An Experimental and Analytical Study of Close-Contact Melting

1986 ◽  
Vol 108 (4) ◽  
pp. 894-899 ◽  
Author(s):  
M. K. Moallemi ◽  
B. W. Webb ◽  
R. Viskanta
Keyword(s):  
Approximate Solution ◽  
Surface Temperature ◽  
Cross Section ◽  
Analytical Study ◽  
Close Contact ◽  
Rectangular Cross Section ◽  
Melting Rate ◽  
Contact Melting ◽  
Series Of Experiments ◽  
Convection Dominated

Close-contact melting was investigated by performing a series of experiments in which blocks of solid n-octadecane (with circular or rectangular cross section) were melted by a horizontal planar heat source at constant surface temperature. Close contact between the source and the solid prevailed throughout the experiments by permitting the uncontained solid to descend under its own weight while squeezing the melt out of the gap separating it from the source. The velocity of the solid was measured and is reported as a function of the instantaneous weight of the solid. Effects of the surface temperature of the source and radius of the solid on its temporal velocity are also reported. A closed-form approximate solution is developed for the motion of solid and predictions are compared with the experimental data. The results for the solid velocity are correlated in terms of the governing parameters of the problem as revealed by the approximate solution. Compared with natural convection-dominated melting from below (solid confined and contained in a rectangular cavity) close contact gives rise to approximately a sevenfold increase in the melting rate of the solid.

scholarly journals On an approximate solution for the bending of a beam of rectangular cross-section under any system of load, with special reference to points of concentrated or discontinuous loading

1902 ◽  
Vol 70 (459-466) ◽  
pp. 491-496
Keyword(s):  
Approximate Solution ◽  
Special Reference ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Elastic Equilibrium ◽  
Elastic Solid ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Applied Stresses

The paper investigates the elastic equilibrium of a long bar of rectangular cross-section in those cases where the problem may be treated as one of two dimensions, namely:— ( a .) When the strain being in the plane of xy , the elastic solid extends indefinitely in the direction of the applied stresses over the bounding planes y = ± b , x = ± a being the same for any two sections parallel to the plane of xy . We then have a strictly two-dimensional strain.

scholarly journals WAVE TRANSMISSION THROUGH PERMEABLE BREAKWATERS

1972 ◽  
Vol 1 (13) ◽  
pp. 99 ◽  
Author(s):  
Charles K. Sollitt ◽  
Ralph H. Cross
Keyword(s):  
Approximate Solution ◽  
Boundary Conditions ◽  
Cross Section ◽  
Wave Breaking ◽  
Wave Reflection ◽  
Rectangular Cross Section ◽  
Wave Component ◽  
Additional Consideration ◽  
Reflection And Transmission ◽  
Theoretical Results

A theory is derived to predict ocean wave reflection and transmission at a permeable breakwater of rectangular cross section. The theory solves for a damped wave component within the breakwater and matches boundary conditions at the windward and leeward breakwater faces to predict the reflected and transmitted wave components. An approximate solution to conventional rubble mound breakwater designs is formulated in terms of an equivalent rectangular breakwater with an additional consideration for wave breaking. Experimental and theoretical results are compared and evaluated.

scholarly journals Numerical Investigation on the Evolution of Thin Liquid Layer and Dynamic Behavior of an Electro-Thermal Drilling Probe during Close-Contact Heat Transfer

2021 ◽  
Vol 11 (8) ◽  
pp. 3443
Author(s):  
Chan Ho Jeong ◽  
Kwangu Kang ◽  
Ui-Joon Park ◽  
Hyung Ju Lee ◽  
Hong Seok Kim ◽  
...  
Keyword(s):  
Liquid Layer ◽  
Close Contact ◽  
Melting Process ◽  
Transient Behavior ◽  
Liquid Films ◽  
Melting Rate ◽  
Contact Melting ◽  
Contact Heat ◽  
Navier Stokes Equation ◽  
Thermal Drilling

This study investigates the transient behavior of an electro-thermal drilling probe (ETDP) during a close-contact melting process within a glacier. In particular, the present work analyzes the effect of the tip temperature on the formation of molten thin liquid films and the subsequent rate of penetration (ROP) through numerical simulation. We used the commercial code of ANSYS Fluent (v.17.2) to solve the Reynolds-averaged Navier–Stokes equation, together with an energy equation considering the solidification and melting model. The ROP of the drilling probe is determined based on the energy balance between the heating power and melting rate of ice. As the results, the ETDP penetrates the ice through a close-contact melting process. The molten liquid layer with less than 1 mm of thickness forms near the heated probe tip. In addition, the ROP increases with the heated temperature of the probe tip.

Close-contact melting on an isothermal surface with the inclusion of non-Newtonian effects

2019 ◽  
Vol 865 ◽  
pp. 720-742 ◽  
Author(s):  
Y. Kozak ◽  
Yi Zeng ◽  
Rabih M. Al Ghossein ◽  
J. M. Khodadadi ◽  
G. Ziskind
Keyword(s):  
Yield Stress ◽  
Layer Thickness ◽  
Close Contact ◽  
Melting Rate ◽  
Analytical Approximation ◽  
Contact Melting ◽  
Viscoplastic Fluid ◽  
Molten Layer ◽  
Isothermal Surface ◽  
Dimensionless Groups

The present study deals with a theoretical investigation of a close-contact melting (CCM) process involving a vertical cylinder on a horizontal isothermal surface, where the liquid phase is a non-Newtonian viscoplastic fluid that behaves according to the Bingham model. Accordingly, a new approach is formulated based on the thin layer approximation and different quasi-steady process assumptions. By analytical derivation, an algebraic equation that relates the molten layer thickness and the solid bulk height is developed. The problem is then solved numerically, coupled with another equation for the melting rate. The new model shows that as the yield stress increases the melting rate decreases and the molten layer thickness increases. It is found that under certain conditions, the model can be reduced to a form that allows an analytical solution. The approximate model predicts an exponential dependence of both the melt fraction and the molten layer thickness. Comparison between the numerical and analytical solutions shows that the analytical approximation provides an excellent estimation for sufficiently large values of the yield stress. Dimensional analysis, which is supported by the analytical model results, reveals the dimensionless groups that govern the problem. For the general case, the melt fraction is a function of two dimensionless groups. For the analytical approximation, it is shown that the melt fraction is governed by a single dimensionless group and that the molten layer thickness is governed by two dimensionless groups.

scholarly journals On an approximate solution for the bending of a beam of rectangular cross-section under any system of load.—additional note

1904 ◽  
Vol 72 (477-486) ◽  
pp. 391-393
Keyword(s):  
Approximate Solution ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Additional Note

My attention has lately been called by M. Flamant to certain discrepancies in some formulæ given by me in a paper recently published under the above title. On investigation I have found that a set of formulæ of the paper in question, namely, those of 41, contained several inaccuracies.

Close-Contact Melting Inside an Elliptical Cylinder

2000 ◽  
Vol 122 (4) ◽  
pp. 192-195 ◽  
Author(s):  
Sergei A. Fomin ◽  
Alexander V. Wilchinsky ◽  
Takeo S. Saitoh
Keyword(s):  
Mathematical Model ◽  
Thermal Energy ◽  
Close Contact ◽  
Energy Systems ◽  
Elliptic Cylinder ◽  
Melting Process ◽  
Melting Rate ◽  
Contact Melting ◽  
Approximate Mathematical Model ◽  
Characteristic Scales

An approximate mathematical model of contact melting in a horizontal elliptic cylinder is developed. The main characteristic scales and nondimensional parameters that describe the principal features of the melting process are found. It is shown that melting rate depends on the shape of the capsule. This is especially important for the design of practical latent heat thermal energy systems. [S0199-6231(00)00504-9]

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