Conjugate mixed convection with surface radiation from a vertical electronic board with multiple discrete heat sources

The problem of combined conduction-mixed convection-surface radiation from a vertical electronic board provided with three identical flush-mounted discrete heat sources is solved numerically. The cooling medium is air that is considered to be radiatively transparent. The governing equations for fluid flow and heat transfer are converted from primitive variable form to stream function-vorticity formulation. The equations, thus obtained, are normalised and then are converted into algebraic form using a finite volume based finite difference method. The resulting algebraic equations are then solved using Gauss–Seidel iterative method. An optimum grid system comprising 151 grids along the board and 111 grids across the board is chosen. The effects of various parameters, such as modified Richardson number, surface emissivity and thermal conductivity on temperature distribution along the board, maximum board temperature and relative contributions of mixed convection and radiation to heat dissipation are studied in detail. Further, the contributions of free and forced convection components of mixed convection to board temperature distribution and peak board temperature are brought out. The exclusive roles played by surface radiation and buoyancy in the present problem are clearly elucidated.     

Slab radiation with initial temperature distribution described by an odd function

Functions describing global characteristics of the temperature field for the slab radiation with initial temperature distribution described by an odd function are given in a graphical form. This form enables rapidly and easily to determine main features of the process.     

On axisymmetrical problem of layer with temperature dependent properties

The paper deals with the axisymmetrical problem of thermoelastic layer with mechanical properties dependent on temperature. The boundary planes of the body are kept at constant but different temperatures. Moreover, the layer is assumed to be ideal fixed to a rigid foundation. The upper boundary plane is loaded by normal forces dependent on the radius. The considered stationary problem is solved according with the following scheme: (1⁰) firstly the distribution of temperature is found, (2⁰) secondly, assuming that the Young modulus is a power function of temperature and Poisson ratio is constant, the displacements and stress are calculated from adequate boundary value problem. The obtained results in the form of Hankel integrals are analysed numerically for the case of linear dependence of Young modulus on the temperature.     

Temperature maps measurements on 3D surfaces with infrared thermography

The use of the infrared camera as a temperature transducer in wind tunnel applications is convenient and widespread. Nevertheless, the infrared data are available in the form of 2D images while the observed surfaces are often not planar and the reconstruction of temperature maps over them is a critical task. In this work, after recalling the principles of IR thermography, a methodology to rebuild temperature maps on the surfaces of 3D object is proposed. In particular, an optical calibration is applied to the IR camera by means of a novel target plate with control points. The proposed procedure takes also into account the directional emissivity by estimating the viewing angle. All the needed steps are described and analyzed. The advantages given by the proposed method are shown with an experiment in a hypersonic wind tunnel.     

Thermophoresis in natural convection with variable properties

The present paper deals with thermophoresis in natural convection with variable properties for a laminar flow over a cold vertical flat plate. Variation of properties like density, viscosity and thermal conductivity with temperature is included in the formulation of the problem. Selection of components for the property ratio is made by fitting the property values between the desired temperature limits. For a selected fluid, Prandtl number variation with temperature is neglected and the Prandtl number corresponding to film temperature is used for the analysis. Solution is carried out by finite difference method. Variation of wall concentration and wall flux along the length of plate is studied. The effect of thermophoretic coefficient on wall concentration is also studied. Results are presented in the form of graphs. The result is compared with similarity solution by Runge-Kutta method and found to be accurate upto second decimal place. Received on 18 May 1998     

Magneto-thermoelasticity for an infinite body with a spherical cavity and variable material properties without energy dissipation

The model of generalized thermoelasticity proposed by Green and Naghdi, is applied to study the electromagneto–thermoelastic interactions in an infinite perfectly conducting body with a spherical cavity. The modulus of elasticity are taking as linear function of temperature. By means of the Laplace transform and Laplace inversion, the problem is solved. The closed form solutions for displacement, temperature, and thermal stresses are represented graphically. A comparison is made with the results in the case of temperature-independent.     

Natural convection near a vertical plate with ramped wall temperature

The unsteady natural convective flow of an incompressible viscous fluid near a vertical plate has been considered. It is assumed that the bounding plate has a ramped temperature profile. The exact solutions of the energy and momentum equations, under the usual Boussinesq approximation, have been obtained in closed form. There are two different solutions for the fluid velocity—one valid for the fluids of Prandtl numbers different from unity, and the other for which the Prandtl number is unity. The variations of the fluid temperature, velocity as well as the Nusselt number and wall skin friction have been presented graphically. The natural convection near a ramped temperature plate has also been compared with the flow near a plate with constant temperature.     

Two-pass countercrossflow heat exchangers with both fluids unmixed throughout

The aim of this paper is to present the formulas for computing the effectiveness and spatial temperature distribution of each stream and the wall of the two-pass countercrossflow heat exchangers with both fluids unmixed throughout for all possible flow arrangements. Making the usual idealizations for analysis of any heat exchanger flow arrangement and giving the coupling conditions for each pass, the problem of finding the spatial temperature distributions in the crossflow heat exchanger core is reduced to the solution of Fredholm's second order integral equation. By using the collocation method the solution of this integral equation is obtainable in the form of power series. The explicit formulas for the spatial temperature distributions and effectiveness are then obtained by simple integrations. The new relations are particularly helpful for computer-aided design procedures of two-pass countercrossflow heat exchangers.     

The sputtering temperature of a cooling cylindrical rod with an insulated core

By a standard application of Jones's method associated with the Wiener-Hopf technique an explicit solution is obtained for the temperature distribution inside a cylindrical rod with an insulated inner core when the rod is allowed to enter into a fluid of large extent with a uniform speed, and a simple integral expression is derived for the value of the sputtering temperature of the rod at the points of entry. Numerical results under certain special circumstances are also obtained and presented in the form of a table.     

Peristaltic flow of a nanofluid with slip effects

The problem of peristaltic flow of a nanofluid in an asymmetric channel is analyzed by taking into account the slip effects. The relevant equations for the nanofluid are presented and simplified by the long wavelength and small Reynolds number. Closed form solutions for stream function and pressure gradient are developed. However series expressions for temperature and Nanoparticle profiles are constructed. Finally, the influence of several parameters on the physical quantities of interest is discussed.     

State space approach to the generalized thermoelastic problem with temperature-dependent elastic moduli and internal heat sources

A two-dimensional equation of generalized thermoelasticity with one relaxation time in an isotropic elastic medium with the elastic modulus dependent on temperature and with an internal heat source is established using a Laplace transform in time and a Fourier transform in the space variable. The problem for the transforms is solved in the space of states. The problem of heating of the upper and the lower surface of a plate of great thickness by an exponential time law is considered. Expressions for displacements, temperature, and stresses are obtained in the transform domain. The inverse transform is obtained using a numerical method. Results of solving the problem are presented in graphical form. Comparisons are made with the results predicted by the coupled theory and with the case of temperature independence of the elastic modulus.     

Transient hyperbolic heat conduction in thick-walled FGM cylinders and spheres with exponentially-varying properties

This paper focuses on non-Fourier hyperbolic heat conduction analysis for heterogeneous hollow cylinders and spheres made of functionally graded material (FGM). All the material properties vary exponentially across the thickness, except for the thermal relaxation parameter which is taken to be constant. The cylinder and sphere are considered to be cylindrically and spherically symmetric, respectively, leading to one-dimensional heat conduction problems. The problems are solved analytically in the Laplace domain, and the results obtained are transformed to the real-time space using the modified Durbin’s numerical inversion method. The transient responses of temperature and heat flux are investigated for different inhomogeneity parameters and relative temperature change values. The comparisons of temperature distribution and heat flux between various time and material properties are presented in the form of graphs.     

Uncoupled thermoelastic analysis for a thick cylinder with radiation

An attempt has been made to study the uncoupled thermoelastic response of thick cylinder of length 2h in which heat sources are generated according to the linear function of the temperature, with boundary conditions of the radiation type. This approach is based upon integral transform techniques, to find out the thermoelastic solution. The results are obtained in terms of Bessel functions in the form of infinite series.     

Transient natural convection along a vertical clyinder with variable surface temperature and mass diffusion

A numerical study is carried out for thermal and concentration driven transient natural convection adjacent to a vertical cylinder. The temperature and concentration level at the cylinder surface are assumed to vary as power-law type functions, with exponents n and m respectively in the streamwise co-ordinate. The governing boundary layer equations are converted into a non-dimensional form. A Crank-Nicolson type of implicit finite-difference method is used to solve the governing non-linear set of equations. Numerical results are obtained and presented with various thermal and mass Grashof numbers and power law variations. Transient effects of velocity, temperature and concentration are analyzed. Local and average skin-friction, Nusselt number and Sherwood number are shown graphically.     

Circular shallow spherical shells with central circular hole under simultaneous actions of arbitrary unsteady temperature field and arbitrary dynamic normal load

In this paper, under assumption that tempeature is linearly distributed along the thickness of the shell, we deal with problems as indicated in the title and obtain general solutions of them which are expressed in analytic form.In the first part, we investigate free vibration of circular shallow spherical shells with circular holes at the center under usual arbitrary boundary conditions. As an example, we calculate fundamental natural frequency of a circular shallow spherical shell whose edge is fixed (m=0). Results we get are expressed in analytic form and check well with E. Reissner’s [1]. Method for calculating frequency equation is recently suggested by Chien Wei-zang and is to be introduced in appendix 3.In the second part, we investigate forced vibration of shells as indicated in the title under arbitrary harmonic temperature field and arbitrary harmonic dynamic normal load.In the third part, we investigate forced vibration of the above mentioned shells with initial conditions under arbitrary unsteady temperature field and arbitrary normal load.In appendix 1 and 2, we discuss how to express displacement boundary conditions with stress function and boundary conditions in the case m=1.     

Effect of magneto-thermo-viscoelasticity in an unbounded body with a spherical cavity subjected to a harmonically varying temperature without energy dissipation

The present work is devoted to study effects of the thermally induced vibration, magnetic field and viscoelasticity in an isotropic homogeneous unbounded body with a spherical cavity. The GN model of thermoelasticity without energy dissipation is applied. The closed form solutions for distributions of displacement, temperature and radial and hoop stresses are illustrated. The boundary conditions for the temperature and mechanical and Maxwell’s stresses are employed. The solutions valid in the case of small frequency are deduced and the results are compared with the corresponding results obtained in other generalized thermoelasticity theories. The results obtained are calculated for a copper material and presented graphically. It’s deduced that the magnetic field, viscosity and thermally induced vibration are very pronounced on displacement, temperature and stresses.     

Generalized thermoelastic problem of an infinite body with a spherical cavity under dual-phase-lags

The aim of the present contribution is the determination of the thermoelastic temperatures, stress, displacement, and strain in an infinite isotropic elastic body with a spherical cavity in the context of the mechanism of the two-temperature generalized thermoelasticity theory (2TT). The two-temperature Lord–Shulman (2TLS) model and two-temperature dual-phase-lag (2TDP) model of thermoelasticity are combined into a unified formulation with unified parameters. The medium is assumed to be initially quiescent. The basic equations are written in the form of a vector matrix differential equation in the Laplace transform domain, which is then solved by the state-space approach. The expressions for the conductive temperature and elongation are obtained at small times. The numerical inversion of the transformed solutions is carried out by using the Fourier-series expansion technique. A comparative study is performed for the thermoelastic stresses, conductive temperature, thermodynamic temperature, displacement, and elongation computed by using the Lord–Shulman and dual-phase-lag models.     

Radiation effect on optimum design analysis of a constructal T-shaped fin with variable thermal conductivity

A constructal T-shaped fin with temperature dependent thermal conductivity of fin the material exposed to both convective and radiative environments is analyzed by Adomian decomposition method. This method provides a closed form of analytical solution for analyzing the temperature distribution, performance and optimum design. A comparative study has been executed among the present and published works. Unlike the published work, dependent parameters on the performance and optimization analysis are highlighted.     

Photothermoelastic study of stress concentrations in a plate with internal heating

This paper describes a photothermoelastic method for simulating, in a three-dimensional model, the temperature gradients that occur in structural parts subjected to internal heating such as is frequently encountered in certain areas of nuclear-reactor design. The method is applied to a plate which has a step change in thickness and sustains a nonlinear temperature gradient through its thickness. The shapes of the gradients simulate internal heating of the plate material. The values for the highest stresses on the free surfaces of the plate, within the thickness of the plate, and at the root of the step are presented in graphical form for a range of internal heat-generated conditions. Thermal-stress-concentration factors are presented for a step change in the thickness of a plate under this type of heating. Its design significance is discussed. The same stress and stress-concentration values are shown to also apply to nonnuclear problems. During shut-down in conventional thermal plants, when the walls sustain linear steady-state temperature drops across their thicknesses, temperature profiles exactly analogous to those presented in this paper occur. The stresses can then be computed from the values presented here.     

Experimental investigation of the temperature stratification of an air flow through a supersonic channel with a central body in the form of a porous permeable tube

The results of an experimental investigation of the gasdynamic temperature separation (stratification) of a supersonic air flow are presented. It is shown that in an axisymmetric supersonic channel the presence of a central body in the form of a cylindrical tube consisting of impermeable and permeable sections leads to the redistribution of the total energy of the flow. At the central body exit the mass-mean stagnation temperature of the air increases compared with its initial temperature.