Physical processes simulation in a precision device for liquid samples thermal cycling

An urgent task is the development of devices that provide a precision temperature change. The devices used in the real-time polymerase chain reaction method require not only repeated cyclic temperature changes with high accuracy, but also the temperature gradient minimization over the working fluid. In this article, the modeling of the working processes taking place in the thermal block of the device with the previously proposed thermohydraulic system, which ensures the temperature change together with the Peltier elements, is carried out. A mathematical model is formulated and a differential equation, boundary and initial conditions are substantiated. Numerical methods for solving the mathematical model in the Elcut software were applied. An experimental setup was developed and a study of heat exchange processes in the thermal block of a nucleic acid analyzer with a thermohydraulic system was carried out, confirming the adequacy of the developed mathematical model.

Maximal and minimal iterative positive solutions for $ p $-Laplacian Hadamard fractional differential equations with the derivative term contained in the nonlinear term

<abstract><p>In this paper, the maximal and minimal iterative positive solutions are investigated for a singular Hadamard fractional differential equation boundary value problem with a boundary condition involving values at infinite number of points. Green's function is deduced and some properties of Green's function are given. Based upon these properties, iterative schemes are established for approximating the maximal and minimal positive solutions.</p></abstract>

Investigation of the shapes of cuts in a plate in contact with a rigid stamp

A mathematical model of a contact interaction between a plate and rigid stamp is derived taking into account physical and design details. The plate is considered to have a crack, that changes its form. The problem of the contact is evaluated based on the theory of variational inequalities. The shape of the stamp is assumed to be perpendicular to the plate surface and the Poisson’s ratio is between 0 and 0.5. Analytical formulation of the study consists of transformation equation, boundary conditions and integral equation. The result is used in maximization and minimization problems for choosing extremal shape of the vertical break in the plate.

Analysis of the Efficiency of Using Heat Exchangers with Porous Inserts in Heat and Gas Supply Systems

The creation of efficient and compact heat exchangers is one of the priority tasks arising during the design of heat and gas supply to industrial and residential buildings. As a rule, finned surfaces and turbulization of heat carrier flows are used to increase the efficiency of heat exchange in heat exchangers. The present paper proposes to use novel materials, namely porous material, in the design of highly efficient heat exchangers. The investigation was carried out experimentally and theoretically. To study the possibility of creating such heat exchangers, a multi-purpose test bench is created. The aim of the study was to assess the intensity of heat transfer in heat exchangers using porous metal. Laboratory tests are carried out as part of the experimental study. In the theoretical study, the classical equation for the change in the heat flux density when the coolant passes through the porous insert was used. As a result, a mathematical model was obtained in the form of a second-order differential equation. Boundary conditions were set and a particular solution was obtained. The results of theoretical calculations were compared with experimental data. The performed study experimentally confirmed the efficiency of using porous metal inserts in the design of shell-and-tube heat exchangers. The compiled mathematical model allows one to perform engineering calculations of the considered heat exchangers with porous inserts.

On the Existence of Three Positive Solutions for a Caputo Fractional Difference Equation

In this paper, we introduce the application of three fixed point theorem by discussing the existence of three positive solutions for a class of Caputo fractional difference equation boundary value problem. We establish the condition of the existence of three positive solutions for this problem.

Existence and Nonexistence of Positive Solutions for High-Order Fractional Differential Equation Boundary Value Problems at Resonance

We investigate positive solution for high-order fractional differential equations with resonant boundary value conditions. By using the spectral theory and the fixed point index theory, both the nonexistence and existence results of the resonant boundary value problems are given.