The article presents the results of studies concerning raw hemp shives obtained from the Polish crop of industrial hemp as a loose-fill thermal insulation material. The study focuses mainly on the measurements of the pore size distribution, thermal conductivity and air permeability of material. An increase in the value of the thermal conductivity coefficient (0.049–0.052 W/(m∙K)) was demonstrated with an increase in the bulk density. The porosity of the individual pieces of shives is 78.7% and the predominant number of pores is in the diameter range of 0.9–3 μm. The paper also presents an example of the use of the tested material as thermal insulation of the wooden frame wall. The heat flow analysis was performed in various wall variants (insulation thickness: 100, 200 and 300 mm and pressure difference 0, 5, 10 and 15 Pa). A clear influence of the variables on the temperature distribution was observed.

Abstract:We study the behaviour of weak solutions (as well as their gradients) of boundary value problems for quasi-linear elliptic divergence equations in domains extending to infinity along a cone. MSC:35B05, 35B45, 35B65, 35D30, 35J66

We investigate the behaviour of weak solutions of boundary value problems (Dirichlet, Neumann, Robin and mixed) for linear elliptic divergence second order equations in domains extending to infinity along a cone. We find an exponent of the solution decreasing rate: we derive the estimate of the weak solution modulus for our problems near the infinity under assumption that leading coefficients of the equations do not satisfy the Dini-continuity condition.

Abstract:We have investigated the behaviour of solutions of elliptic quasi-linear problems in a neighbourhood of boundary singularities in bounded and unbounded domains. We found exponents of the solution's decreasing rate near the boundary singularities.

We investigate the behaviour of weak solutions of boundary value problems for quasi-linear elliptic divergence second order equations in unbounded domains. We show the boundedness of weak solutions to our problem. Using barrier function and applying the comparison principle, we find the exact exponent of weak solutions decreasing rate near the infinity.