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We consider a two-dimensional singularly perturbed transmission problem with two different diffusion coefficients, in a domain with smooth (analytic) boundary. The solution will contain boundary layers only in the part of the domain where…

We are investigating the effective heat transfer in complex systems involving porous media and surrounding fluid layers in the context of mathematical homogenization. We differentiate between two fundamentally different cases: Case (a),…

This is the second part of a two parts work on the analysis of heat-type equations on manifolds with fibered boundary equipped with a $\Phi$-metric. This setting generalizes the asymptotically conical (scattering) spaces and includes…

We study a model that intermediates among the wave, heat, and transport equations. The approach considers the propagation of initial disturbances in a one-dimensional medium that can vibrate. The medium is nonlinear in such a form that…

This paper studies a two-material optimal design problem for the time-averaged duality pairing between a (possibly time-dependent) heat source and the weak solution of an initial-boundary value problem for the heat equation with a…

We consider time-harmonic electromagnetic wave equations in composites of a dispersive material surrounded by a classical material. In certain frequency ranges this leads to sign-changing permittivity and/or permeability. Previously meshing…

We consider thermodynamic properties, e.g. specific heat, magnetic susceptibility, of alternating Heisenberg spin chains. Due to a hidden Ising symmetry these chains can be decomposed into a set of finite chain fragments. The problem of…

In recent times the possibility of non-reciprocity in heat transfer between two bodies has been extensively studied. In particular the role of strong magnetic fields has been investigated. A much simpler approach with considerable…

We consider the problem of heat diffusion in branched systems and networks on the basis of a model described in terms of heat equation on metric graphs. Using the explicit analytical solutions of the latter, evolution of the temperature…

We discuss the non-radiative heat transfer in non-equilibrium double layer graphene system. We show that at the neutrality point the heat exchange is dominated by the inter-layer plasmon modes and derive analytic expressions for the heat…

We design heat exchangers using level-set method based topology optimization. The heat exchange between two fluids in separate channels is maximized while constraining the pressure drop across each channel. The flow is modeled by an…

This paper presents two remarkable phenomena associated with the heat equation with a time delay: namely, the propagation of singularities and periodicity. These are manifested through a distinctive mode of propagation of singularities in…

We consider the asymptotic behaviour of the effective thermal conductivity of a two-phase composite obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material and of size proportional to…

We consider a heat transmission problem across an irregular interface -- that is, non-Lipschitz or fractal -- between two media (a hot one and a cold one). The interface is modelled as the support of a d-upper regular measure. We introduce…

We study a two-phase parabolic free boundary problem motivated by the jump of conductivity in composite materials that undergo a phase transition. Each phase is governed by a heat equation with distinct thermal conductivity, and a…

Analytic solutions for cylindrical thermal waves in solid medium is given based on the nonlinear hyperbolic system of heat flux relaxation and energy conservation equations. The Fourier-Cattaneo phenomenological law is generalized where the…

A fast inverse heat conduction model (IHCM) is developed for estimating unknown properties of multi-layer composites considering internal heat generation. This work builds on the validated analytical forward models presented in Part I.…

This work establishes a closed-form analysis for two-dimensional transient heat transfer in an absorber plate based on the thermal wave model when the collector starts to work. The method of separation of variables is employed to determine…

A unification of characteristic mode decomposition for all method-of-moment formulations of field integral equations describing free-space scattering is derived. The work is based on an algebraic link between impedance and transition…

We show that periodic multilayered structures allow to drastically enhance near-field radiative heat transfer between nanoparticles. In particular, when the two nanoparticles are placed on each side of the multilayered structure, at the…