Casimir free energy for massive fermions: a comparative study of various approaches

We compute the Casimir thermodynamic quantities for a massive fermion field between two parallel plates with the MIT boundary conditions, using three different general approaches and present explicit solutions for each. The Casimir thermodynamic quantities include the Casimir Helmholtz free energy, pressure, energy and entropy. The three general approaches that we use are based on the fundamental definition of Casimir thermodynamic quantities, the analytic continuation method represented by the zeta function method, and the zero temperature subtraction method. We include the renormalized versions of the latter two approaches as well, whereas the first approach does not require one. Within each general approach, we obtain the same results in a few different ways to ascertain the selected cancellations of infinities have been done correctly. We then do a comparative study of the three different general approaches and their results, and show that they are in principle not equivalent to each other and they yield in general different results. In particular, we show that the Casimir thermodynamic quantities calculated only by the first approach have all three properties of going to zero as the temperature, the mass of the field, or the distance between the plates increases.

Introduction of a novel electric field-based plate heat sink for heat transfer enhancement of thermal systems

Purpose The purpose of this study is to use an electric field technique to design novel heat sinks capable of rejecting as much heat as possible in a limited space. Configuration of electrodes in this study can be used for increasing the efficiency of heat sinks. Design/methodology/approach This study investigates a novel electrohydrodynamic (EHD)-based heat sink for thermal management of electronic devices and thermal systems. The significant part of designing an EHD heat sink is the arrangement of the electrodes. A numerical simulation is performed for a heat sink with two parallel plates to determine the optimum dimensional configuration of electrodes. The upper plate of this heat sink is the ground electrode with a constant atmosphere temperature, and the lower plate of it with flush-mounted high-voltage electrodes has uniform heat flux. Findings The results show that heat transfer changes by the size of the vortices and the number of them. These vortices are emerged by the electric field, and the number of them increases with increasing the number of electrodes. The interaction of vortices size and number leads to having the lowest average temperature in the optimum case by two high voltage electrodes with widths of 7.5 mm and a 17.5 mm gap between them. In comparison with the case without the electric field, with increasing the applied voltage to 30 kV, the efficiency of this EHD heat sink increases up to 37%. Originality/value Improvements in electrical equipment make them more compact with higher heat fluxes. Hence, the amount of heat to be dissipated per area increases and needs thermal management to operate at their design temperatures. Therefore, to improve the performance and life span of electronic components and increase their efficiency, it is necessary to design heat sinks to decrease their maximum (peak) temperature.

Characterisation of glue behaviour under thermal and mechanical stress conditions

New low-cost measuring devices require that the box housing and electronics have the cost aligned with the sensing system. Nowadays, metallic clips and/or glue are commonly used to fix the electronics to the box, thus providing the same motion of the structure to the sensing element. However, these systems may undergo daily or seasonal thermal cycles, and the combined effect of thermal and mechanical stress can determine significant uncertainties in the measurand evaluation. To study these effects, we prepared some parallel plates capacitors by using glue as a dielectric material. We used different types of fixing and sample assembly to separate the effects of glue softening on the capacitor active area and plates distance. Therefore, we assessed the sample modification by measuring the capacitance variation during controlled temperature cycles. We explored possible non-linear behaviour of the capacitance vs. temperature, and possible effects of thermal cycles on the glue geometry. Further work is still needed to properly assess the nature of this phenomenon and to study the effect of mechanical stress on the sample’s capacitance.

The Effects of Electrical Conductivity on Fluid Flow between Two Parallel Plates in a Porous Medioum

This paper deals with a mathematical model of a fluid flowing between two parallel plates in a porous medium under the influence of electromagnetic forces (EMF). The continuity, momentum, and energy equations were utilized to describe the flow. These equations were stated in their nondimensional forms and then processed numerically using the method of lines. Dimensionless velocity and temperature profiles were also investigated due to the impacts of assumed parameters in the relevant problem. Moreover, we investigated the effects of Reynolds number , Hartmann number M, magnetic Reynolds number , Prandtl number , Brinkman number , and Bouger number , beside those of new physical quantities (N , ). We solved this system by creating a computer program using MATLAB.