Related papers: Two optimization problems in thermal insulation
We consider the problem of optimizing the product of the distances from a given point in a triangle to each vertex. There are two possible cases in general. For isosceles triangles, we explicitly show exactly when both cases occur.
We study a refrigerator model which consists of two $n$-level systems interacting via a pulsed external field. Each system couples to its own thermal bath at temperatures $T_h$ and $T_c$, respectively ($\theta\equiv T_c/T_h<1$). The…
A method for density-based topology optimization of heat exchangers with two fluids is proposed. The goal of the optimization process is to maximize the heat transfer from one fluid to the other, under maximum pressure drop constraints for…
In this article a topology optimization method is developed, which is aware of material uncertainties. The uncertainties are handled in a worst-case sense, i.e. the worst possible material distribution over a given uncertainty set is taken…
We investigate corrector estimates for the solutions of a thermoelasticity problem posed in a highly heterogeneous two-phase medium and its corresponding two-scale thermoelasticity model which was derived in an earlier paper by two-scale…
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
In this paper we show how to efficiently achieve thermal cloaking from a computational standpoint in several virtual scenarios by controlling a distribution of active heat sources. We frame this problem in the setting of PDE-constrained…
The classical problem of the thermal explosion in a long cylindrical vessel is modified so that only a fraction $\a$ of its wall is ideally thermally conducting while the remaining fraction $1-\a$ is thermally isolated. Partial isolation of…
Thermal rectification in heat conduction problems has been extensively studied in planar slabs. Here we consider the rectification problem in planar, cylindrical and spherical geometries involving two layers one of which has a temperature…
A design problem of finding an optimally stiff membrane structure by selecting one-dimensional fiber reinforcements is formulated and solved. The membrane model is derived in a novel manner from a particular three-dimensional linear elastic…
This work focuses on determining the coefficient of thermal diffusivity in a one-dimensional heat transfer process along a homogeneous and isotropic bar, embedded in a moving fluid with heat generation. A first type (Dirichlet) condition is…
A framework for topology optimization of cooling channels is proposed, which paves the way towards automated design of additively-manufactured cooling channels, required in applications such as the efficient heat management of die casting…
The problem of crack pattern formation due to thermal shock loading at the surface of half-space is solved numerically using two-dimensional boundary element method. The results of numerical simulations with 100-200 random simultaneously…
A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints…
We consider an optimization problem for spatial power distribution generated by an array of transmitting elements. Using ultrasound hyperthermia cancer treatment as a motivating example, the signal design problem consists of optimizing the…
Inspired by the unique design of the shells of snails inhabiting the deep-sea hydrothermal environment, here we theoretically study the temperature response of a bilayer to an external thermal impulse. A semi-analytical solution to the…
Optimization analyses of thermoelectric generators operation is of importance both for practical applications and theoretical considerations. Depending on the desired goal, two different strategies are possible to achieve high performance:…
We study optimization problems for partially hinged rectangular plates, modeling bridge roadways, in the presence of real and artificial obstacles. Real obstacles represent structural constraints to avoid, while artificial ones are…
We consider optimization problems that are formulated and solved in the framework of tropical mathematics. The problems consist in minimizing or maximizing functionals defined on vectors of finite-dimensional semimodules over idempotent…
We consider a system of equations that model the temperature, electric potential and deformation of a thermoviscoelastic body. A typical application is a thermistor; an electrical component that can be used e.g. as a surge protector,…