Numerical investigations of planar solidification of an undercooled liquid

We investigate evolution of a planar interface during unstable solidification of a pure undercooled liquid between two parallel plates. The governing equations are solved using a front tracking/finite difference technique that allows discontinuous material properties between the phases and interfacial anisotropy. The simulations produce some of the futures of the dendritic solidification which are in good qualitative agreement with the works of the previous investigators. The effects of the physical parameters on the crystal growth and interface instability are also examined. © 1997 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87387/2/629_1.pd

On interface dynamics

An intuitive study is presented for unstable interfacial waves. The maximum wavelength obtained for the most rapid unstable growth is shown to have a universal part which also characterizes the isotropic scales of buoyancy-driven turbulence. © 2000 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70336/2/PHFLE6-12-5-1244-1.pd

Entropy production in radiation-affected boundary layers

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76157/1/AIAA-1988-2640-236.pd

Radiative deformation

An infinitesimal change δQδQ in heat flux Q is shown, in terms of entropy flux Ψ=Q/T,Ψ=Q/T, to have two parts, δQ=TδΨ+ΨδT.δQ=TδΨ+ΨδT. The first part being the thermal displacement and the second part being the thermal deformation. Only the second part dissipates into internal energy and generates entropy. Thermodynamic arguments are extended to transport phenomena. It is shown that the thermal part of the rate of local entropy generation is related to the local rate of thermal deformation by s′′′=−ψi/T(∂T/∂xi),s′′′=−ψi/T(∂T/∂xi), where ψi=qi/T,ψi=qi/T, ψiψi being the rate of entropy flux vector, and qiqi the rate of heat flux vector. The part of this generation related to radiation is illustrated in terms of an example. © 2000 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70807/2/JAPIAU-87-6-3093-1.pd

Radiative entropy production

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76465/1/AIAA-9535-710.pd

Microscales of turbulence and heat transfer correlations

The small-scale structure of forced, turbulent flows developed after Taylor and Kolmogorov is extended to that of buoyancy-driven flows. A thermal microscale is proposed. Here Pr = v/a denotes the Prandtl number and [Weierstrass p]B the production of buoyant, turbulent energy. Three limits of this scale are the Kolmogorov, Oboukhov-Corrsin and Batchelor scales, respectively. When expressed in terms of the buoyancy force rather than that of the buoyant production (energy), the proposed scale becomes or, relative to a length scale l characteristic for geometry [eta][theta]/l~PN-1/3 where is the fundamental dimensionless number for buoyancy-driven flows and Ra is the Rayleigh number. A heat transfer model based on this dimensionless number explains why the well-known correlation for natural convection, Nu~Ran, leads to an exponent less than 1/3 when it is considered for the buoyancy-driven flow between two horizontal plates.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/26094/1/0000170.pd

Steady axially symmetric three-dimensional thermoelastic stresses in fuel rods

Steady axially symmetric three-dimensional thermoelastic stresses in solid rods having space dependent energy generation are given in terms of the Goodier and the Love-Galerkin or the Boussinesq-Papkovich potentials. Results find applications in nuclear technology.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24745/1/0000167.pd

Microscales of hydromagnetic channel flow

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76904/1/AIAA-1994-695-101.pd

Radiative entropy production--lost heat into entropy

Heat flow [delta]Q of the First Law of Thermodynamics is expressed in terms of the entropy flow [delta](Q/T)[delta]Q [triple bond] [delta][T(Q/T)] = T[delta](Q/T)+(Q/T)dT where T[delta](Q/T) denotes the energy equivalent of the entropy flow, and (Q/T)dT introduces the concept of lost heat into entropy production. Here Q = QK + QR where superscripts K and R indicate conduction and radiation, respectively. In terms of the lost heat, dimensionless entropy productions on the wall of a thermal boundary layer and in a quenched laminar flame are respectively shown to be Px ~ (1+qxR/qxK)Nux2 and Ps ~ (1+qR/qK)Pe-2 where qR and qK are the one-dimensional fluxes associated with QR and QK, Nux is a local Nusselt number, and Pe is a Peclet number based on the laminar flame speed at the adiabatic flame temperature. The tangency condition, [part]Pe/[part]Tb = 0, customarily used in the evaluation of minimum quench distance without any physical justification, is shown to correspond to an extremum in entropy production.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/26568/1/0000107.pd

Theory of transient heat transfer in laminar flow, applied to the entrance region of tubes with heat capacity

Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1958.Includes bibliographical references (leaves 36-37).by Vedat S. Arpaci.Sc.D