Benjamin T.F. Chung

A Continuous Exchange Factor Method for Radiative Exchange in Enclosures with Participating Media

A continuous exchange factor method for the analysis of radiative exchange in gray enclosures with absorbing-emitting and isotropically scattering media and diffuse surfaces is developed. In this method two type of exchange function are defined: the direct exchange function and the total exchange functions are developed. These integral equations are solved using a Gaussian quadrature integration method. The results obtained based on the present approach are found to be more accurate than those of the zonal method. Unlike the zonal method, in the present approach, there is no need for evaluation of multiple integrations for calculating direct exhange factors.

Transient Convective Heat Transfer for Laminar Boundary Layer Flow With Effects of Wall Capacitance and Resistance

Transient forced convective heat transfer from a laminar boundary layer flow over a flat plate with appreciable thermal capacity and resistance is studied analytically. In the analysis, the flow is assumed to be steady and incompressible and the solid plate is subjected to a uniform step heat input at the lower surface. The integral method is utilized to reduce systems of nonlinear partial differential equations to a single integro-differential equation in terms of interfacial temperature which is then solved with the aid of finite difference technique. Numerical results for the fluid-solid interface temperature, heat transfer coefficient, and temperature distributions within the fluid and solid are presented. Some limiting solutions are found to agree well with the results of the previous theoretical analyses.

Mushy zone equilibrium solidification of a semitransparent layer subject to radiative and convective cooling

Abstract Equilibrium solidification in a semitransparent planar layer is studied using an isothermal mushy zone model. The layer is made up of a pure material being emitting, absorbing and isotropically scattering and is subject to radiative and convective cooling. The model involves solving simultaneously the transient energy equation and the radiation transport equation. An implicit finite volume scheme is employed to solve the energy equation, with the discrete ordinate method being used to deal with the radiation transport. A systematical parametric study is performed and the effects of various materials optical properties and processing conditions are investigated. It is found that decreasing the optical thickness and increasing the scattering albedo both lead to a wider mushy zone and a slower rate of solidification.

A unified matrix formulation for the zone method: a stochastic approach

Abstract A new approach based on the Markov chain theory is utilized to derive three explicit matrix relations for the total exchange areas of the zone method. These relations are identical to those published earlier. The same method is used to derive a single explicit matrix relation for the total exchange areas. This expression is so general that it covers the same function as the aforementioned relations.

A Stochastic Approach for Radiative Exchange in Enclosures With Nonparticipating Medium

A stochastic method is developed for calculating radiation interchange in enclosures with a finite number of isothermal surfaces but without a participating medium. Different types of surface properties are considered. They are diffuse and specular surfaces. In this work, a stochastic n model is proposed that is based on the Markov chain theory and leads to some explicit matrix relationships for the absorption factor from which the heat transfer characteristics of the enclosure can be determined. The present approach provides an exact solution as long as the necessary view factors can be determined. The accuracy of approximate solutions can be improved as n increases.

The surface rejuvenation model for turbulent convective transport—an exact solution

Abstract A new approach to the formulation-solution of the surface rejuvenation model for turbulent convective transport is presented that leads to an exact analytical solution for the mean transport properties.

Nonequilibrium Planar Interface Model for Solidification of Semitransparent Radiating Materials

A nonequilibrium solidie cation model for semitransparent materials is presented. Consideration is given to a planar layer of emitting, absorbing, and scattering medium subject to radiative and convective cooling. The enthalpy method is used to formulate the phase-change problem together with radiative transfer equation taking into account internal emitting, absorbing, and scattering. A planar interface nonequilibrium solidie cation is assumed with crystalline phase nucleated on the surface at a given nucleation temperature, which may be signie cantly lower than the equilibrium melting temperature of the material. A linear kinetics relationship is introduced to correlate the unknown solidie cation temperature to the interface velocity. A fully implicit e nite volume scheme is used to solve the problem with the solidie cation interface tracked by a modie ed interface tracking method. Theradiative transfer equation issolved using the discreteordinates method. Internal radiation enhances the latent heat removal and thus leads to a higher interface velocity and a larger melt undercooling. Optical thickness and the conduction-radiation parameter are two important parameters that affect the solidie cation process. In the presence of external convective cooling, effect of internal radiation is small in the early stage of solidie cation.

Some Exact Solutions for Radiation View Factors from Spheres

Based on a new formulation for radiative view factor from a sphere to a class of axisymmetric bodies, closedform expressions are developed for the radiation view factors from a sphere to the external surface of a coaxial cylinder and from a sphere to an intersecting coaxial disk. The numerical results of the view factors are presented graphically in a wide range of parameters. At a limiting condition, one of the present formulas leads to the view factor from an annular ring to a coaxial hemisphere. The results are compared with those obtained earlier based on the Monte Carlo technique.

A Simpler Formulation for Radiative View Factors From Spheres to a Class of Axisymmetric Bodies

A simpler formulation is developed for radiative view factor from a sphere to a class of axisymmetric bodies. The new formulation is semianalytical in nature and only requires a single numerical integration at most.

Thermal Analysis on Planar Interface Stability in Solidification of Semitransparent Materials

Significant melt undercooling may be developed in the melt in front of the solid/liquid interface during solidification of semitransparent materials because of internal radiative heat transfer with the environment. A nonequilibrium planar interface solidification model has been developed recently to permit the melt undercooling near the interface. A thermal analysis is presented for the stability of such a planar interface. An absolute stability theory derived by Ludwig for opaque materials has been employed as a first approximation. The stability theory takes into account the stabilizing effect of efficient cooling through the solid layer and defines a heat flux parameter to quantify the latent heat released that is transferred into the undercooled melt. When the variation of the heat flux parameter during solidification is calculated based on the present nonequilibrium planar interface model, the stability of the interface for given process conditions can be determined