Non-linear transient heat transfer analysis based on Lanczos co-ordinates using pseudo-force method

A New Multistep Technique Based on the Nonuniform Rational Basis Spline Curves for Nonlinear Transient Heat Transfer Analysis of Functionally Graded Truncated Cone

The time-dependent distributions of temperature and stresses in a box-column welded from ultra thick plates with a center segregation were analyzed using the commercial finite element package SYSWELD+ for several types and angles of groove. The welding method used in the current study was SAW(submerged arc welding), which was initially simulated using the commercial finite element package MSC/MARC, combined with a user-defined subroutine, to identify the weld thermal cycle. The major points of investigation were the optimum type and angle of groove that would minimize the weld stress, especially at the center segregation. A nonlinear transient heat transfer analysis was accomplished. The thermal properties, i.e. conductivity and specific heat, were found to be temperature dependent, plus the effects arising from a phase change, convection, and radiation were also taken into account.

Based on the meshless local natural neighbor interpolation method (MLNNI), a novel solution procedure is developed for the analysis of nonlinear steady and transient heat transfer of two-dimensional structures in this paper. Nonlinearities arising from temperature dependence of material properties and nonlinear boundary conditions have been taken into account. The present method is developed based on the natural neighbor interpolation (NNI) for constructing shape functions at scattered nodes. The three-node triangular FEM shape function is employed as the test function, which reduces the orders of integrands involved in domain integrals. Due to the delta function property of the natural neighbor shape functions, there is no need to employ special techniques to enforce the essential boundary conditions. The backward difference method is employed for the time integration scheme in transient analysis and the Newton–Raphson iterative procedure is required at each time step. Three numerical examples with different geometries and boundary conditions are presented at the end to demonstrate the validity and accuracy of the proposed method for the solution of a wide class of nonlinear steady and transient heat transfer problems.

The nonlinear inverse heat transfer problem is important in numerous scientific research and engineering applications. Considering the erosion-corrosion phenomenon of refractory brick walls in the melting furnace is a necessary research process for safe operation of the furnace. In this paper we present a nonlinear inverse heat transfer analysis approach for predicting wall erosion and time-varying thickness of the bank layer covering the inner surface of refractory brick walls of a melting furnace. The direct problem is a nonlinear one-dimensional mathematical model for the phase change process using the enthalpy method, which describes the concentrate melting process in the melting furnace. The numerical solution of this mathematical model uses finite difference method. In the nonlinear inverse heat transfer problem considered here, the time-varying heat flux and the thickness of the bank layer are unknown. We aim to determine these unknown parameters using temperature measurements obtained from the sensor. The inverse approach is based on the high-order modified Levenberg-Marquardt method (HMLMM) combined with the Broyden method. HMLMM combined with Broyden method can save a lot of Jacobian calculations and reduce the computational cost. Numerical results show that the proposed method is computationally more efficient than the inverse method in which the conventional Levenberg-Marquardt method (LMM) is used.

An approximate analytical method for nonlinear transient heat transfer through a metallic thermal protection system

The present study is focused on accurate prediction of the Morton effect problem including journal asymmetric heating and the corresponding long period amplitude oscillations using a nonlinear time transient rotor-dynamic simulation. This paper presents a theoretical model of thermal induced synchronous instability problems in a nonlinear rotor–bearing system, and suggests a new computational algorithm for the nonlinear transient analysis of the Morton effect where the dynamic and thermal problems are combined. For the analysis of the Morton effect problem, a variable viscosity Reynolds equation and a 3D energy equation are coupled via temperature and viscosity, and solved simultaneously. Three-dimensional heat transfer equations of bearing and shaft are modeled by a finite element method, and thermally coupled with the fluid film via a heat flux boundary condition. Asymmetric heat flux into the synchronously whirling rotor is solved by the orbit time averaged heat flux from fluid film to the spinning shaft surface. The journal orbit is calculated by the nonlinear transient dynamic analysis of a rotor–bearing system with a variable time step numerical integration scheme. For the computation time reduction, modal coordinate transformation is adopted in dynamic and thermal transient analysis. Thermal bow effect makes a significant change to the dynamic behavior of a rotor–bearing system, and a thermal hysteresis bode plot, that is one of the characteristics of the Morton effect problem, is presented with time varying spin speed.

Nonlinear flow and heat transfer dynamics of a slot jet impinging on a slightly curved concave surface

Numerical simulation of forced flow in sudden-expansion followed by sudden-contraction rectangular channel was presented for the whole flow region. The nonlinear flow and heat transfer characteristics were investigated by various Reynolds number and geometrical dimension and the critical Reynolds numbers under different conditions have been calculated. The results show flow and heat transfer from symmetric state to asymmetric state with the increase of Re. When Re<Rec (critical Reynolds number for flow transformation), the symmetric state is stable. On the other hand, when Re ≥Rec, the flow loses stability and from symmetric to asymmetric via a symmetry-breaking bifurcation. And the heat transfer performance have relevant characteristics as fluid flow.

An analysis is carried out to study the generalized slip condition and MHD flow of a nanofluid due to a contracting cylinder in the presence of non-linear radiative heat transfer using Buongiorno’s model. The Navier-Stokes along with energy and nanoparticle concentration equations is transformed to highly nonlinear ordinary differential equations using similarity transformations. These similar differential equations are then solved numerically by employing a shooting technique with Runge–Kutta–Fehlberg method. Dual solutions exist for a particular range of the unsteadiness parameter. The physical influence of the several important fluid parameters on the flow velocity, temperature and nanoparticle volume fraction is discussed and shown through graphs and table in detail. The present study indicates that as increase of Brownian motion parameter and slip velocity is to decrease the nanoparticle volume fraction.

Nonlinear radiative heat transfer in magnetohydrodynamic (MHD) stagnation point flow of nanofluid past a stretching sheet with convective boundary condition

We study the diffusive limit approximation for a nonlinear radiative heat transfer system that arises in the modeling of glass cooling and greenhouse effects and in astrophysics. The model is considered with the reflective radiative boundary conditions for the radiative intensity and with periodic, Dirichlet and Robin boundary conditions for the temperature. The global existence of weak solutions for this system is given by using a Galerkin method with a careful treatment of the boundary conditions. Using the compactness method, averaging lemma and Young measure theory, we prove our main result that the weak solution converges to a nonlinear diffusion model in the diffusive limit. Moreover, under more regularity conditions on the limit system, the diffusive limit is also analyzed by using a relative entropy method. In particular, we get a rate of convergence. The initial and boundary conditions are assumed to be well-prepared in the sense that no initial or boundary layer exists.

New equivalent damping for the ATC nonlinear static procedure

Non-linear thermal analysis of light concrete hollow brick walls by the finite element method and experimental validation

In this study, An optimization on a structure of Pb(Zr,Ti)O3 (PZT) thin film pyroelectric infrared (IR) sensor was investigated. Since the pyroelectric sensor detects the temperature change of the PZT film, the temperature of the PZT film is required to keep changing in detection time periods in order to obtain high detectivity. Therefore optimal pyroelectric sensor structures were investigated by transient heat transfer analysis using finite element model for fabrication of pyroelectric IR sensor with high performance. Various sensor models were simulated to investigate effects of parameters such as lengths, widths, and thickness of the sensor structures. As a result, the optimal PZT film pyroelectric sensor structure can be obtained from transient heat transfer analysis.

This paper presents a finite element analysis of transient heat transfer in and around a hypothetical deep geological repository for a spent nuclear fuel (SNF) disposal canister and the heat generation of the SNF inside the canister to provide basic information for dimensioning the repository and configuring the repository components. Three geometric models are compared to determine the most suitable assuming the periodic allocation of boreholes where canisters are deposited. These models consist of several different material regions. Each model is horizontally limited to a region around and including a single canister, bounded by midsurfaces with variant distances between adjacent deposition tunnels and adjacent canisters, and vertically bounded by the ground surface located 500 m above the deposition tunnel and the surface located 500 m below the bottom of the borehole. Using a commercial finite element analysis code and detailed realistic finite element models of repository components, transient heat transfer analyses are carried out for up to 1000 yr after deposition of the canister into the repository. Time-dependent temperature curves at selected positions are obtained for each geometric model. Various temperature distribution changes of material regions in geometric models are also obtained.