Hygrothermoelastic response in the bending analysis of elliptic plate due to hygrothermal loading

Abstract

This study investigates the theoretical outline to couple both classical Fourier’s and Fick’s laws to frame a new model of two-temperature hygrothermoelastic diffusion theory for a non-simple rigid material. Based on hygrothermoelasticity method, a system of linearly coupled partial differential equations for the thermal and moisture diffusion for the case of a non-simple medium is established. The transient response using the decoupled technique of a multilayered elliptic plate perpendicular to the axial axis, subjected to hygrothermal loading is considered, to derive closed-form expressions for temperature, moisture, deflection, bending moments, and hygrothermal stresses. The solutions to the governing coupled equations and its boundary conditions are solved by employing a new integral transform technique. The small deflection equation is found and utilized to preserve the intensities of bending moments and stresses, involving the Mathieu functions and its derivatives. Moreover, the elliptical region can be degenerated into a circular part by applying limitations. Numerical results of the transient response of hygrothermoelastic fields are established graphically for the better understanding the underlying elliptic structure, improved understanding of its relationship to circular profile, and better estimates of the effect of the associated hygrothermoelastic responses.     

An analytical solution of the potential velocity field induced by a growing bubble from a plate orifice

An analytical solution is derived with the mirror image method of the velocity field of an inviscid liquid induced by a growing bubble from a plate orifice. The flow is assumed potential, and the bubble shape is idealised as spherical. In deriving the motion equation, the spherical image of a point source, which is a combination of a point source and a line source, is proved approximate to a double source. This approximation enables continuation of the effectiveness of mirror image method to the case studied in this paper. The derived velocity potential equation is verified for the boundary conditions on the bubble surface and the orifice plate. The streamlines of the velocity field are presented and compared with experimental results in the literature.     

Dynamic response of an infinite medium with a spherical cavity on temperature-dependent properties subjected to a thermal shock under fractional-order theory of thermoelasticity

In this work, we consider the problem for an infinite medium with a spherical cavity on temperature-dependent properties subjected to a stress shock and thermal shock under the fractional-order theory of generalized thermoelasticity. The modulus of elasticity and the coe?cient of thermal conductivity are taken as linear function of temperature. The governing equations for the problem are formulated and then solved by Laplace transform together with its numerical inversion. The nondimensional temperature, displacement, radial stress, and hoop stress are obtained and illustrated graphically. In the calculation, the emphasis is focused on investigating the effect of temperature-dependent properties on the variations of the considered variables. The graphical results indicate that the temperature-dependent modulus of elasticity plays a significant role on all the physical quantities.     

An exact analytical solution for two-dimensional,unsteady, multilayer heat conduction in spherical coordinates

Analytical series solution is proposed for the transient boundary-value problem of multilayer heat conduction in r–θ spherical coordinates. Spatially non-uniform, but time-independent, volumetric heat sources may exist in the concentric layers. Proposed solution is valid for any combination of homogenous boundary conditions of the first or second kind in the θ -direction. However, inhomogeneous boundary conditions of the first, second or third kind may be applied at the inner and outer radial boundaries of the concentric layers. It is noted that the proposed solution is “free” from imaginary eigenvalues. Real eigenvalues are obtained by virtue of precluded explicit dependence of radial eigenvalues on those in the θ-direction. Solution is shown to be relatively simple for the most common spherical geometries?(multilayer) hemisphere and full sphere. An illustrative problem of heat conduction in a three-layer hemisphere is solved. Results along with the isotherms are shown graphically and discussed.     

An analytical solution for two-dimensional inverse heat conduction problems using Laplace transform

An analytical method has been developed for two-dimensional inverse heat conduction problems by using the Laplace transform technique. The inverse solutions are obtained under two simple boundary conditions in a finite rectangular body, with one and two unknowns, respectively. The method first approximates the temperature changes measured in the body with a half polynomial power series of time and Fourier series of eigenfunction. The expressions for the surface temperature and heat flux are explicitly obtained in a form of power series of time and Fourier series. The verifications for two representative testing cases have shown that the predicted surface temperature distribution is in good agreement with the prescribed surface condition, as well as the surface heat flux.     

Integral transform solution for hyperbolic heat conduction in a finite slab

An analytical integral transformation of the thermal wave propagation problem in a finite slab is obtained through the generalized integral transform technique (GITT). The use of the GITT approach in the analysis of the hyperbolic heat conduction equation leads to a coupled system of second order ordinary differential equations in the time variable. The resulting transformed ODE system is then numerically solved by Gear's method for stiff initial value problems. Numerical results are presented for the local and average temperatures with different Biot numbers and dimensionless thermal relaxation times, permitting a critical evaluation of the technique performance. A comparison is also performed with previously reported results in the literature for special cases and with those produced through the application of the Laplace transform method (LTM), and the finite volume-Gear method (FVGM).     

An exact solution for surface temperature in down grinding

A model has previously been developed for heat transfer in down grinding. A numerical solution algorithm was used to solve the system of equations. In this paper, an exact solution is found for this set of equations. The effect of the location of heat generation (i.e., at wear flats or shear planes) is explored for three typical grinding conditions: conventional grinding with aluminum oxide abrasives, creep feed grinding with aluminum oxide abrasives, and conventional grinding with cubic boron nitride (CBN) abrasives. It is found that during grinding with CBN, there is a strong effect of the assumed location of heat generation.     

An analytical solution for a Stefan problem with variable latent heat

Governing equations for a one-phase Stefan melting problem with variable latent heat are presented. It is shown that these equations model the movement of the shoreline in a sedimentary basin. An analytical solution for the sedimentation rate and shoreline movement--based on a similarity variable--shows a square root dependence of shoreline position with time.     

An analytical solution for air dehumidification by liquid desiccant in a packed column

This paper presents a new analytical solution of heat and mass transfer processes in a packed bed liquid desiccant dehumidifier based on the equilibrium humidity on the interface is assumed to be constant. In order to maintain the partial pressure difference on the interface, a high liquid desiccant flow rate is often applied in the practical absorber. Therefore, for a narrow range of operating conditions for practical dehumidification process, we can assume that the equilibrium humidity ratio on the interface is constant. The assumption of constant humidity ratio is applied in this paper for derivation of the analytical solution. The model and the analytical solution predictions were compared against a reliable set of experimental data available in the literature, with very good agreement. According to the Lewis definition in this present study, the Lewis number obtains 0.9. The effects of variables such as air and liquid desiccant flow rate, air temperature and humidity, desiccant temperature and concentration have been investigated on the condensation rate. The results present that design variables such as desiccant concentration, desiccant temperature, air flow rate, and air humidity ratio have the greatest impact on the performance of the dehumidifier. The liquid flow rate and the air temperature have not a significant effect. Furthermore, the effects of air and liquid desiccant flow rate have been reported on the humidity effectiveness of the column.     

Integral transform methods for inverse problem of heat conduction with known boundary of a thin rectangular object and its stresses

The three-dimensional inverse transient thermoelastic problem for a thin rectangular object is considered within the context of the theory of generalized thermoelasticity. The upper surface of the rectangular object occupying the space D: a≤x≤a; b≤y≤b; 0≤z≤h; with the known boundary conditions. Laplace and Finite Marchi-Fasulo transform techniques are used to determine the unknown temperature, temperature distribution, displacement and thermal stresses on upper plane surface of a thin rectangular object. The distributions of the considered physical variables are obtained and represented graphically.     

An analytical and experimental analysis of a very fast thermal transient

According to some international standards, some products, developed for use under heavy thermal conditions, have to be tested by subjecting them for a short time to a particular heating and cooling thermal stress to allow them an acceptable future operative life. It is possible to obtain these fast thermal gradients in confined environments, called climatic chambers where the air is heated by an electrical resistance and is cooled with a finned evaporator which is linked to a vapour compression system subjected to a particular control system of the refrigerating power. In particular, in this paper the air and object tested thermal transients are studied from an analytical and experimental point of view. The study of the mathematical model is realized assuming simplified hypotheses about the air, the object and the air cooled evaporator temperature. The most complex circumstances are related to a very fast temperature decrease because under this working condition the mathematical model is characterized by a nonlinear differential system. The nonlinear term is represented by the refrigerating power that varies in a definite range with the evaporator temperature according to a sinusoid trend. For this power a suitable analytical expression, derived by the control system performance and by the compressor characteristic, has been found. The analytical–experimental comparison during a cooling thermal stress of typical products subjected to international standard tests as the electronic boards, has been carried out showing acceptable results. The model presented is useful to foresee the climatic chamber performances in the presence of a specific refrigerating power trend; this is the start‐point for the design of the vapour compression plant and its control system. Copyright © 2001 John Wiley & Sons, Ltd.     

An analytical solution for the field of a hysteresis motor based oncomplex permeability

A closed-form solution for the electromagnetic field distribution inside a hysteresis motor is presented. The solution is based upon Maxwell's field equations, considering the case of a circumferential-flux-type machine at synchronous speed. A hysteresis loop in the shape of an inclined ellipse is adopted. The application of the complex permeability concept to space rotating vectors is explained. A new form for the general solution of Laplace's equation is used. This new form makes it possible to obtain a proper matching between the field components at the rotor outer surface when the scalar potential function is used and the hysteresis is considered. The torque equation is developed in order to allow comparison with test results. The proposed solution is simple, accurate, and rigorous. Comparison with test results shows the accuracy of the method     

Experimental study on transient natural convection in a cube enclosure with an isolated vertical cyclically heated plate

INTRODUCTIONNaturalconvectioninsideenclosuresisatopicofconsiderablecurrentinterestandimportance.Ofparticularinterestarethetransientcoolingproblemsinenclosureswithinternalisolatedheatedbodies,inwhichnaturalconvectionisoftenthedominantheattransfermecha...     

An exact elasto-plastic solution for a closed-end thick-walled cylinder of elastic linear-hardening material with large strains

An exact elasto-plastic analytical solution for a large-strained internal-pressurized thick-walled cylinder made of elastic linear-hardening material is derived in this paper. This solution is based on the notion of finite strains, the deformation theory of Hencky and the yield criterion of von Mises. Being applicable for both the linear-elastic response and the plastic strain-hardening stages of a large-strained closed-end thick-walled cylinder, the present solution can uniformly represent the whole expanding process of the cylinder from its initial yield at the inner surface to its full yield over the wall up to its ultimate bursting with an increase of its operating pressure. It is shown that this exact solution is of general characteristics, from which three specific solutions of practical interest can be obtained. The calculation formulae for the full-yield pressure and the bursting pressure of the large-strained cylinder deduced in this paper are of value for the strength design of a strain-hardening material cylinder. The present exact solution together with the deduced formulae furnish a new analytical pattern for the elasto-plastic analysis and strength design of a large-strained, internal-pressurized, closed-end, thick-walled cylinder made of strain-hardening material.     

Effect of immersion in NaOH solution on ferritic stainless steel as a bipolar plate for polymer electrolyte membrane fuel cells

The surface of 446M ferritic stainless steel (FSS) is modified by immersing in NaOH solution to understand its effect on the interfacial contact resistance (ICR) and corrosion. Immersion in NaOH solution under optimum condition can lead to decrease the ICR value of 446M FSS with no decrease in the corrosion resistance. Immersion of 446M FSS in NaOH solution increases the ratio of Cr oxy-hydroxide/oxide, which contributes to decrease the ICR value. This means that the bound water present in the form of the OH⁻ group in the passive film acts as a donor-type impurity and provides the active sites for electrical conduction in the oxide. This imparts positive effect on the electrical conduction and leads to decrease in the ICR value even after the long-term immersion in the simulated PEMFC environment.     

An exact solution of magnetohydrodynamic convection flow past an accelerated surface embedded in a porous medium

We analyze the transient hydromagnetic and thermal behavior of free convection flow past an impulsively started vertical plate which is embedded in a porous medium. The governing equations are solved in closed form by the Laplace-transform technique. A parametric study illustrating the influence of various parameters on the temperature, velocity as well as on the skin-friction and rate of heat transfer is conducted. The results of this parametric study are shown graphically.     

An analytical expression for the instantaneous efficiency of a flat plate solar water heater and the influence of absorber plate absorptance and emittance

Standard test results to quantify the instantaneous efficiency, η, of a glazed flat plate solar water heater are normally expressed in terms of a reduced temperature parameter, x, and global insolation, G, as η = η₀ ? a₁x ? a₂Gx². We show that the Hottel–Whillier–Bliss relation for the efficiency can be expressed in the same form with each of the coefficients η₀, a₁, and a₂ in terms of algebraic expressions of standard mechanical, fluid and thermal parameters of a single glazed, finned heater, including the absorber plate absorptance, α, and thermal emittance, ε. The advantage of the derived expression is that the effect on the efficiency of changes in various heater parameters can be readily evaluated. Furthermore, it is shown that for selectivity α/ε > 2, each coefficient η₀, a₁, and a₂ can be expressed as η₀ = η_0C ? εη_0R, etc., in order to separate out the role of absorber radiation from other losses. This allows one to easily compare selective solar absorbers with different α and ε and, for example, to suggest an optimum coating thickness for thickness sensitive selective solar absorbers. In particular it can be seen that care should be taken in reducing ε at the expense of also reducing α in order to increase the selectivity, α/ε, since this will often be detrimental to the efficiency. The analytical expressions for η₀, a₁, and a₂ can be easily programmed on a spreadsheet and, for convenience, are summarised in an appendix.     

An investigation into nickel implanted 316L stainless steel as a bipolar plate for PEM fuel cell

A nickel-rich layer about 100 μm in thickness with improved conductivity was formed on the surface of austenitic stainless steel 316L (SS316L) by ion implantation. The effect of ion implantation on the corrosion behavior of SS316L was investigated in 0.5 M H₂SO₄ with 2 ppm HF solution at 80 °C by potentiodynamic test. In order to investigate the chemical stability of the ion implanted SS316L, the potentiostatic test was conducted in an accelerated cathode environment and the solutions after the potentiostatic test were analyzed by inductively coupled plasma atomic emission spectrometer (ICP-AES). The results of potentiodynamic test show that the corrosion potential of SS316L is shifted toward the positive direction from −0.3 V versus SCE to −0.05 V versus SCE in anode environment and the passivation current density at 0.6 V is reduced from 11.26 to 7.00 μA cm⁻² in the cathode environment with an ion implantation dose of 3 × 10¹⁷ ions cm⁻². The potentiostatic test results indicate that the nickel implanted SS316L has higher chemical stability in the accelerated cathode environment than the bare SS316L, due to the increased amount of metallic Ni in the passive layer. The ICP results are in agreement with the electrochemical test results that the bare SS316L has the highest dissolution rate in both cathode and anode environments and the Ni implantation markedly reduces the dissolution rate. A significant improvement of interfacial contact resistance (ICR) is achieved for the SS316L implanted with nickel as compared to the bare SS316L, which is attributed to the reduction in passive layer thickness caused by the nickel implantation. The ICR values for implanted specimens increase with increasing dose.     

Effect of pharmaceutical agent degradation on axonal transport drug delivery: An analytical solution for a transient situation

This paper is motivated by recent experimental research that demonstrated pharmacological efficiency of axonal transport drug delivery. The purpose is to develop a model of this process and to study how the rate of destruction of pharmaceutical agent complexes (PACs) affects their transport in the axon. The model includes two populations of PACs: PACs in the state when they are driven retrogradely (from the axon terminal toward the neuron soma) by dynein motors and PACs residing in the accumulated state (but can still be re-released to the dynein-driven state). The coupling between the kinetic states is accounted for by first-order reactions. Utilizing Laplace transform, analytical solutions for concentrations of these two populations of PACs are obtained. The effect of PAC destruction is investigated for different values of other parameters. It is shown that the shapes of the waves describing the PAC concentrations can be significantly affected by transport parameters.