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Purpose The purpose of this paper is to present the multicriteria identification method used for solving the microscale heat transfer problem. The thin film exposed to ultrashort laser pulse is modeled using the finite difference method. The parameters of the model are tuned on the basis of experimental data. The multicriteria identification of the numerical model parameters is performed for subsets of experimental data. Design/methodology/approach The multicriteria identification method is used in the paper. The Pareto front for two criterions is created. The two-temperature model of heat transfer in microscale is used in the numerical model. Findings The multicriteria identification for two subsets of experimental data leads to different results. The obtained Pareto front allows to choose the most suitable set of numerical model parameters. Originality/value The multicriteria identification method was used for the first time to solve the microscale heat transfer problem.

Purpose – The purpose of this paper is to propose a computational model for thin layers, for problems of linear time-dependent heat conduction. The thin layer is replaced by a zero-thickness interface. The advantage of the new model is that it saves the need to construct and use a fine mesh inside the layer and in regions adjacent to it, and thus leads to a reduction in the computational effort associated with implicit or explicit finite element schemes. Design/methodology/approach – Special asymptotic models have been proposed for linear heat transfer and linear elasticity, to handle thin layers. In these models the thin layer is replaced by an interface with zero thickness, and specific jump conditions are imposed on this interface in order to represent the special effect of the layer. One such asymptotic interface model is the first-order Bövik-Benveniste model. In a paper by Sussmann et al., this model was incorporated in a FE formulation for linear steady-state heat conduction problems, and was shown to yield an accurate and efficient computational scheme. Here, this work is extended to the time-dependent case. Findings – As shown here, and demonstrated by numerical examples, the new model offers a cost-effective way of handling thin layers in linear time-dependent heat conduction problems. The hybrid asymptotic-FE scheme can be used with either implicit or explicit time stepping. Since the formulation can easily be symmetrized by one of several techniques, the lack of self-adjointness of the original formulation does not hinder an accurate and efficient solution. Originality/value – Most of the literature on asymptotic models for thin layers, replacing the layer by an interface, is analytic in nature. The proposed model is presented in a computational context, fitting naturally into a finite element framework, with both implicit and explicit time stepping, while saving the need for expensive mesh construction inside the layer and in its vicinity.

PurposeThis paper aims to develop and describe an improved process for determining the rate of heat generation in living tissue.Design/methodology/approachPrevious work by the authors on solving the bioheat equation has been updated to include a new localized meshless method which will create a more robust and computationally efficient technique. Inclusion of this technique will allow for the solution of more complex and realistic geometries, which are typical of living tissue. Additionally, the unknown heat generation rates are found through genetic algorithm optimization.FindingsThe localized technique showed superior accuracy and significant savings in memory and processor time. The computational efficiency of the newly proposed meshless solver allows the optimization process to be carried to a higher level, leading to more accurate solutions for the inverse technique. Several example cases are presented to demonstrate these conclusions.Research limitations/implicationsThis work includes only 2D development of the approach, while any realistic modeling for patient‐specific cases would be inherently 3D. The extension to 3D, as well as studies to improve the technique by decreasing the sensitivity to measurement noise and to incorporate non‐invasive measurement positioning, are under way.Practical implicationsAs medical imaging continuously improves, such techniques may prove useful in patient diagonosis, as heat generation can be correlated to the presence of tumors, infections, or other conditions.Originality/valueThis paper describes a new application of meshless methods. Such methods are becoming attractive due to their decreased pre‐processing requirements, especially for problems involving complex geometries (such as patient specific tissues), as well as optimization problems, where geometries may be constantly changing.

PurposeThe purpose of this paper is to present a reduced order computational strategy for a multi-physics simulation involving a fluid flow, electromagnetism and heat transfer in a hot-wall chemical vapour deposition reactor. The main goal is to produce a multi-parametric solution for fast exploration of the design space to perform numerical prototyping and process optimisation.Design/methodology/approachDifferent reduced order techniques are applied. In particular, proper generalized decomposition is used to solve the parameterised heat transfer equation in a five-dimensional space.FindingsThe solution of the state problem is provided in a compact separated-variable format allowing a fast evaluation of the process-specific quantities of interest that are involved in the optimisation algorithm. This is completely decoupled from the solution of the underlying state problem. Therefore, once the whole parameterised solution is known, the evaluation of the objective function is done on-the-fly.Originality/valueReduced order modelling is applied to solve a multi-parametric multi-physics problem and generate a fast estimator needed for preliminary process optimisation. Different order reduction techniques are combined to treat the flow, heat transfer and electromagnetism problems in the framework of separated-variable representations.

Purpose – The purpose of this paper is to present outcomes of efforts made over the last 20 years to extend the applicability of the Richardson extrapolation procedure to numerical predictions of multidimensional, steady and unsteady, fluid flow and heat transfer phenomena in regular and irregular calculation domains. Design/methodology/approach – Pattern-preserving grid-refinement strategies are proposed for mathematically rigorous generalizations of the Richardson extrapolation procedure for numerical predictions of steady fluid flow and heat transfer, using finite volume methods and structured multidimensional Cartesian grids; and control-volume finite element methods and unstructured two-dimensional planar grids, consisting of three-node triangular elements. Mathematically sound extrapolation procedures are also proposed for numerical solutions of unsteady and boundary-layer-type problems. The applicability of such procedures to numerical solutions of problems with curved boundaries and internal interfaces, and also those based on unstructured grids of general quadrilateral, tetrahedral, or hexahedral elements, is discussed. Findings – Applications to three demonstration problems, with discretizations in the asymptotic regime, showed the following: the apparent orders of accuracy were the same as those of the numerical methods used; and the extrapolated results, measures of error, and a grid convergence index, could be obtained in a smooth and non-oscillatory manner. Originality/value – Strict or approximate pattern-preserving grid-refinement strategies are used to propose generalized Richardson extrapolation procedures for estimating grid-independent numerical solutions. Such extrapolation procedures play an indispensable role in the verification and validation techniques that are employed to assess the accuracy of numerical predictions which are used for designing, optimizing, virtual prototyping, and certification of thermofluid systems.

Purpose – The purpose of this paper is to present a numerical method for the simulation of steady and unsteady incompressible laminar flows, including convective heat transfer. Design/methodology/approach – A node centered, finite volume discretization technique is applied on hybrid meshes. The developed solver, is based on the artificial compressibility approach. Findings – A sufficient number of representative test cases have been examined for the validation of this numerical solver. A wide range of the various dimensionless parameters were applied for different working fluids, in order to estimate the general applicability of our solver. The obtained results agree well with those published by other researchers. The strongly coupled solution of the governing equations showed superiority compared to the loosely coupled solution as inviscid effects increase. Practical implications – Convective heat transfer is dominant in a wide variety of practical engineering problems, such as cooling of electronic chips, design of heat exchangers and fire simulation and suspension in tunnels. Originality/value – A comparison between the strongly coupled solution and the loosely coupled solution of the Navier-Stokes and energy equations is presented. A robust upwind scheme based on Roe’s approximate Riemann solver is proposed.

Purpose – The purpose of this paper is to study the steady mixed convection boundary layer flow of a nanofluid past a horizontal circular cylinder in a stream flowing vertically upwards for both cases of a heated and cooled cylinder.Design/methodology/approach – The resulting system of nonlinear partial differential equations is solved numerically using an implicit finite‐difference scheme known as the Keller‐box method. This method is very efficient for solving boundary layer problems.Findings – The solutions for the flow and heat transfer characteristics are evaluated numerically for various values of the parameters, namely the nanoparticle volume fraction φ and the mixed convection parameter λ at Prandtl number Pr=1 and 6.2. Three different types of nanoparticles considered are Cu, Al2O3 and TiO2 by using water‐based fluid with Pr=6.2. It is found that for each particular nanoparticle, as the nanoparticle volume fraction φ increases, the skin friction coefficient and heat transfer rate at the surface a...

Purpose – The purpose of this paper is to numerically examine the conjugate natural convection in an inclined enclosure with a conducting centred block. This enclosure is filled with an Ethylene Glycol‐copper nanofluid. This study utilises numerical simulations to quantify the effects of pertinent parameters such as the Rayleigh number, the solid volume fraction, the length and the thermal conductivity of the centred block and the inclination angle of the enclosure on the conjugate natural convection characteristics.Design/methodology/approach – The SIMPLE algorithm is utilised to solve the governing equations with the corresponding boundary conditions. The convection‐diffusion terms are discretised by a power‐law scheme and the system is numerically modelled in FORTRAN.Findings – The results show that the utilisation of the nanofluid enhances the thermal performance of the enclosure and that the length of the centred block affects the heat transfer rate. The results also show that the higher block therma...

PurposeThe purpose of this paper is to present a micromechanical model based on a new truly local meshless method for analysis of heat transfer in composite materials.Design/methodology/approachThe presented meshless method is based on the integral form of energy equation in the sub‐particles in the material. In the presented meshless method due to elimination of domain integration the computational efforts are decreased substantially.FindingsNumerical results are presented for temperature distribution, heat flux and thermal conductivity. Numerical results show that the presented meshless method is simple, effective, accurate and less costly method in micromechanical modeling of heat conduction in heterogeneous materials.Research limitations/implicationsA small area of the composite system called representative volume element is considered as the solution domain. The fully bonded fiber‐matrix interface is considered and contact thermal resistant is neglected from the fiber matrix interface and so the continuity of temperature and reciprocity of heat flux is satisfied in the fiber‐matrix interface.Originality/valueFor the first time a new truly local meshless method based on the integral form of energy equation for the sub‐particles in the materials is presented for analysis of heat transfer in composite materials.

PurposeThe purpose of this paper is to describe the development and employment of an hp‐adaptive finite element method (FEM) algorithm for solving heat transfer problems in partitioned enclosures, which has attracted the attention of both experimental and theoretical researchers in recent years.Design/methodology/approachIn the hp‐adaptive FEM algorithm presented here, both the element size and the shape function order are dynamically controlled by an a posteriori error estimator based on the L2 norm; a three‐step adaptation strategy is used with a projection algorithm for the flow solver.FindingsSimulation results are obtained for 2D and 3D natural convection within partitioned enclosures. Results show refined and enriched elements that develop near the partition edges and side walls of the enclosure, as expected. The heat transfer between the heated and cooled side walls is reduced in the presence of a partial partition.Research limitations/implicationsThe Rayleigh numbers were set to 105 in the 2D case and 103 in the 3D case. Efforts are underway to apply the hp‐adaptive algorithm to partitioned enclosures at much higher Rayleigh numbers, including comparison with available experimental data.Practical implicationsHeat transfer within partitioned enclosures occurs in many engineering situations: heat transfer across thermo pane windows, solar collectors, fire spread and energy transfer in rooms and buildings, cooling of nuclear reactors and heat exchanger design.Originality/valueThe hp‐adaptive FEM algorithm is one of the best mesh‐based algorithms for improving solution quality, whilst maintaining computational efficiency. The method shows considerable promise in solving a wide range of heat transfer problems including fluid flow.