Seungho Paik

Unsteady mixed convection heat transfer from a solid sphere: The conjugate problem

Abstract Heat transfer associated with a spherical particle under simultaneous free and forced convection is numerically investigated using a combined Chebyshev Legendre spectral method. Both internal and external thermal resistances are taken into consideration by means of a conjugate model consisting of the full Navier -Stokes equations for external flow and the energy equations for both inside and outside the sphere. An influence matrix technique is employed to resolve the difficulties created by the lack of vorticity boundary conditions and to decouple the energy equations from interfacial couplings. Simulation results reveal that effects due to natural convection are most remarkable in the wake where the flow structure is changed. The overall Nusselt number and the drag coefficient show an increase or decrease in magnitude depending on whether gravity-induced flow aids or opposes the main flow. However, the change does not exceed 17% for the cases Gr/Re2 ⩽ 40 . When the buoyancy and the free stream are in the same direction, the effects are less pronounced than when they are in the opposite direction.

Unsteady mixed convection about a rotating circular cylinder with small fluctuations in the free-stream velocity

Abstract Heat transfer from a rotating circular cylinder immersed in a spatially uniform, time-dependent convective environment is investigated numerically including the effects due to buoyancy force. The flow equations, based on the vorticity and stream function, are solved along with the energy equation by a hybrid spectral scheme that combines the Fourier spectral method in the angular direction and a spectral element method in the radial direction. Several cases are simulated for Grashof numbers up to 2 × 104, Reynolds numbers up to 200, and a range of speed of rotation from −0.5 to +0.5. The results show that vortex shedding is promoted by the cylinder rotation but is vanished by the presence of the buoyancy force. In opposing flows, the counter flow currents cause a large expansion of the streamlines and isotherms in the direction normal to the free stream velocity. These changes in the structure of the flow and the temperature fields greatly modify the heat flux along the surface of the cylinder and consequently, the heat transfer rate is strongly dependent upon Reynolds number, Grashof number, rotational speed, and the gravity direction. Effects due to flow pulsation are also reflected in the Nusselt number history in the form of periodic oscillations.

Unsteady conjugate heat transfer associated with a translating spherical droplet: a direct numerical simulation

Thermal behavior of a liquid drop moving in an incompressible fluid of infinite extent is investigated numerically. Dynamical equations describing the temporal evolution of the flow and temperature fields of dispersed and continuous phases are solved by a hybrid spectral scheme in conjunction with the influence matrix technique to resolve the lack of vorticity boundary conditions. Both Chebyshev and Legendre polynomials are employed to expand the flow variables and temperature in the radial and angular directions, respectively. With the aid of the Galerkin and collocation methods, together with the first-order backward Euler time differencing, the governing partial differential equations reduce to a nonlinear system of algebraic equations. Numerical results reveal a discrepancy between quasi-steady and fully transient analyses at high Peclet numbers.

Numerical modeling of multiphase plasma/soil flow and heat transfer in an electric arc furnace

Abstract A study on an arc melter used for waste minimization process is presented. The plasma phase of the arc and the liquid-solid phases of the molten soil are simulated simultaneously. Newtonian fluid model is used for both the plasma and the molten phases. Parametric study is made on different arc lengths and arc currents with varying input powers. Calculations show that both convective heat transfer and Joule heating mechanism yield high heat dissipation in the melt pool. It is found that the buoyancy and the surface shear driven convection established in the melt pool are the major contribution to the more uniform mixing of the molten soil. For the long arc, the gas environment above the molten soil has large heated volume while the melted soil volume is small compared to those of short arc. The induced circulation in the melt pool is stronger for the short arc than that of long arc. For the same input power, increasing current results more heat dissipation inside the melt pool than increasing voltage drop.

Transient thermal convection in a spherical enclosure containing a fluid core and a porous shell

Abstract Transient natural convection in a spherical enclosure containing a central core fluid and a porous shell fully saturated with the same fluid is investigated numerically. Simulations are based on a mathematical model consisting of the Navier-Stokes equations for the fluid region, the Brinkman equation for flow through porous media, a convective diffusion equation for energy transport, and the Boussinesq approximation for buoyancy. Solutions are obtained by a hybrid spectral method which combines the concepts of Galerkin and collocation methods with Legendre and Chebyshev polynomials employed as basis functions, respectively. Time advancement is accomplished by a combined Adams-Bashforth and backward Euler schemes. The numerical results exhibit remarkable effects along the porous-fluids interface; however, the overall heat flux is only sensitive to the thermal conductivity ratio of the solid matrix to the fluid.

Unsteady mixed convection from a sphere in water-saturated porous media with variable surface temperature/heat flux

Abstract Mixed convection about a sphere buried in a porous medium saturated with water is numerically investigated using a Chebyshev-Legendre spectral method. Both Darcys law and the Boussinesq approximation together with effects due to nonlinear dependence of density on temperature are used to formulate the governing equations. Two types of surface condition are considered including variable surface temperature and surface heat flux which are modeled by Legendre expansions. Calculated results for the nonuniform heating and the nonuniform surface temperature cases demonstrate that the flow structures are not much different from the non-porous medium except for the recirculation zones which appear when the direction of the free stream velocity is opposite to the direction of the buoyancy force. Effects of nonuniform surface temperature are seen to dictate the heat flux distribution along the sphere surface and vice versa.

Transient conjugated heat transfer analysis from a sphere

The phenomena of conjugate unsteady heat transfer from a solid spherical particle in a convective environment is numerically investigated for Reynolds numbers in the range from 0.1 to 100. The flow and energy equations for both dispersed and continuous phases are solved using a Chebyshev-Legendre spectral method. This work is an extension of the previous effort of simulating flow around a sphere using spectral method [2] to include heat transfer. General findings indicate that quasi-steady analysis underestimates the overall heat transfer rate significantly at very early time stages, however the extent of underprediction becomes less as time progresses. The underprediction of the quasi-steady assumption becomes larger as Reynolds number increases for a fixed Prandtl number.ZusammenfassungDer Modellfall des gekoppelten, nichtstationären Wärmeübergangs von einem festen, kugelförmigen Partikel an ein Konvektionsfeld wird numerisch für Reynoldszahlen von 0,1 bis 100 untersucht. Die Lösung der Impuls- und Energiegleichungen für den dispersen wie den kontinuierlichen Bereich erfolgt unter Verwendung einer Chebyshev-Legendre Spektralmethode. Diese Arbeit setzt frühere Untersuchungen fort, wobei jetzt unter Verwendung derselben Methode auch der Wärmeübergang Berücksichtigung findet. Es zeigte sich, daß die quasistationäre Behandlung den Gesamtwärmeübergang im frühen Anlaufstadium erheblich unterbewertet. Dieser Effekt verringert sich im weiteren Verlauf des Austauschvorganges; er wächst (bei festgehaltener Prandtlzahl) mit der Reynoldszahl.

A study of argon thermal plasma flow over a solid sphere

The phenomena of momentum and heat transfer associated with an impulsively started spherical particle in a quiescent argon thermal plasma environment is considered. The changing plasma thermodynamics and transport property effects are studied using a Chebyshev-Legendre spectral method. Steady-state solutions for the case of constant sphere surface temperature are obtained and compared with previously published results. Transient solutions with particle internal heat conduction included are also presented. Results indicate that the magnitude of the drag force increases as the plasma free-stream temperature increases, while the Nusselt number decreases with increasing free-stream temperature. Effects due to different initial particle temperatures on the transient Nusselt number and drag coefficient are demonstrated.