iahs_124_0339

iahs_124_0339 - Prediction of Heat, Mass, and Momentum...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Prediction of Heat, Mass, and Momentum Transfer during Laminar Forced Convective Melting of Ice in Saline Water N. W. WILSON and T. S. SARMA ABSTRACT A two-dimensional analysis is made for the melting of a flat plate of pure ice into saline water flowing under laminar conditions. The velocity and temperature profiles are shown to be largely self-similar along the plate. However, the salinity profiles are largely convective in nature and strongly influenced by melting. For freestream temperatures of 2°C, 5 C C, and 10°C, a velocity of 4 m/s, and a salinity of 35°/ 00 , the ratios of boundary layer thicknesses decrease along a 1 m plate length. INTRODUCTION The heat transfer process near a melting flat surface has been investigated analytically in the past for forced convective laminar flow. Yen and Tien (1963) employed an extension of the Leveque solution to the melting process. Pozvon- kov et al. (1970) and Griffin (1973, 1974, 1975) refined the application of the von Kârmân/Pohlnausen integral method for the case of heat and mass transfer combined with melting. Griffin assumed that the momentum, temperature, and salinity boundary layer thicknesses bear constant ratios to one another and that the thermal boundary layer thickness is giyen by a relation for the pure water case by Pozvonkov et al. These assumptions do simplify the application of the integral method, but they also limit the applicability of the solution to large distances along the plate. Therefore, the present work was undertaken to obviate the difficulties which arise with the integral methods. ANALYSIS The melting system for the flow of saline water over an ice surface is shown in Figure 1. Following Roberts (1958) the phase transformation is assumed to occur 339
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
340 N. w. WILSON and T. s. SARMA u = u„ , T = T oe , S = S oe , «i=0, -|*- = />.u 0 v=0 T=T„ O - OoO <u = 0 SALINE WATER f- ax 11 3x as ax =o ^ 1CE\ Figure 1. Schematic diagram of the flow field. under steady-state conditions so that the co-ordinate system may be affixed to the melt interface. In the absence of body forces the governing equations of motion, energy, and mass for two-dimensional incompressible flow are as follows: For vorticity, w = dvldx - duldy, d j wdè\ d__ I fxdu) d I wdé dx \ dy dv dx dx dx d I p-dw dy \ dv (1) where it and v are the x and y components of the velocity vector, and p, is the fluid dynamic viscosity. The stream function, é, is related to the mass velocity com- ponents by j pu = —*- and pv = dy dx where p is the fluid density. The stream function can be related to the vorticity by dx \p dx d_ dy , P dy (2) For energy dx d_ dy dv k ar pC„ dy JL 9v dx dx \pC p dx
Background image of page 2
Prediction of Heat, Mass, and Momentum Transfer 341 For salinity fU D f ox \ ox d i pD^)= 0 dy \ dy (4) In the above equations T is temperature and 5 is salinity in parts per thousand. The fluid properties are the thermal conductivity
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 8

iahs_124_0339 - Prediction of Heat, Mass, and Momentum...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online