0
Research Papers: Melting and Solidification

Solidification of Two-Dimensional Viscous, Incompressible Stagnation Flow

[+] Author and Article Information
Asghar B. Rahimi

Professor
e-mail: rahimiab@yahoo.com
Faculty of Engineering,
Ferdowsi University of Mashhad,
P. O. Box No. 91775- 1111,
Mashhad, Iran

Three diagonal matrix algorithm.

Alternating direction implicit.

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 2, 2012; final manuscript received March 1, 2013; published online June 17, 2013. Assoc. Editor: Ali Ebadian.

J. Heat Transfer 135(7), 072301 (Jun 17, 2013) (8 pages) Paper No: HT-12-1344; doi: 10.1115/1.4023936 History: Received July 02, 2012; Revised March 01, 2013

The history of the study of fluid solidification in stagnation flow is limited to a few cases. Among these few studies, only some articles have considered the fluid viscosity and yet pressure variations along the thickness of the viscous layer have not been taken into account and the energy equation has been assumed to be one-dimensional. In this study the solidification of stagnation flows is modeled as an accelerated flat plate moving toward an impinging fluid. The unsteady momentum equations, taking the pressure variations along viscous layer thickness into account, are reduced to ordinary differential equations by the use of proper similarity variables and are solved by using a fourth-order Runge-Kutta integrating method at each prescribed interval of time. In addition, the energy equation is numerically solved at any step for the known velocity and the problem is presented in a two-dimensional Cartesian coordinate. Comparisons of these solutions are made with existing special ranges of past solutions. The fluid temperature distribution, transient velocity component distribution, and, most important of all the rate of solidification or the solidification front are presented for different values of nondimensional Prandtl and Stefan numbers. The results show that an increase of the Prandtl numbers (up to ten times) or an increase of the heat diffusivity ratios (up to two times) causes a decrease of the ultimate frozen thickness by almost half, while the Stefan number has no effect on this thickness and its effect is only on the freezing time.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 2

Explanation of strain and stream lines

Grahic Jump Location
Fig. 3

Ultimate solidification thickness after stability of the thermal boundary layer for various Pr numbers and αr = 1

Grahic Jump Location
Fig. 4

Comparison of the present study and the Ref. [15] results for (Pr = 1, St = 1, kr = 1, αr = 1 and θi = 1)

Grahic Jump Location
Fig. 5

Solidification front for Pr = 10 and (St = 1, kr = 1, αr = 1, and θi = 1)

Grahic Jump Location
Fig. 6

Solidification front for kr = αr = 0.5 and (Pr = 1, St = 1, and θi = 1)

Grahic Jump Location
Fig. 7

Solidification front for θi = 0.5 and (Pr = 1, St = 1, kr = 1, and αr = 1)

Grahic Jump Location
Fig. 8

Effect of the St number upon the solidification front for (Pr = 1, St = 1, kr = 1, and αr = 1)

Grahic Jump Location
Fig. 9

Effect of the Pr number upon the solidification front for (St = 1, kr = 1, αr = 1, and θi = 1)

Grahic Jump Location
Fig. 10

Effect of the kr and αr variations upon the solidification front for (Pr = 1, St = 1, and θi = 1)

Grahic Jump Location
Fig. 11

Effect of the θi variations upon the solidification front for (Pr = 1, St = 1, kr = 1, and αr = 1)

Grahic Jump Location
Fig. 12

Effect of the inlet temperature variations to the freeze point versus freeze time for (Pr = 10, St = 1, kr = 1, αr = 1, and θi = 1)

Grahic Jump Location
Fig. 13

Comparison of the conduction and convection terms contribution for (Pr = 10, St = 1, kr = 1, αr = 1, and θi = 1)

Grahic Jump Location
Fig. 14

Evolution of the solidification front for water with α° = 1

Grahic Jump Location
Fig. 15

Thermal profile for (Pr = 1, St = 1, kr = 1, αr = 1, and θi = 1)

Grahic Jump Location
Fig. 16

Velocity profile in the x direction for (Pr = 1, St = 1, kr = 1, αr = 1, and θi = 1)

Grahic Jump Location
Fig. 17

Velocity profile in the z direction for (Pr = 1, St = 1, kr = 1, αr = 1, and θi = 1)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In