Constant wall heat flux boundary conditions in micro-channels filled with porous material with internal heat generation under local thermal non-equilibrium conditions

Forced convection heat transfer in a micro-channel filled with a porous material saturated with rarefied gas with internal heat generation is studied analytically in this work. The study is performed by analysing the boundary conditions for constant wall heat flux under local thermal non-equilibrium (LTNE) conditions. Invoking the velocity slip and temperature jump, the thermal behaviour of the porous-fluid system is studied by considering thermally and hydrodynamically fully-developed conditions. The flow inside the porous material is modelled by the Darcy–Brinkman equation. Exact solutions are obtained for both the fluid and solid temperature distributions for two primary approaches models A and B using constant wall heat flux boundary conditions. The temperature distributions and Nusselt numbers for models A and B are compared, and the limiting cases resulting in the convergence or divergence of the two models are also discussed. The effects of pertinent parameters such as fluid to solid effective thermal conductivity ratio, Biot number, Darcy number, velocity slip and temperature jump coefficients, and fluid and solid internal heat generations are also discussed. The results indicate that the Nusselt number decreases with the increase of thermal conductivity ratio for both models. This contrasts results from previous studies which for model A reported that the Nusselt number increases with the increase of thermal conductivity ratio. The Biot number and thermal conductivity ratio are found to have substantial effects on the role of temperature jump coefficient in controlling the Nusselt number for models A and B. The Nusselt numbers calculated using model A change drastically with the variation of solid internal heat generation. In contrast, the Nusselt numbers obtained for model B show a weak dependency on the variation of internal heat generation. The velocity slip coefficient has no noticeable effect on the Nusselt numbers for both models. The difference between the Nusselt numbers calculated using the two models decreases with an increase of the temperature jump coefficient.

The role of plug design in determining wall thickness distribution in thermoforming

An experimental investigation has been carried out into the effects of changes in plug design on the wall thickness distribution of thermoformed products. Plugs were machined with a series of geometrical variations and their effects on the process were measured. The overall results show that the plug has a crucial role in controlling the wall thickness distribution in thermoforming. Larger plugs tend to distribute more material to the base of the product, but the introduction of a small sidewall taper, base radius, or a reduction in plug diameter tend to lead to more balanced distributions. However, larger changes in any of the variables tend to destroy these benefits. It has also been demonstrated that the frictional and thermal properties of the plug are important in determining the deformation response of the sheet material. There is a clear evidence of slip in the sheet during plug contact and, although the cooling effect of the plug appears to be minimal, cooling in the highly deformed regions away from the plug appears to be a significant factor.

Effect of wall thickness on the ferroelastic domain size of BaTiO3

Extremely regular self-organized patterns of 90^o ferroelastic domains have been reported in freestanding single crystal thin films of ferroelectric BaTiO₃. Lukyanchuk et al. [Phys Rev B 79, 144111 (2009)] have recently shown that the domain size as a function of thickness for such free standing films can be well described assuming that the domains are due to stress caused by a surface tension layer that does not undergo the paraelectric–ferroelectric transition. From the starting point of Lukyanchuk’s model, it is shown here that the ‘‘universal’’relationship between domain size and domain wall thickness previously observed in ferroelectrics, ferromagnets and multiferroics is also valid for ferroelastic domains.Further analysis of experimental data also shows that the domain wall thickness can vary considerably (an order of magnitude) from sample to sample even for the same material (BaTiO₃), in spite of which the domain size scaling model is still valid, provided that the correct,sample dependent, domain wall thickness is used.

Dynamic modelling of die melt temperature profile in polymer extrusion: Effects of process settings, screw geometry and material

Extrusion is one of the major methods for processing polymeric materials and the thermal homogeneity of the process output is a major concern for manufacture of high quality extruded products. Therefore, accurate process thermal monitoring and control are important for product quality control. However, most industrial extruders use single point thermocouples for the temperature monitoring/control although their measurements are highly affected by the barrel metal wall temperature. Currently, no industrially established thermal profile measurement technique is available. Furthermore, it has been shown that the melt temperature changes considerably with the die radial position and hence point/bulk measurements are not sufficient for monitoring and control of the temperature across the melt flow. The majority of process thermal control methods are based on linear models which are not capable of dealing with process nonlinearities. In this work, the die melt temperature profile of a single screw extruder was monitored by a thermocouple mesh technique. The data obtained was used to develop a novel approach of modelling the extruder die melt temperature profile under dynamic conditions (i.e. for predicting the die melt temperature profile in real-time). These newly proposed models were in good agreement with the measured unseen data. They were then used to explore the effects of process settings, material and screw geometry on the die melt temperature profile. The results showed that the process thermal homogeneity was affected in a complex manner by changing the process settings, screw geometry and material.

Temperature fields in a channel partially filled with a porous material under local thermal non-equilibrium condition-an exact solution

This work examines analytically the forced convection in a channel partially filled with a porous material and subjected to constant wall heat flux. The Darcy–Brinkman–Forchheimer model is used to represent the fluid transport through the porous material. The local thermal non-equilibrium, two-equation model is further employed as the solid and fluid heat transport equations. Two fundamental models (models A and B) represent the thermal boundary conditions at the interface between the porous medium and the clear region. The governing equations of the problem are manipulated, and for each interface model, exact solutions, for the solid and fluid temperature fields, are developed. These solutions incorporate the porous material thickness, Biot number, fluid to solid thermal conductivity ratio and Darcy number as parameters. The results can be readily used to validate numerical simulations. They are, further, applicable to the analysis of enhanced heat transfer, using porous materials, in heat exchangers.