Thermal Wave Front Research Articles

NUMERICAL SOLUTION OF TWO-DIMENSIONAL NONLINEAR HYPERBOLIC HEAT CONDUCTION PROBLEMS

Two-dimensional hyperbolic heat conduction (HHC) problems with temperature-dependent thermal properties are investigated numerically. The present numerical method involves the hybrid application of the Laplace transform and control-volume methods. The Laplace transform technique is used to remove time-dependent terms, and then the transformed equation is discretized in the space domain by the control-volume formulation. Nonlinear terms induced by temperature-dependent thermal properties are linearized by using the Taylor's series approximation. In general, the numerical solution of the HHC problem has the phenomenon of the jump discontinuity in the vicinity of the thermal wave front. This phenomenon easily causes numerical oscillations in this region. In order to suppress these numerical oscillations, the selection of shape functions is an important task in the present study. The bi-hyperbolic shape function is introduced in the present control-volume formulation. Three examples involving a problem with a...

Propagation of thermal waves with lateral heat transfer

The wave nature of heat propagation in a one-dimensional semi-infinite medium with lateral convective heat transfer is investigated by solving the hyperbolic heat conduction equation in the longitudinal direction. The situation involves a large relaxation time which is relevant at low temperatures or for materials with a non-homogeneous inner structure, and the heat conduction in the lateral direction is assumed to be parabolic due to the number of lateral heat wave reflections compared to those in the longitudinal direction. The results for a unit heat flux condition at the boundary are compared with those obtained from parabolic heat conduction. This reveals that the classical heat diffusion theory predicted by parabolic heat conduction significantly underestimates the magnitude of the temperature and heat flux in thermal wave propagation. The results also reveal that when the dimensionless lateral heat transfer, known as the wave shape factor, is equal to unity, the thermal wavefront which travels through the medium at a finite speed decays exponentially along its path of travel while retaining the shape of the input wave. This theoretical prediction can be implemented experimentally for estimation of thermal relaxation times.

Turbulent transient heat transfer in channel flow with step change in inlet temperature

The transient forced convection in tubulent channel flow with a step change in inlet temperature is solved by using a hybrid scheme, namely, by combining the generalized integral transform technique with a second-order accurate finite-differences. Stability and convergence of the scheme are examined. Numerical results are presented for the fluid bulk temperature and local Nusselt number as a function of position along the channel at different times, and the propagation of the thermal wave front during temperature transients is examined.

Analysis of two-dimensional hyperbolic heat conduction problems

Two-dimensional hyperbolic heat conduction problems are investigated by using the hybrid numerical scheme. The thermal wave of such problems propagates with a finite velocity. Thus numerical oscillations in the vicinity of the thermal wave front can be observed, and a hybrid numerical method is presented, to reduce these oscillatory magnitudes. This method is that the time-dependent terms in the governing differential equations are removed by using the Laplace transform technique, and then the control volume method is used to discretize the space domain in the transform domain. The key of the present method is the selection of the shape functions. Various examples with the irregular geometry are illustrated.

Cylindrical shock waves generated by a spark discharge and their interaction with the shock waves from a pulsed induction discharge

An experimental investigation of a spark discharge in argon is described. The existence of a shock wave and a following thermal wave is demonstrated. The experimental law of propagation of the thermal wave front is obtained. The effect of the discharge parameters on the dynamics of both waves is studied. The interaction between the cylindrical shock waves generated by a pulsed induction discharge and the shock waves formed in a spark discharge is considered.

Propagation and reflection of thermal waves in a finite medium due to axisymmetric surface sources

For situations involving extremely short times following the start of transients, or very high heat fluxes, the classical diffusion theory of heat conduction breaks down since the wave nature of thermal energy transport dominates. In this work, the hyperbolic temperature response in a finite, isotropic medium with one surface insulated and the other surface irradiated with an axially symmetric heat flux is considered. The spatial profile of the heat flux is chosen to be either Gaussian, doughnut-shaped, or some combination of the two. The temporal profile is either continuous or a rectangular pulse. The choice of these profiles is based upon the premise that they approximate the outputs from some common laser sources. Calculations for a Gaussian source reveal the existence of a severe thermal wavefront which propagates through the medium, dissipating energy in its wake upon reflection at the boundaries. Also discussed is the relative importance of the parabolic and hyperbolic heat conduction models for a metal exposed to three ranges of rectangular pulse duration.

Ramp Wave Analysis of the Solid/Vapor Heat Pump

A theramlly driven heat pump using a solid/vapor adsorption/desorption compression process in a vapor compression cycle is thermodynamically analyzed. The cycle utilizes a simple heat transfer fluid circulating loop for heating and cooling of two solid adsorbent beds. This heat transfer fluid loop also serves to transmit heat recovered from the adsorbing bed being cooled to the desorbing bed being heated. This heat recovery process greatly improves the efficiency of the single-stage solid/vapor adsorption process without the complication of a two-stage cycle. During the heating and cooling processes a thermal wave profile travels through the beds. Previous studies of this cycle used a square wave model to simulate the thermal wave front. This paper utilizes a more physically realistic ramp wave model to overcome the shortcomings of the square wave model. The ramp wave model is integrated into a thermodynamic cycle which provides detailed information on the performance of the beds as well as the COP and the heating and cooling outputs of the heat pump system. Significant cycle design and operating parameters are varied to determine their effect on cycle performance.

Pebble bed-oil thermal energy storage for solar thermo-electric power systems

Results of a study to examine the operating characteristics of a 100 kWh thermal energy storage (TES) system suitable for solar thermo electric applications is described. The system chosen consisted of a pebble bed as the primary storage medium and oil as the heat transfer cum storage medium. The operating temperatures considered were between 230 and 250°C with a 20 deg C swing. A full-size unit consisting of a steel tank of volume 10 m3 with 50 mm pebbles, suitable instrumentation and facility for heating the oil was built. The important operating variables and characteristics of the system studied included the transient behaviour of the bed, namely the thermal wave front characteristics. Results of the theoretical analysis of the transient bed behaviour were compared with the experimental data on the wave front propogation characteristics and the comparisons are discussed. The uniformity of flow distribution is also examined.

SPECIALLY TAILORED TRANS FINITE-ELEMENT FORMULATIONS FOR HYPERBOLIC HEAT CONDUCTION INVOLVING NON-FOURIER EFFECTS

The phenomenon of hyperbolic heat conduction in contrast to the classical (parabolic) form of Fourier heat conduction involves thermal energy transport that propagates only at finite speeds as opposed to an infinite speed of thermal energy transport. To accommodate the finite speed of thermal wave propagation, a more precise form of heat flux law is involved, thereby modifying the heat flux originally postulated in the classical theory of heat conduction. As a consequence, for hyperbolic heat conduction problems, the thermal energy propagates with very sharp discontinuities at the wave front. The primary purpose of the present paper is to provide accurate solutions to a class of one-dimensional hyperbolic heat conduction problems involving non-Fourier effects that can precisely help understand the true response and furthermore can be used effectively for representative benchmark tests and for validating alternate schemes. As a consequence, the present paper purposely describes modeling/analysis formulations via specially tailored hybrid computations for accurately modeling the sharp discontinuities of the propagating thermal wave front. Comparative numerical test models are presented for various hyperbolic heat conduction models involving non-Fourier effects to demonstrate the present formulations.

Integral equation solution for hyperbolic heat conduction with surface radiation

Temperature distributions for the hyperbolic heat conduction in a semi-infinite medium with surface radiation are found from the solutions of a nonlinear Volterra equation for the surface temperature. The integral equation is obtained by the Laplace transform. This method has the advantage that the temperature distributions do not involve numerical oscillations around the thermal wave front.

Propagation and reflection of thermal waves in a finite medium

For situations involving extremely short times following the start of transients or for very low temperatures near absolute zero, the classical diffusion theory of heat conduction breaks down since the wave nature of thermal energy transport becomes dominant. In this work, analytical solutions are developed for the hyperbolic heat conduction equation describing the wave nature of thermal energy transport in a finite slab with insulated boundaries subjected to a volumetric energy source in the medium. The exact analytical solutions developed for the temperature field and heat flux show that the release of a concentrated pulse of energy gives rise to a severe thermal wave front which travels through the medium at a finite propagation speed, dissipating energy in its wake and reflecting from the insulated surfaces.

Growth and Decay of a Thermal Pulse Predicted by the Hyperbolic Heat Conduction Equation

The wave nature of heat propagation in a semi-infinite medium containing volumetric energy sources is investigated by solving the hyperbolic heat conduction equation. Analytic expressions are developed for the temperature and heat flux distributions. The solutions reveal that the spontaneous release of a finite pulse of energy gives rise to a thermal wave front which travels through the medium at a finite velocity, decaying exponentially while dissipating its energy along its path. When a concentrated pulse of energy is released, the temperature and heat flux in the wave front become severe. For situations involving very short times or very low temperatures, the classical heat diffusion theory significantly underestimates the magnitude of the temperature and heat flux in this thermal front, since the classical theory leads to instantaneous heat diffusion at an infinite propagation velocity.

Motion of a thermal wave front in a nonlinear medium with absorption

We study the evolution of a thermal perturbation in a nonlinear medium whose thermal conductivity depends on the temperature and the temperature gradient according to a power law.