical Surface ◽  
Shading Devices ◽  
The One ◽  
The Impact ◽  
Venetian Blind

A simplified 1-D numerical model of a window and horizontal Venetian blind assembly has been developed. This model provides a realistic estimate of the advantage of using blinds to control the window heat gain or loss. The free convective heat transfer rate from an isothermal vertical surface adjacent to a set of horizontal louvres has been studied numerically. This configuration is an approximate model of an indoor window glazing with a Venetian-type blind. Knowledge of the effect of blinds on the free convection at the indoor window surface is important for understanding and predicting the impact of shading devices on the overall thermal performance of a window. The convective heat transfer results are used in the one-dimensional model of the complete fenestration system to study the effect on key performance parameters. The results show that louvred blinds can have a significant beneficial effect on window thermal performance.

scholarly journals Thermal-hydraulic modeling of the steady-state operating conditions of a fire-tube boiler

2009 ◽  
Vol 24 (1) ◽  
pp. 29-37 ◽  
Author(s):  
Ahmed Rahmani ◽  
Ahmed Dahia
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Hydraulic Modeling ◽  
Sensitivity Study ◽  
Operating Conditions ◽  
Saturated Steam ◽  
Operating Pressure ◽  
Operating Data ◽  
Boiler Operation ◽  
Calculation Results

In this work, we are interested to simulate the thermal-hydraulic behavior of three-pass type fire-tube boiler. The plant is designed to produce 4.5 tons per hour of saturated steam at 8 bar destined principally for heating applications. A calculation program is developed in order to simulate the boiler operation under several steady-state operating conditions. This program is based upon heat transfer laws between hot gases and the fire-tube internal walls. In the boiler combustion chamber, the heat transfer has been simulated using the well-stirred furnace model. In the convection section, heat balance has been carried out to estimate the heat exchanges between the hot gases and the tube banks. The obtained results are compared to the steady-state operating data of the considered plant. A comparative analysis shows that the calculation results are in good agreement with the boiler operating data. Furthermore, a sensitivity study has been carried out to assess the effects of input parameters, namely the fuel flow rate, air excess, ambient temperature, and operating pressure, upon the boiler thermal performances.

Two-Dimensional Analysis of Conduction-Controlled Rewetting With Precursory Cooling

1976 ◽  
Vol 98 (3) ◽  
pp. 407-413 ◽  
Author(s):  
S. S. Dua ◽  
C. L. Tien
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Dimensional Analysis ◽  
Vertical Surface ◽  
Dimensionless Temperature ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
One Dimensional ◽  
The One

This paper presents a two-dimensional analysis of the effect of precursory cooling on conduction-controlled rewetting of a vertical surface, whose initial temperature is higher than the sputtering temperature. Precursory cooling refers to the cooling caused by the droplet-vapor mixture in the region immediately ahead of the wet front, and is described mathematically by two dimensionless constants which characterize its magnitude and the region of influence. The physical model developed to account for precursory cooling consists of an infinitely extended vertical surface with the dry region ahead of the wet front characterized by an exponentially decaying heat flux and the wet region behind the moving film-front associated with a constant heat transfer coefficient. Apart from the two dimensionless constants describing the extent of precursory cooling, the physical problem is characterized by three dimensionless groups: the Peclet number or the dimensionless wetting velocity, the Biot number and a dimensionless temperature. Limiting solutions for large and small Peclet numbers have been obtained utilizing the Wiener-Hopf technique coupled with appropriate kernel substitutions. A semiempirical matching relation is then devised for the entire range of Peclet numbers. Existing experimental data with variable flow rates at atmospheric pressure are very closely correlated by the present model. Finally a comparison is drawn between the one-dimensional limit of the present analysis and the corresponding one-dimensional solution obtained by treating the dry region ahead of the wet front characterized by an exponentially decaying heat transfer coefficient.

Analytical and Experimental Investigation of Simultaneous Melting-Condensation on a Vertical Wall

1982 ◽  
Vol 104 (1) ◽  
pp. 24-33 ◽  
Author(s):  
K. Taghavi-Tafreshi ◽  
V. K. Dhir
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Saturated Vapor ◽  
Vertical Wall ◽  
Saturated Steam ◽  
Interface Temperature ◽  
Boundary Layer Equations ◽  
Similarity Transformations ◽  
High Prandtl Number ◽  
Variable Gravity

Melting of a vertical wall as a result of condensation of saturated vapor is investigated both analytically and experimentally. Employing similarity transformations, full boundary layer equations governing laminar films of melt and condensate are solved numerically for high Prandtl number liquids. Numerical results for the melting and condensation heat transfer and for the melt-condensate interface temperature are obtained. Experiments are conducted by condensing saturated steam on vertical surfaces of slabs made of naphthalene, biphenyl and stearic acid. The data are found to compare well with the predictions. The analysis is extended to condensation on melting surfaces with shapes yielding variable gravity in the direction of flow.

Transition of transient vertical natural-convection flows in water

1987 ◽  
Vol 179 ◽  
pp. 407-438 ◽  
Author(s):  
Yogendra Joshi ◽  
Benjamin Gebhart
Keyword(s):  
Steady State ◽  
Natural Convection ◽  
Energy Input ◽  
Fluid Layer ◽  
High Surface ◽  
Leading Edge ◽  
Vertical Surface ◽  
Steady Flows ◽  
Wide Range ◽  
The One

Experimental results and interpretations are given for transient natural convection adjacent to a suddenly heated flat vertical surface in quiescent water. The 1.24 m high surface resulted in laminar, transition and turbulent regimes downstream, in transients and in steady state, over a wide range of surface-energy input rates. Flows were visualized and velocity and temperature measurements made at various downstream locations, after imposing a uniform internal-energy generation rate within the very thin surface. Upflow development from quiescence to steady state was found to depend strongly on the downstream location x and imposed input heat flux. Laminar flow persisted into steady state, for short downstream distances. Further downstream, the flow became turbulent during the transient. Relaminarization at later time occurred only for lower flux inputs. Local measurements across the fluid layer show that the transient disturbances close to the leading edge of the surface are confined to within the final steady boundary layer. Downstream, they extend much further into the ambient. First disturbances always arose before the leading-edge-effect propagation estimates. The trend of data was in agreement with theory for a non-dimensional time τ < 85. For larger τ, turbulence instead terminated the one-dimensional transport regime simultaneously, at all downstream locations. This single value of τ also amounts to a single value of the non-dimensional thermal energy of the flow, ETT = 19.7. Disturbance frequency data early in the transient suggest the presence of a strongly selective amplification mechanism, very similar to that found in steady flows. The non-dimensional times at which local steady state was achieved were best correlated by a Fourier number, over a wide range of energy input conditions. Turbulence arising during the transient enhances the thermal transport significantly. Local convection coefficients then were found to be as much as 40% higher than the eventual steady values.

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