This paper presents a semi-analytical, mesh-free space–time Collocation Trefftz Method (SCTM) for solving two-dimensional (2D) wave equations. Given prescribed initial and boundary data, collocation points are placed on the space–time (ST...
This paper discusses a 1D one-dimensional mathematical model for the thermoelasticity problem in a two-layer plate. Basic equations in dimensionless form contain both temperature and displacement. General solutions of homogeneous equations (displacem...
This paper summarizes the results of the flow boiling heat transfer study with ethanol in a 1.8 mm deep and 2.0 mm wide horizontal, asymmetrically heated, rectangular mini-channel. The test section with the mini-channel was the main part of the exper...
In this paper, the issue of flow boiling heat transfer in an annular minigap was discussed. The main aim of the paper was determining the boiling heat transfer coefficient at the HFE-649 fluid–heater contact during flow along an annular minigap...
This paper presents a space–time meshfree method for solving transient inverse problems in subsurface flow. Based on the transient groundwater equation, we derived the Trefftz basis functions utilizing the method of separation of variables. Due...
In this study, we developed a novel boundary-type meshless approach for dealing with two-dimensional transient flows in heterogeneous layered porous media. The novelty of the proposed method is that we derived the Trefftz space–time basis function fo...
In this paper, a novel semi-analytical collocation solver, the spatial–temporal radial Trefftz collocation method (STRTCM) is proposed to solve 3D transient wave equations with specified sound source excitations. Unlike the traditional time dis...
The study presents the experimental and numeric heat transfer investigations in flow boiling of water through an asymmetrically heated, rectangular and horizontal minichannel, with transparent side walls. A dedicated system was designed to record ima...
The intensification of heat transfer using two-phase boiling flow in mini-channels is widely used to dissipate the high heat fluxes in miniaturized electronic devices. However, the process itself is not fully recognized and still requires experimenta...
The main objective of this study was to investigate boiling heat transfer during refrigerant flow in a mini-channel heat sink. The test section consisted of multiple parallel mini-channels, each with a depth of 1 mm. The working fluid was heated by a...
The new projective solutions methods (PSMs) for solving the Stokes, Oseen, and Brinkman flow problems are presented in this paper. They automatically satisfy the governing equations and are therefore Trefftz-type methods. Utilizing the third-order fo...
In this paper, a spacetime meshless method utilizing Trefftz functions for modeling subsurface flow problems with a transient moving boundary is proposed. The subsurface flow problem with a transient moving boundary is governed by the two-dimensional...
In this paper, a novel meshless method for the transient modeling of subsurface flow in unsaturated soils was developed. A linearization process for the nonlinear Richards equation using the Gardner exponential model to analyze the transient flow in...
In this article, a solution to nonlinear moving boundary problems in heterogeneous geological media using the meshless method is proposed. The free surface flow is a moving boundary problem governed by Laplace equation but has nonlinear boundary cond...
The main aim of this work was to provide heat transfer calculations of flow boiling in mini-channels with an application for the Trefftz functions. The test section comprised five parallel mini-channels with a depth of 1 mm, with a common heated wall...
In this article, a newly developed multiple-source meshless method (MSMM) capable of solving inverse heat conduction problems in two dimensions is presented. Evolved from the collocation Trefftz method (CTM), the MSMM approximates the solution by usi...
This paper investigates flow resistance and heat transfer during flow boiling of HFE-649 in a vertical annular minigap formed between an outer glass tube and an inner copper tube heated by a centrally located cartridge heater. Two variants of the cop...
This paper discusses a mathematical model for airflow through a cross-flow plate heat exchanger. The exhaust air is used to heat the supply air. Three kinds of plates are considered: made of aluminium, copper, and steel. The purpose of this research...
The paper discusses two mathematical models for the air flow through a plate heat exchanger with parallel plates. The first exhausts the used air and then supplies the fresh air. The second exhausts the used air above the plate and simultaneously sup...
The presented research addresses a problem occurring in a biogas plant, which we know plays an important role in sustainable development. The sludge deposited on the walls of the digester’s heat exchanger impairs heat transfer to the substrate....
This paper presents the modeling of tide–induced groundwater response using the spacetime collocation approach (SCA). The newly developed SCA begins with the consideration of Trefftz basis functions which are general solutions of the governing...
In this article, we propose a novel meshless method for solving two-dimensional stationary heat conduction problems in layered materials. The proposed method is a recently developed boundary-type meshless method which combines the collocation scheme...
A new concept of projective solution is introduced for the multi-dimensional Laplace equations. We project the field point onto a characteristic vector to obtain a projective variable, which can be used to reduce the Laplace equations to a second-ord...
This paper presents a study for solving the modified Helmholtz equation in layered materials using the multiple source meshfree approach (MSMA). The key idea of the MSMA starts with the method of fundamental solutions (MFS) as well as the collocation...
In this work, we consider Cauchy-type problems for Laplace’s equation with a dynamical boundary condition on a part of the domain boundary. We construct a discrete-in-time, meshless method for solving two inverse problems for recovering the spa...
This study focuses on the phenomenon of boiling heat transfer during fluid flow (Fluorinert FC-72) in minichannels. The research stand was built around a specially designed test section incorporating sets of aligned minichannels, each 1 mm deep. Thes...
Even though two-phase heat transfer of refrigerants in minichannel heat sinks has been studied extensively, there is still a demand for improvements in overall thermal performance of miniature heat transfer exchangers. Experimental investigation and...
This work focuses on subcooled boiling heat transfer during flow in a minichannel heat sink with three or five minichannels of 1 mm depth. The heated element for FC-72 flowing along the minichannels was a thin foil of which temperature on the outer s...
The article aims to explore boiling heat transfer in mini-channels with a rectangular cross-section using various fluids (HFE-649, HFE-7000, HFE-7100, and HFE-7200). Temperature measurements were conducted using infrared thermography for the heated w...