Arbitrary Temperature Distribution Research Articles

Response of a sandwich panel subject to fire or elevated temperature on one of the surfaces

The paper presents the analysis of deformations and stresses in a large aspect ratio sandwich panel subject to fire or another source of elevated temperature. The panel, assumed to bend into a cylindrical surface, is simply supported at the edges. The edges are also prevented from in-plane displacements providing an elastic restraint as the panel stretches due to bending. The solution is obtained in a closed form when the deformations are small and when geometrically nonlinear effects are incorporated into the analysis. The solution is open to modification with arbitrary temperature and property distributions through the thickness of the panel, enabling a designer to incorporate the results from a multitude of heat transfer scenarios so long as the structural problem can be treated as quasi-static.

Plane Thermal Stress Analysis of an Orthotropic Cylinder Subjected to an Arbitrary, Transient, Asymmetric Temperature Distribution

A closed-form, analytical solution is presented for the transient, plane thermal stress analysis of a linearly elastic, homogeneously orthotropic hollow cylinder subjected to an arbitrary temperature distribution. The thermoelastic solution, obtained by a stress function approach, can be used as the basis for the corresponding thermoviscoelastic solution for thermorheologically simple viscoelastic materials by invoking the viscoelastic Correspondence Principle. This solution can also be directly extended to the class of weakly inhomogeneously orthotropic cylinders using perturbation methods. The transient asymmetric temperature field is characterized by Fourier-Bessel eigenfunction expansions. The analytically derived stress function satisfies a linear, fourth-order inhomogeneous partial differential equation and the Cesaro integral conditions, which assure the existence of a single-valued displacement field. The corresponding thermal stresses are then computed by the stress-stress function relations. A key feature of the analytical solution is that the hoop, radial, and shear stresses, due to the transient arbitrary temperature distribution, are expressed explicitly in terms of the scalar temperature field. A polymer composite example is presented to validate the current method and to qualitatively illustrate the distribution of thermal stresses due to an asymmetric temperature distribution. Numerical results are presented for the thermally driven hoop, radial and (interlaminar) shear stresses in a hollow, hoop-wound glass/epoxy cylinder. This analysis demonstrates that potentially debilitating interlaminar shear stresses can develop in laminated composites when subjected to an even modest transient asymmetric temperature distribution. Their magnitudes depend on the severity of the spatial and temporal thermal gradients in the circumferential direction. While still relatively low compared to the hoop stress, the shear stress may cause thermal failure due to the typically low interlaminar shear strengths of laminated composite materials.

Thermoelasticity Solutions for Straight Beams

This paper presents a thermoelastic solution technique for beams with arbitrary quasi-static temperature distributions that create large transverse normal and shear stresses. This technique calculates the stress resultants and centroid displacements along a beam. Then, the stress resultants and temperature distribution are used to calculate the stress distributions on a cross section of the beam. Simple examples demonstrate the numerical efficiency of the proposed technique and the inadequacy of the strength of materials theory to solve these types of problems.

Thermal Calculation and Study of Local and Integral Thermal Characteristics of Finned Surfaces with Conjugate Formulation of the Problem

A technique for thermal calculation of developed heat transfer surfaces in the conjugate formulation of the problem is developed on the basis of integral methods of thermal calculation of the transfer equations for an outer heat carrier. New functional relations for a heat flux removed on the surface with an arbitrary temperature distribution are obtained for a turbulent boundary layer and a developed channel flow with natural convection. Thermal calculation is conducted and local and integral characteristics of a vertical surface with continuous finning in a developed flow of a heat carrier in an inner plane channel and free-convective cooling of the outer finned surface are obtained.

Thermal stresses in work rolls during the rolling of metal strip

Abstract In the strip-rolling process, inadequate work roll cooling often produces high roll temperature and temperature gradients. High thermal stresses resulting from high temperature gradients are responsible for roll surface cracking and spalling. An understanding of the thermal induced stresses is essential toward evaluating roll wear and designing a proper roll-cooling system for increasing roll life and securing better product quality. In this paper, a quasi-static thermal stress solution presented in integral form is developed for an arbitrary temperature distribution in the work roll. The importance of mechanical and thermal stresses in the work roll under cold rolling and hot rolling conditions is investigated.

Threshold condition for traveling wave excitation in an annular prime-mover

The threshold condition for thermoacoustic instability in an annular prime-mover is derived. The region of spatially inhomogeneous temperature distribution (due to the presence of a stack and hot and cold heat exchangers) is assumed to be acoustically thin. The interaction of acoustic waves with the stack is assumed to be quasiadiabatic. Theoretical approach (based on the transformation of differential wave equation into Volterra integral equation, which is solved by iterative procedure) is valid for arbitrary spatial temperature distribution. Nevertheless, it was found that the threshold for the excitation of a traveling acoustic wave does not depend on the details of temperature spatial distribution but just on the ratio of the temperatures of hot and cold heat exchangers. Moreover, the critical temperature ratio does not depend on the thickness of the stack if the acoustic losses inside the heated region are negligible in comparison with acoustic losses in the rest part of the annular system. In this important limiting case critical temperature ratio diminishes when the dimensions of the system are scaled up. [Work supported by DGA.]

Forced convection heat transfer from a heated circular cylinder with arbitrary surface temperature distributions

A Fredholm-type boundary integral expression for evaluation of the forced convection heat transfer from an object with arbitrary surface temperature distributions is proposed. The Fredholm kernel function for a heated circular cylinder was calculated by numerical simulation of the forced convection fields, and then generalized heat transfer coefficients for arbitrary surface temperature distributions were defined. By use of the generalized heat transfer coefficients, it is shown that the difference in local heat transfer characteristics between the case of an isothermal cylinder and that of a uniform heat flux one can be interpreted only as the difference of the surface temperature distributions. Moreover, the mechanism of the effect of the surface temperature distribution on the characteristics of forced convection heat transfer from a cylinder is clarified in detail through the generalized heat transfer coefficients. © 1999 Scripta Technica, Heat Trans Asian Res, 28(6): 484–499, 1999

Forced convection heat transfer from a heated circular cylinder with arbitrary surface temperature distributions

A Fredholm-type boundary integral expression for evaluation of the forced convection heat transfer from an object with arbitrary surface temperature distributions is proposed. The Fredholm kernel function for a heated circular cylinder was calculated by numerical simulation of the forced convection fields, and then generalized heat transfer coefficients for arbitrary surface temperature distributions were defined. By use of the generalized heat transfer coefficients, it is shown that the difference in local heat transfer characteristics between the case of an isothermal cylinder and that of a uniform heat flux one can be interpreted only as the difference of the surface temperature distributions. Moreover, the mechanism of the effect of the surface temperature distribution on the characteristics of forced convection heat transfer from a cylinder is clarified in detail through the generalized heat transfer coefficients. © 1999 Scripta Technica, Heat Trans Asian Res, 28(6): 484–499, 1999

Thermal boundary condition effects on forced convection heat transfer

We propose a numerical solution of an adjoint problem of forced convection heat transfer to evaluate the mean heat transfer characteristics under arbitrary thermal boundary conditions. Using the numerical solution of the adjoint problem under the Dirichlet condition, which can be computed by slightly modifying a conventional heat transfer code, we obtain an influence function of local surface temperature on total heat transfer. As a result, the total heat transfer for arbitrary surface temperature distributions can be calculated by the influence function. Similarly, using the numerical solution of the adjoint problem under the Neumann condition, we can also obtain an influence function of the local heat flux on the mean surface temperature. The influence functions for a circular cylinder and for an in-line square rod array are presented to illustrate the capability of this method. © 1999 Scripta Technica, Heat Trans Asian Res, 28(3): 227–238, 1999

Thermal Boundary Condition Effects on Forced Convection Heat Transfer. Application of Numerical Solution of Adjoint Problem.

A numerical approach based on the adjoint formulation of forced convection heat transfer is proposed, to evaluate the total or mean heat transfer rate under arbitrary thermal boundary conditions. Using the numerical solution of the adjoint problem under the uniform Dirichlet condition, which can be computed by a slightly modified CFD code, an influence function of the local surface temperature can be obtained. As a result, the total heat transfer for arbitrary surface temperature distributions can be calculated by the influence function. In a similar fashion, using the numerical solution of the adjoint problem under the Neumann condition, the mean surface temperature can also be expressed as an influence function of the local heat flux distributions. The influence functions for a circular cylinder and for an in-line square rod array are presented to illustrate the present method.

Forced convection heat transfer from a heated circular cylinder with arbitrary surface temperature distributions

Forced convection heat transfer from a heated circular cylinder with arbitrary surface temperature distributions

The Cosserat spectrum in the theory of elasticity and applications

The homogeneous Navier equations o2 u + yo(o· u ) = 0, (y = (u + w)/w = 1/(1-2 v ), with homogeneous boundary conditions of place or traction admit non-trivial solutions when y takes values in a set of points (lying of course outside the physical range for Poisson's ratio) called the Cosserat spectrum. The properties of the spectrum and the corresponding eigenfunctions were studied by S.G. Mikhlin who proved completeness, and orthogonality, to be reviewed here briefly. By using these properties we investigate how solutions of the equations of elasticity depend on Poisson's ratio. Furthermore we show that any eigenfunction u of the above eigenvalue problem may be visualized as displacement in an equilibrium thermoelastic problem with temperature distributions T div u . Using that the collection of the divergences of the eigenfunctions is complete in L 2 we are able to expand the solutions of the equilibrium equations of thermoelasticity under arbitrary temperature distribution in a rapidly convergent series of the eigenfunctions. We prove that the eigenfunctions can be characterized as stationary points of the Helmholtz free energy (and elastic energy) under the constraint that the thermal part of the free energy Z T 2dV is constant.

Measurements of heat transfer in a separated and reattaching flow with spatially varying thermal boundary conditions

Abstract The effect of highly varying thermal boundary conditions on the convective heat transfer in a backward-facing step flow was investigated in a two-dimensional (2D) boundary-layer tunnel in air. A modified form of the transient heat transfer technique was used that allowed variable surface temperature distributions to be imposed by heating the test surface with a radiative lamp prior to cooling. The experiments were restricted to axial variations in surface temperature. Surface temperatures were measured with both cement-on foil thermocouples and thermochromic liquid crystal thermography. A semianalytic superposition technique was developed that was capable of predicting the heat transfer for any arbitrary axial surface temperature distribution, given the general solution or “Green's” function. The Green's function was measured to a limited spatial resolution by solving a simultaneous set of equations using data from 30 experiments. The techniques were developed and tested in a 2-D flat-plate boundary layer with Re δ2 of 3500 at the leading edge and qualified against a well-verified boundary-layer code. The Green's function and inverse Green's function were then measured in a turbulent backward-facing step flow with Re based on step height of 26,000. In the separated flow, it was found that the effect of localized heating extended only a short distance upstream and downstream, and that the heat transfer was less sensitive to temperature boundary conditions than would be expected from attached flow behavior. This corroborates the conclusion of previous workers that the primary resistance to the heat transfer is localized near the wall. This localized behavior, and the spatial insensitivity of the Green's function, suggest that with proper scaling, the results could be extended to other separated flows.

Forced Convection Heat Transfer from a Heated Circular Cylinder with Arbitrary Surface Temperature Distributions.

A Fredholm-type boundary integral expression for evaluation of the forced convection heat transfer from an object with arbitrary surface temperature distributions is proposed. The Fredholm kernel function for a heated circular cylinder was calculated by numerical simulation of the forced convection fields, and then generalized heat transfer coefficients for arbitrary surface temperature distributions were defined. By use of the generalized heat transfer coefficients, it is shown that the difference in local heat transfer characteristics between the case of an isothermal cylinder and that of a uniform heat flux one can be explained only as the difference of the surface temperature distributions. Moreover, the mechanism of the effect of the surface temperature distribution on the characteristics of forced convection heat transfer from a cylinder is clarified in detail through the generalized heat transfer coefficients.

Fredholm-Type Boundary Integral Expression of Forced Convection Heat Transfer and Its Application to Convection-Conduction Conjugated Heat Transfer Problem.

We propose a Fredholm-type boundary integral expression of the forced convection heat transfer coefficient from an object. When the Fredholm's kernel function is obtained by a numerical simulation of the forced convection field, it is possible to predict the local heat transfer coefficient from the object with arbitrary surface temperature distributions. Moreover, this expression can be easily applied to the boundary element method(BEM)as a boundary condition of fourth kind, and then the convection-conduction conjugated heat transfer problem can be formulated as a heat conduction problem. Some examples demonstrate the usefulness of the proposed expression.

Stress Intensity Factor of Circumferential Crack of Cylinders under Radial Temperature Distribution.

A simole equation to approximately calculate the stress intensity factor of the circumferential crack of cylinders under axisymmetric bending was derived first. By applying it, and equation to evaluate the stress intensity factor for the same crack under thermal stress distribution with practically sufficient accuracy was deduced theoretically. The latter equation is valid for arbitrary axisymmetric temperature distribution, which has its gradient in the radial direction. The effect of the length of the cylinder on the stress intensity factor can be evaluated by using the equation. Investigation of the characteristics of the stress intensity factor of cylinders under radial temperature distribution was conducted, by using the equation. It was shown that the stress intensity factor is in proportion to the'equivalent moment, 'which is calculated from the temperature distribution. In addition, for cylinders with practical dimensions such as Rm/W<20 (Rm : mean radius, W : thickness), the stress intensity factor showed a peak value with the increase of the crack length. The reason the stress intensity factor shows a peak value, was concluded to be because of the fundamental characteristics of the structure of the cylinder, which produces reaction force to close the crack.

Thermal Boundary Condition Effects on Forced Convection Heat Transfer. Application of a Numerical Solution of an Adjoint Problem.

We propose a numerical solution for the adjoint operator of a forced convection heat transfer problem to evaluate mean heat transfer characteristics under arbitrary thermal conditions. Using the numerical solutions of the adjoint problems under Dirichlet and Neumann conditions, both of which can be computed using a conventional CFD code, the influence function of the local surface temperature on the total heat transfer and that of the local surface heat flux on the mean surface temperature are obtained. As a result, the total heat fluxes for arbitrary surface temperature distributions and the mean surface temperatures for arbitrary surface heat flux distributions can be calculations using these influence functions. The influence functions for a circular cylinder and for an in-line square rod array are presented.

Fredholm-Type Integral Expression of Forced Convection Heat Transfer Coefficient and Its Application to Conjugated Heat Transfer Problem.

We propose a Fredholm-type boundary integral expression of the forced convection heat transfer coefficient from an object. When the Fredholm's kernel function is obtained by a numerical simulation of the forced convection field, it is possible to predict the local heat transfer coefficient from the object with arbitrary surface temperature distributions. Moreover, this expression can be easily applied to the boundary element method (BEM), and then the convection-conduction conjugated heat transfer problem can be formulated as a heat conduction problem, Some examples demonstrate the usefulness of the proposed expression.

Study of the analytical solution to the heat transfer problem and surface temperature in a semi-infinite body with a constant heat flux at the surface and an initial temperature distribution

In many practical cases, one heats a semi-infinite solid with a constant heat flux source. For such an unsteady heat transfer problem, if the body has a uniform initial temperature, the analytical solution has been given by Carslaw and Jaeger. The surface temperature of the semi-infinite body follows the $$\sqrt t $$ -rule, that is, the surface temperature changes in proportion to square root of heating time. But if, instead of the uniform initial temperature, the body has a temperature distribution at the beginning of heating, the analytical solution has not yet been developed. Analytical solutions to the same problem with an exponential or a linear initial temperature distribution are obtained in this paper. It is shown, that in the case of a linear initial temperature distribution the surface temperature also changes according to $$\sqrt t $$ -rule Approximating the initial temperature distribution near the surface by its tangent at the surface, it is found that the surface temperature within a short time after the start of heating should also satisfy the $$\sqrt t $$ -rule, in spite of an arbitrary initial temperature distribution. The experimental data support this argument. Furthermore, the constant heat flux can be calculated after relationship between the surface temperature and heating time according to the equation derived in this paper, if the initial temperature distribution or its first-order derivative at the surface is known.

Thermal-image generation by line-scanning technique: a new computer model

A new computer model for the generation of thermal images of a flat terrain by the line-scanning technique from a moving platform is presented. The model is based on a bottom-up simulation process and the pixel-by-pixel generation of infrared thermal images. The terrain is modeled by a periodic repetition of an arbitrary two-dimensional temperature distribution over a flat area. The double discrete Fourier series of the terrain temperature, including correlation length and the transfer function of the scanning optics, is used. Several computer-generated thermal images are produced to illustrate the model. The geometrical deformations, the space filtration, and the gray-level variation with the scanning angle on generated images are in agreement with theoretical predictions.