Unsteady flow and heat transfer between rotating coaxial disks

A study is made on the flow and heat transfer of a viscous fluid confined between two parallel disks. The disks are allowed to rotate with different time dependent angular velocities, and the upper disk is made to approach the lower one with a constant speed. Numerical solutions of the governing parabolic partial differential equations are obtained through a fourth-order accurate compact finite difference scheme. The normal forces and torques that the fluid exerts on the rotating surfaces are obtained at different nondimensional times for different values of the rate of squeezing and disk angular velocities. The temperature distribution and heat transfer are also investigated in the present analysis.

Measurement of sensitivities for the thermal recording of laser beams

A simple technique for determining the energy sensitivities for the thermographic recording of laser beams is described. The principle behind this technique is that, if a laser beam with a known spatial distribution such as a Gaussian profile is used for imaging, the radius of the thermal image formed depends uniquely on the intensity of the impinging beam. Thus by measuring the radii of the images produced for different incident beam intensities the minimum intensity necessary (that is, the threshold) for thermographic imaging is found. The diameter of the laser beam can also be found from this measurement. A simple analysis based on the temperature distribution in the laser heated material shows that there is an inverse square root dependence on pulse duration or period of exposure for the energy fluence of the laser beam required, both for the threshold and the subsequent increase in the size of the recording. It has also been shown that except for low intensity, long duration exposure on very low conductivity materials, heat losses are not very significant.

Modelling conical rock-bed solar thermal storage tank

An important application of solar thermal storage is for power generation or process heating. Low-temperature thermal storage in a packed rock bed is considered the best option for thermal storage for solar drying applications. In this chapter, mathematical formulations for conical have been developed. The model equations are solved numerically for charging/discharging cycles utilizing MATLAB. Results were compared with rock-bed storage with standard straight tank. From the simulated results, the temperature distribution was found to be more uniform in the truncated conical rock-bed storage. Also, the pressure drop over a long period of time in the conical thermal storage was as low as 25 Pa. Hence, the amount of power required from a centrifugal fan would be significantly lower. The flow of air inside the tank is simulated in SolidWorks software. From flow simulation, 3D modelling of flow is obtained to capture the actual scenario inside the tank.

Mathematical modelling of rock-bed solar thermal storage tank

An important application of thermal storage is solar energy for power generation or process heating. Low temperature thermal storage in a packed rock bed is considered best option for thermal storage for solar drying applications. In this paper, mathematical formulations for conical and cylindrical rock bed storage tanks have been developed. The model equations are solved numerically for charging/discharging cycles. From the simulated results, it was observed that for the same aspect ratio between the diameter and the length of the thermal storages, the conical thermal storage had better performance. The temperature distribution was found to be more uniform in the truncated conical shape rock bed storage. Also, the pressure drop over long period of time in the conical thermal storage was lower than that of the cylindrical thermal storage. Hence, the amount of power required from a centrifugal fan was lower.

An asymptotic analysis of a simple model for the structure and dynamics of the Ramdas layer

This paper presents a complete asymptotic analysis of a simple model for the evolution of the nocturnal temperature distribution on bare soil in calm clear conditions. The model is based on a simplified flux emissivity scheme that provides a nondiffusive local approximation for estimating longwave radiative cooling near ground. An examination of the various parameters involved shows that the ratio of the characteristic radiative to the diffusive timescale in the problem is of order 10(-3), and can therefore be treated as a small parameter (mu). Certain other plausible approximations and linearization lead to a new equation whose asymptotic solution as mu --> 0 can be written in closed form. Four regimes, consishttp://eprints.iisc.ernet.in/cgi/users/home?screen=EPrint::Edit&eprintid=27192&stage=core#tting of a transient at nominal sunset, a radiative-diffusive boundary ('Ramdas') layer on ground, a boundary layer transient and a radiative outer solution, are identified. The asymptotic solution reproduces all the qualitative features of more exact numerical simulations, including the occurrence of a lifted temperature minimum and its evolution during night, ranging from continuing growth to relatively sudden collapse of the Ramdas layer.

Thermal stresses in rectangular plates

A method of determining the thermal stresses in a flat rectangular isotropic plate of constant thickness with arbitrary temperature distribution in the plane of the plate and with no variation in temperature through the thickness is presented. The thermal stress have been obtained in terms of Fourier series and integrals that satisfy the differential equation and the boundary conditions. Several examples have been presented to show the application of the method.

Numerical procedure for second order non-linear ordinary differential equations and application to heat transfer problem

In this paper, we have first given a numerical procedure for the solution of second order non-linear ordinary differential equations of the type y″ = f (x;y, y′) with given initial conditions. The method is based on geometrical interpretation of the equation, which suggests a simple geometrical construction of the integral curve. We then translate this geometrical method to the numerical procedure adaptable to desk calculators and digital computers. We have studied the efficacy of this method with the help of an illustrative example with known exact solution. We have also compared it with Runge-Kutta method. We have then applied this method to a physical problem, namely, the study of the temperature distribution in a semi-infinite solid homogeneous medium for temperature-dependent conductivity coefficient.

Numerical simulation of solidification of liquid aluminum alloy flowing on cooling slope

Preparation of semisolid slurry using a cooling slope is increasingly becoming popular, primarily because of the simplicity in design and ease control of the process. In this process, liquid alloy is poured down an inclined surface which is cooled from underneath. The cooling enables partial solidification and the incline provides the necessary shear for producing semisolid slurry. However, the final microstructure of the ingot depends on several process parameters such as cooling rate, incline angle of the cooling slope, length of the slope and initial melt superheat. In this work, a CFD model using volume of fluid (VOF) method for simulating flow along the cooling slope was presented. Equations for conservation of mass, momentum, energy and species were solved to predict hydrodynamic and thermal behavior, in addition to predicting solid fraction distribution and macrosegregation. Solidification was modeled using an enthalpy approach and a volume averaged technique for the different phases. The mushy region was modeled as a multi-layered porous medium consisting of fixed columnar dendrites and mobile equiaxed/fragmented grains. The alloy chosen for the study was aluminum alloy A356, for which adequate experimental data were available in the literature. The effects of two key process parameters, namely the slope angle and the pouring temperature, on temperature distribution, velocity distribution and macrosegregation were also studied.

Induction reheating of A356.2 aluminum alloy and thixocasting as automobile component

The development work for producing an automobile component by thixocasting using A356.2 alloy was introduced. As the first step, the alloy was electromagnetically stirred and solidified to produce a billet with non-dendritic microstructure. The microstructure depended on several process parameters such as stirring intensity, stirring frequency, cooling rate, and melt initial superheat. Through a series of computational studies and controlled experiments, a set of process parameters were identified to produce the best microstructures. Reheating of a billet with non-dendritic microstructure to a semisolid temperature was the next step for thixo-casting of the components. The reheating process was characterized for various reheating cycles using a vertical-type reheating machine. The induction heating cycle was optimized to obtain a near-uniform temperature distribution in radial as well as axial direction of the billet, and the heating was continued until the liquid fraction reached about 50%. These parameters were determined with the help of a computational fluid dynamics (CFD) model of die filling and solidification of the semisolid alloy. The heated billets were subsequently thixo-cast into automobile components using a real-time controlled die casting machine. The results show that the castings are near net shape, free from porosity, good surface finish and have superior mechanical properties compared to those produced by conventional die casting processes using the same alloy.

Cooling of a composite slab in a two-fluid medium

A mixed boundary value problem associated with the diffusion equation that involves the physical problem of cooling of an infinite parallel-sided composite slab in a two-fluid medium, is solved completely by using the Wiener-Hopf technique. An analytical solution is derived for the temperature distribution at the quench fronts being created by two different layers of cold fluids having different cooling abilities moving on the upper surface of the slab at constant speedv. Simple expressions are derived for the values of the sputtering temperatures of the slab at the points of contact with the respective layers, assuming the front layer of the fluid to be of finite width and the back layer of infinite extent. The main problem is solved through a three-part Wiener-Hopf problem of a special type and the numerical results under certain special circumstances are obtained and presented in the form of a table.

Numerical estimation of hotspot temperatures in electrodes subjected to pulsed electron beam heating in vacuum

A numerical solution for the transient temperature distribution in a cylindrical disc heated on its top surface by a circular source is presented. A finite difference form of the governing equations is solved by the Alternating Direction Implicit (ADI) time marching scheme. This solution has direct applications in analyzing transient electron beam heating of target materials as encountered in the prebreakdown current enhancement and consequent breakdown in high voltage vacuum gaps stressed by alternating and pulsed voltages. The solution provides an estimate of the temperature for pulsed electron beam heating and the size of thermally activated microparticles originating from anode hot spots. The calculated results for a typical 45kV (a.c.) electron beam of radius 2.5 micron indicate that the temperature of such spots can reach melting point and could give rise to microparticles which could initiate breakdown.

Cooling of an infinite slab in a two-fluid medium

A mixed boundary-valued problem associated with the diffusion equation, that involves the physical problem of cooling of an infinite slab in a two-fluid medium, is solved completely by using the Wiener-Hopf technique. An analytical solution is derived for the temperature distribution at the quench fronts being created by two different layers of cold fluids having different cooling abilities moving on the upper surface of the slab at constant speed. Simple expressions are derived for the values of the sputtering temperatures of the slab at the points of contact with the respective layers, assuming one layer of the fluid to be of finite extent and the other of infinite extent. The main problem is solved through a three-part Wiener - Hopf problem of a special type, and the numerical results under certain special circumstances are obtained and presented in the form of a table.

Numerical and experimental study of the thermal behaviour of coining and upsetting processes

A numerical simulation technique has been employed to study the thermal behavior of hot-forging type forming processes. Experiments on the coining and upsetting of an aluminum billet were conducted to validate the numerical predictions. Typical forming conditions for both the coining and upsetting processes were then studied in detail. an electrical analogy scheme was used to determine the thermal contact resistance. This scheme can conviniently provide the interface characteristics for typical processing conditions, which normally involve high pressures and temperatures. A single forging cycle was first considered, and then a batch of twenty-five forgings was studied. Each forging cycle includes the billet mounting, ascent, loading, dwelling, unloading, descent, and billet removal stages. The temperature distribution in the first forging to be formed is found to be significantly different from that at the end of the batch. In industry, forging is essentially a batch operation. The influence of forming speed and reduction on thermal characteristics was investigated also. The variations that can occur in the process design by considering differences in temperature characteristics are discussed also.

Studies on helium flow in experimental loops with different impedances operated with fountain effect pumps

An experimental flow loop with He II flow driven by fountain effect pumps (FEPs) is studied with respect to operation at different flow impedances and with thermal loads applied at different positions. The measured values of temperature, flow rate and pressure drop are compared with calculations resulting from a simplified model which assumes ideal performance of the porous plug and of the heat exchangers and which does not take into account Gorter-Mellink (GM) conduction. The main features of the loop are shown to be well described by this model. Refined calculations with a more complex model, including GM conduction of the He II, are only required for predicting the temperature distribution in some discrete regions of the loop.

Role of surface tension driven convection in pulsed - laser melting and solidification

Surface melting by a stationary, pulsed laser has been modelled by the finite element method. The role of the surface tension driven convection is investigated in detail. Numerical results are presented for a triangular laser pulse of durations 10, 50 and 200 ms. Though the magnitude of the velocity is high due to the surface tension forces, the present results indicate that a finite time is required for convection to affect the temperature distribution within the melt pool. The effect of convection is very significant for pulse durations longer than 10 ms.