Ramp-type Heating Research Articles

Modeling of One-Dimensional Thermoelastic Dual-Phase-Lag Skin Tissue Subjected to Different Types of Thermal Loading

This work introduces a mathematical model of thermoelastic skin tissue in the context of the dual-phase-lag heat conduction law. One-dimensional skin tissue has been considered with a small thickness and its outer surface traction free. The bounding plane of the skin tissue is subjected to three different types of thermal loading; thermal shock, ramp type heating, and harmonic heating. The inner surface has no temperature increment and traction free. Laplace transform techniques have been used, and its inversions have been calculated by using the Tzuo method. The numerical results have been represented in figures. The thermal shock time parameter, the ramp-type heat parameter, and the angular thermal parameter have significant effects on the temperature increment, the strain, the displacement, and the stress distributions, and they play vital roles in the speed propagation of the thermomechanical waves through the skin tissue.

Effects of Hall Current and Rotation in a Fractional Ordered Magneto-Micropolar Thermoviscoelastic Half-Space Due to Ramp-Type Heat

Present work studies a two dimensional problem in a rotating magneto-micropolar thermoviscoelastic medium under a ramp type heating. The interaction due to viscosity, hall current and rotation are explored by using theory of fractional order thermoelasticity given by Sherief et al. (Int J Solids Struct 47(2):269–275, 2010). Analytical–numerical technique based on Laplace and Fourier transform has been employed to solve the resulting non–dimensional coupled field equations. Using numerical inversion technique the components of displacement, stress and temperature distribution are obtained in the physical domain. Numerical computed values of stresses and temperature fields are presented graphically to capture the effects of viscosity, hall current, rotation and fractional order parameter.

Effects of nonlocality and two temperature in a nonlocal thermoelastic solid due to ramp type heat source

This investigation is focused on the effects of nonlocality due to 2-D deformations arising in a nonlocal homogeneous isotropic thermoelastic solid which is subjected to a ramp type heat source with two temperature. There has been the use of Laplace and Fourier transforms for solving the equations. The expressions for displacement components, stress components and conductive temperature have been computed in the transformed domain. The numerical inversion technique has been used for obtaining the results in the physical domain. The effect of nonlocal parameter on the displacement components, conductive temperature and stress components have been represented graphically.

Modified DPL Green–Naghdi theory for thermoelastic vibration of temperature-dependent nanobeams

A unified multi-dual-phase-lag thermoelasticity theory is presented to study the vibration of a temperature-dependent nanobeam subjected to a ramp-type heating. The nonlocal thermoelasticity theory based on Euler-Bernoulli hypothesis is applied. Laplace transform domain is adopted to solve the governing partial differential equations using the state space approach. Numerical computations are carried out using the inverse of Laplace transforms. The present heat conduction and constitutive equations are covering at least five models of the generalized thermoelasticity. Comparison between the classical thermoelasticity (CTE), the Lord–Shulman (L–S), the Green–Lindsay (G–L), and the simple and refined-phase-lag models are made. The effects of nonlocal, ramp-type heating, and temperature-dependent parameters on all quantities have been discussed and presented graphically. It is found that the ramp-type heating parameter has significant effects on all quantities. However, the thermoelastic deflection, axial displacement, dilatation, and bending moment have strong dependencies on the nonlocal and temperature-dependent parameters.

Dynamic model of fractional thermoelasticity due to ramp-type heating with two relaxation times

This is an attempt to design a fractional heat conduction model in a bounded cylindrical region exposed to axisymmetric ramp-type heat flux and discuss its thermal behaviour. This model is drafted using the classical theory of fractional thermoelasticity due to the involvement of two relaxation times to the heat conduction equation and the equations of motion. In order to achieve finite thermal wave speed, the heat conduction equation is derived from the viewpoint of Maxwell–Cattaneo law in the context of fractional derivative. Analytical results for the distribution of temperature, displacement and thermal stresses are obtained using integral transforms in the Laplace domain. The Gaver–Stehfest method has been used to invert the results of Laplace domain. The convergence of infinite series solutions has been discussed. As a specific case this model has been applied to a thick circular plate subjected to the axisymmetric ramp-type heat flux. The results obtained for the thermal variations are validated by comparing to coupled and generalized theory of thermoelasticity. These comparisons are shown graphically.

Transient hygrothermoelastic response in a porous cylinder subjected to ramp-type heat-moisture loading

The classical theory of heat conduction (Fourier theory) predicts an infinite speed for thermal disturbance propagation, which is physically unrealistic. By extending the classical Fourier heat conduction and Fick’s diffusion, this article develops hyperbolic diffusion/heat conduction laws with phase lags of heat/moisture flux to simulate coupled heat-moisture diffusion-propagation behavior with the Defour and Soret effects. A porous cylinder subjected to a ramp-type heating and humidifying at the surface is studied. The Laplace transform is used to obtain a closed-form solution of the temperature, moisture, displacements and stresses in the cylinder. Numerical results are calculated via the inversion of the Laplace transform. Obtained results show that the thermal/moisture relaxation time or phase lag plays a significant role in affecting transient hygrothermoelastic field. For a non-vanishing phase lag, non-Fourier and non-Fickian effects exist and hygrothermal waves have finite propagation speeds. The influences of the phase lag of heat/moisture flux and ramp-type time parameter on the transient response of hygrothermoelastic field are presented graphically. A comparison of the numerical results based on the classical model and the present one is made. The non-Fourier heat conduction and non-Fickian diffusion can effectively avoid the shortcomings induced by the classical Fourier and Fick laws.

On thermoelectric materials with memory-dependent derivative and subjected to a moving heat source

We develop a model of generalized thermoelasticity with memory-dependent derivative (MDD) heat conduction law for a thermoelectric half-space. Some urgent theories take after as most remote point cases. The Laplace transform and state-space procedures are utilized to urge the overall account for any arrangement of limit conditions. The general solution acquired is connected to the particular issue of a half-space exposed to a uniform magnetic field, a moving heat source with consistent speed and ramp-type heating. The inverse Laplace transforms are registered numerically. The impacts of various estimations of the figure-of-merit quantity, heat source speed, MDD parameters, the magnetic number and the ramping time parameter are thought about.

Modeling of memory-dependent derivative in a functionally graded plate

ABSTRACT Enlightened by the Caputo fractional derivative, this study deals with a novel mathematical model of heat transport in a functionally graded thick plate in the context of Taylor's series expansion involving memory-dependent derivative for the dual-phase-lag (DPL) heat conduction law, which is defined in an integral form of a common derivative with a kernel function on a slipping interval. The medium is considered as a thick plate, both the surfaces of which is taken to be traction free and the lower surface is subjected to different time-dependent thermal loadings (thermal shock, periodically varying thermal loading and ramp-type heating) while the upper surface is kept at zero temperature. Laplace transform technique is employed to find out the analytical solutions and the inversion of Laplace transform is carried out using a method based on Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusion about the new theory is constructed due to the effect of nonhomogeneity. Excellent predictive capability is demonstrated due to the presence of memory-dependent derivative and nonhomogeneity also.

Ramp Type Heating in a Semiconductor Medium under Photothermal Theory

The present investigation is concerned with study the two-dimensional deformation in a semi-infinite semiconducting medium subjected to ramp type heating. The deformation in the medium is caused subjected to a thermal source of ramp-type nature applied along the free surface of a semiconducting medium. The semiconductor thermoelastic medium is under the influence of an internal heat source of constant magnitude. Integral Transform method has been used to obtain the transformed expression of displacement components, stress components, temperature distribution, and carrier density. The transformed expressions are then inverted using numerical inversion technique. The effect of ramp-type source and thermoelectric coupling parameter on the components of displacement, force stress, temperature distribution, and carrier density has been shown graphically.

A Two Dimensional Random Model in the Theory of Generalized Thermoviscoelasticty for a Thick Plate Subjected to Stochastic Ramp-Type Heating

A Two Dimensional Random Model in the Theory of Generalized Thermoviscoelasticty for a Thick Plate Subjected to Stochastic Ramp-Type Heating

Eigen value approach for dual phase lag micropolar porous thermoelastic circular plate with ramp type heating

PurposeThe purpose of this paper is to investigate a two dimensional problem of micropolar porous thermoelastic circular plate subjected to ramp type heating.Design/methodology/approachThree phase lag theory of thermoelasticity has been used to formulate the problem. A numerical inversion technique is applied to obtain the result in the physical domain. The numerical values of the resulting quantities are presented graphically to show the effect of porosity and dual phase lag model. Some particular cases are also presented.FindingsThe Laplace and Hankel transforms are employed followed by the eigen value approach to obtain the components of displacements, microrotation, volume fraction field, temperature distribution and stresses in the transformed domain.Originality/valueThis paper fulfils the need to study the two-dimensional problem of micropolar porous thermoelastic circular plate subjected to ramp type heating.

Response of thermoelastic functionally graded beam due to ramp type heating in modified couple stress with dual-phase-lag model

PurposeThe purpose of this paper is to investigate the thermoelastic functionally graded beam in a modified couple stress theory subjected to a dual-phase-lag model.Design/methodology/approachThe governing equations are solved by using the Euler-Bernoulli beam assumption and the Laplace transform technique. The lateral deflection, temperature change, displacement component, axial stress and thermal moment of the beam are obtained by ramp type heating in the transformed domain. A general algorithm of the inverse Laplace transform is developed to recover the results in a physical domain.FindingsThe lateral deflection, temperature change, displacement component, axial stress and thermal moment of the beam are computed numerically and presented graphically to show the effect of ramp time parameter and phase lags of heating.Originality/valueComparisons are made in the absence and presence of coupled dual-phase-lag thermoelastic and coupled thermoelastic L-S theories and also different values of ramp type parameter.

Eigenvalue approach to nanobeam in modified couple stress thermoelastic with three-phase-lag model induced by ramp type heating

This article deals with the study of a thermoelastic nanobeam in a modified couple stress theory subjected to ramp-type heating. The mathematical model is prepared for the nanobeam in thermoelastic three-phase-lag. The Laplace transform and the eigenvalue approach are used to find the displacement component, lateral deflection, temperature change and axial stress of the thermoelastic beam. The general algorithm of the inverse Laplace transform is developed to compute results numerically. The comparison of three-phase-lag, dual-phaselag and GN-III (1993) models are represented, and their illustration is depicted graphically. This study finds the applications in engineering, medical science, sensors, etc.

Thermoelastic response of nanobeam resonators subjected to exponential decaying time varying load

This work investigates the vibrational response of thermoelastic nanobeam resonators in- duced by ramp-type heating and subjected to exponential decaying time varying load via Euler-Bernoulli beam theory. Governing equations are derived in the context of nonlocal generalized thermoelasticity theory with dual phase lags. The nonlocal nanobeam theory incorporates a nonlocal parameter to capture the small scale effect. Using the Laplace trans- form technique, an analytical solution has been attained. and inversions of the transformed solutions have been carried out by means of calculus of residues. The effects of nonlocal, po- int load and ramping-time parameters on all studied fields of the nanobeam are investigated and discussed.

Unsteady general solution for MHD natural convection flow with radiative effects, heat source and shear stress on the boundary

PurposeThe purpose of this note is to provide general solutions for radiative magnetohydrodynamic natural convection flow.Design/methodology/approachTo obtain exact solutions for such motions of Newtonian fluids, as seen in the existing literature, the Laplace transform technique is used.FindingsGeneral solutions are obtained for temperature, velocity and Nusselt number in the presence of heat source and shear stress on the boundary. They can generate exact solutions for any motion with technical relevance of this type. Fluid velocity is presented as the sum of mechanical and thermal components. Influence of physical parameters on temperature and velocity is graphically underlined for ramp-type heating plate that applies a constantly accelerating shear stress to the fluid. Thermal and mechanical effects are significant and must be taken into consideration.Practical implicationsFor illustration, as well as for a check of results, three special cases with applications in engineering are considered and some known results are recovered.Originality/valueObtained solutions are presented in the simplest forms. In addition, the solutions corresponding to cosine oscillatory heating and oscillating shear are presented so that they can be immediately reduced to those corresponding to constant heating and uniform shear if the oscillations’ frequency becomes zero. Heat transfer characteristics with thermal radiation are graphically illustrated using one parameter only for such motions.

Dynamic response of a nanobeam induced by ramp-type heating and subjected to a moving load

The problem considered is that of an isotropic, thermoelastic nanobeam subjected to a moving concentrated loading. The solution of the problem is presented in the context of generalized theory of nonlocal thermoelasticity. Modal analysis along with Laplace’s transform technique is employed to obtain analytical solution of the governing partial differential equations. Effect of velocity of the moving load, nonlocal parameter and ramping-time parameter on dynamic deflection, temperature and flexural moment of the nanobeam has been investigated. Numerical results obtained from the present study are presented graphically and discussed.

Effect of temperature-dependent physical properties on nanobeam structures induced by ramp-type heating

The classical Euler-Bernoulli beam theory based upon the nonlocal theory of thermoelasticity is constructed and employed to investigate the vibrating nanobeam due to a ramp-type heating. The thermal conductivity and modulus of elasticity are taken as temperature-dependent functions. The generalized theory of thermoelasticity with Dual-Phase-Lags (DPLs) model is also employed to solve the problem. Analytical and numerical techniques based on Laplace transforms and their inversions are used to calculate the vibrational deflection and temperature of the nanobeam. The effects of the PLs and ramping-time parameters on the lateral vibration, the temperature, the displacement and the flexure moment of the nanobeam are investigated. Some plots have been presented for comparison purposes to estimate the effects of the nonlocal parameter on the field quantities. For the sake of completeness a comparison is also made between the present results and those obtained in the case of temperature-independent thermal and mechanical properties.

On dual-phase-lag thermoelasticity theory with memory-dependent derivative

ABSTRACTA new mathematical model of generalized thermoelasticity with memory-dependent derivatives for the dual-phase-lag heat conduction law is constructed. The governing equations of the new model are applied to a half-space subjected to ramp-type heating. Laplace transforms technique is used. The solution is obtained for different types of functions representing the thermal shock and for different values of the parameter of the time fraction derivative of the model. The effects of time-delay and arbitrary kernel function on elastic material are studied and represented graphically. The predictions of the theory are discussed and compared with dynamic classical coupled theory.

Effects of Hall current and two temperatures in transversely isotropic magnetothermoelastic with and without energy dissipation due to ramp-type heat

ABSTRACTThe present article is concerned with the investigation of disturbances in a homogeneous transversely isotropic thermoelastic rotating medium with two temperatures, in the presence of the combined effects of Hall currents and magnetic field. The formulation is applied to the thermoelasticity theories developed by Green-Naghdi theories of type-II and type-III. Laplace and Fourier transform techniques are applied to solve the problem. The analytical expressions of displacements, stress components, temperature change, and current density components are obtained in the transformed domain. A numerical inversion technique has been applied to obtain the results in the physical domain. Numerical simulated results are depicted graphically to show the effect of Hall current and two temperatures on resulting quantities. Some special cases are also deduced from the present investigation.

The effect of magnetic field on a thermoelastic fiber-reinforced material under GN-III theory

In this work, the two-dimensional generalized magneto-thermoelastic problem of a fiber-reinforced anisotropic material is investigated under Green and Naghdi theory of type III. The solution will be obtained for a certain model when the half space subjected to ramp-type heating and traction free surface. Laplace and exponential Fourier transform techniques are used to obtain the analytical solutions in the transformed domain by the eigenvalue approach. The inverses of Fourier transforms are obtained analytically. The results have been verified numerically and are represented graphically. Comparisons are made with the results predicted by the presence and absence of reinforcement and magnetic field.