1 / 14

Melting by Natural Convection

Melting by Natural Convection. Solid initially at T s = uniform Exposed to surfaces at T > T s , resulting in growth of melt phase Important for a number of applications: Thermal energy storage using phase change materials

india
Download Presentation

Melting by Natural Convection

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Melting by Natural Convection • Solid initially at Ts = uniform • Exposed to surfaces at T > Ts, resulting in growth of melt phase • Important for a number of applications: • Thermal energy storage using phase change materials • Materials processing: melting and solidification of alloys, semiconductors • Nature: melting of ice on structures (roadways, aircraft, autos, etc.)

  2. Liquid Solid, Ts Tw Melting by Natural Convection • Solid initially at Ts = uniform • At t = 0, left wall at Tw > Ts • Ts = Tm • Liquid phase appears and grows • Solid-liquid interface is now an unknown • Coupled with heat flow problem • Interface influences and is influenced by heat flow

  3. Melting by Natural Convection

  4. Melting by Natural Convection • Conduction regime • Heat conducted across melt absorbed at interface • s = location of solid-liquid interface • hsf= enthalpy of solid-liquid phase change (latent heat of melting) • ds/dt = interface velocity

  5. Melting by Natural Convection • Non-dimensional form: • Where dimensionless parameters are:

  6. Melting by Natural Convection • Note that melt thickness, s ~ t1/2 • Nusselt number can be written as • Mixed regime: • Conduction and convection • Upper portion, z, wider than bottom due to warmer fluid rising to top • Region z lined by thermal B.L.’s, dz • Conduction in lower region (H-z)

  7. Melting by Natural Convection • Mixed regime • At bottom of z, (boundary layer ~ melt thickness) • Combining Eqs. (10.107, 10.106, and 10.102), we can get relation for size of z …

  8. Melting by Natural Convection • Height of z is: • Where we have re-defined: • Thus: • Convection zone, z, moves downward as t2 • z grows faster than s • We can also show that: • Constants K1, K2 ~ 1

  9. Melting by Natural Convection • From Eq. (10.110), we can get two useful pieces of information: z ~ H when • Quasisteady Convection regime • z extends over entire height, H • Nu controlled by convection only

  10. Melting by Natural Convection • Height-averaged melt interface x-location: • Average melt location, savextends over entire width, L, when • Can only exists if: • Otherwise, mixed convection exists during growth to sav ~ L

  11. Melting by Natural Convection • Numerical simulations verify Bejan’s scaling • Fig. 10.25: Nu vs. q for several Ra values

  12. Melting by Natural Convection • Nu ~ q-1/2 for small q (conduction regime) • Numin at qmin ~ Ra-1/2 (in mixed regime) • Nu ~ Ra1/4 (convection regime)

  13. Melting by Natural Convection • For largeq (q > q2) • sav ~ L • Scaling no longer appropriate • Nu decreases after “knee” point

  14. Melting by Natural Convection • Fig. 10.26 re-plots data scaled to Ra-1/2,Ra1/4 or Ra-1/4

More Related