The use of forced-air warming is associated with costs for the disposable blankets. As an alternative method, we studied heat transfer with a reusable gel-coated circulating water mattress placed under the back in eight healthy volunteers. Heat flux was measured with six calibrated heat flux transducers. Additionally, mattress temperature, skin temperature, and core temperature were measured. W...

This work presents a new analytical method to transform exact solutions of linear diffusion equations into exact ones for nonlinear advection-diffusion models. The proposed formulation, based on Bäcklund transformations, is employed to obtain velocity fields for the unsteady two-dimensional Helmholtz equation, starting from analytical solutions of a heat conduction type model.

Hydrodynamic model simulations of a steady-state electron shock wave in a 1-pm Si semiconductor device at 77 K are compared with a Monte Carlo simulation of the Boltzmann equation using the DAMOCLES program. Excellent agreement between the two different methods for simulating the electron shock wave can be obtained by adjusting the amount of heat conduction in the hydrodynamic model.

A theoretical solution is presented for the forced convection heat transfer of a viscoelastic fluid obeying the Giesekus constitutive equation in a concentric annulus under steady state, laminar, and purely tangential flow. A relative rotational motion exists between the inner and the outer cylinders, which induces the flow. A constant temperature was set in both cylinders, in this study. The f...

The identification of the space-dependent perfusion coefficient in the onedimensional transient bio-heat conduction equation is investigated. In this inverse coefficient identification problem, the additional measurement necessary to render a unique solution is a boundary temperature measurement. A numerical approach based on a Crank-Nicolson finitedifference scheme combined with Tikhonov’s reg...

Fractional integro-differential equations arise in the mathematical modelling of various physical phenomena like heat conduction in materials with memory, diffusion processes etc. In this paper, we have taken the fractional integro-differential equation of type Dy(t) = a(t)y(t) + f(t) + ∫ t

The Boltzmann Transport Equation (BTE) for phonons has found prolific use for the prediction of non-equilibrium heat conduction phenomena in semiconductor materials. This article presents a new hybrid formulation and associated numerical procedures for solution of the BTE for phonons. In this formulation, the phonon intensity is first split into two components: ballistic and diffusive. The gove...

Applying simultaneously the methodology of Non-Equilibrium Thermodynamics with Internal Variables (NET-IV) and framework General Equation for Reversible-Irreversible Coupling (GENERIC), we demonstrate that, in heat conduction theories, entropy current multipliers can be interpreted as relaxed state variables. Fourier's law its various extensions -- Maxwell-Cattaneo-Vernotte, Guyer-Krumhansl, Je...

Heat conduction modelling ........................................................................................................................... 1 Case studies ........................................................................................................................................... 2 Analytical solutions.........................................................................