Temperature stresses in an annular anisotropic plate with temperature-dependent heat transfer coefficient

The nonsteady temperature stresses are determined for an annular plate, an infinite plate with a circular opening, and a circular plate, whose coefficients of heat transfer from the lateral surfaces are functions of temperature.Physico-Mechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. Translated from Mekhanika Polimerov, No. 5, pp. 949–950, September–October, 1971.     

Analytic solutions to heat transfer problems on a basis of determination of a front of heat disturbance

With the use of additional boundary conditions in integral method of heat balance, we obtain analytic solution to nonstationary problem of heat conductivity for infinite plate. Relying on determination of a front of heat disturbance, we perform a division of heat conductivity process into two stages in time. The first stage comes to the end after the front of disturbance arrives the center of the plate. At the second stage the heat exchange occurs at the whole thickness of the plate, and we introduce an additional sought-for function which characterizes the temperature change in its center. Practically the assigned exactness of solutions at both stages is provided by introduction on boundaries of a domain and on the front of heat perturbation the additional boundary conditions. Their fulfillment is equivalent to the sought-for solution in differential equation therein. We show that with the increasing of number of approximations the accuracy of fulfillment of the equation increases. Note that the usage of an integral of heat balance allows the application of the given method for solving differential equations that do not admit a separation of variables (nonlinear, with variable physical properties etc.).     

Response of heat transfer from a moving flat plate in a parabolic flow

This paper deals with the solutions of steady as well as unsteady three-dimensional incompressible thermal boundary layer equations and the study of the response of heat transfer when there is a parabolic flow over a moving flat plate. The components of velocity in boundary layer are discussed by Sarma and Gupta and those results are used to analyse thermal boundary layer equations. A general analysis is made from which we deduce (i) Solutions of two-dimensional thermal boundary layer on a moving flat plate, (ii) Solutions of thermal boundary layer on a yawed flat plate, (iii) Solutions of thermal boundary layer when there is a parabolic flow over a moving flat plate by giving different values to β and Cx. Solutions are developed for large and small times and curves are drawn representing the variations of heat transfer from the plate with time for all the cases. The limiting time is also calculated.     

Speed-optimized control of heating of a thermoelastic plate with the help of internal heat sources

Speed-optimized control of the heating of a plate with restrictions on the thermal stresses is constructed as a junction of the distribution of internal heat sources by the method of the inverse problem of heat conduction.Translated from Matematicheskie Methody i Fiziko-mekhanicheskie Polya, No. 26, pp. 55–59, 1987.     

Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition

The steady laminar boundary layer flow over a permeable flat plate in a uniform free stream, with the bottom surface of the plate is heated by convection from a hot fluid is considered. Similarity solutions for the flow and thermal fields are possible if the mass transpiration rate at the surface and the convective heat transfer from the hot fluid on the lower surface of the plate vary like x^−1/2, where x is the distance from the leading edge of the solid surface. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically. The effects of the governing parameters on the flow and thermal fields are thoroughly examined and discussed.     

On the heat transfer from a finite plate in channel flow for vanishing Prandtl number

Summary The temperature field produced by a finite, hot plate at zero incidence in uniform channel flow is solved exactly for the limiting case of zero prandtl number by means of the Wiener-Hopf technique. The heat transfer on the plate is found to agree with the corresponding boundary layer result over most of the plate for Péclét numbers as low as ten. Extensions to similar Ossen-flow problems are indicated.     

Convective flow and heat transfer of a viscous heat generating fluid in the presence of a moving,infinite, vertical,porous plate

The analysis of convective flow and heat transfer of a viscous heat generating fluid past a uniformly moving, infinite, vertical, porous plate has been made systematically with a view to throw adequate light on the effects of the plate-motion and the presence of heat generation/absorption on the flow and heat transfer characteristics. The equations of conservation of momentum and energy which govern the flow and heat transfer of the said problem have been solved numerically by the method of Runge-Kutta-Gill. The numerical results thus obtained for the flow and heat transfer characteristics have revealed many an interesting behaviour, of the skin friction and the rate of heat transfer coefficient at the plate.     

Group method analysis of magneto-elastico-viscous flow along a semi-infinite flat plate with heat transfer

The group theoretic method is applied for solving problem of the flow of an elastico-viscous liquid past an infinite flat plate in the presence of a magnetic field normal to the plate. The application of one-parameter transformation group reduces the number of independent variables, by one, and consequently the system of governing partial differential equations with boundary conditions reduces to a system of ordinary differential equations with appropriate corresponding conditions. Numerical solution of the velocity field and heat transfer have been obtained. The effect of the magnetic parameter M on velocity field, shear stress, temperature fields and heat transfer has been discussed.     

The influence of coupled diffusion of heat and moisture on the state of stress in a plate

The fundamental results of previous reports on the coupling of the processes of diffusion of heat and moisture in solids are reviewed. The influence of the coupling on diffusion into an infinite plate from both its surfaces is discussed with the aim of clarifying what can and cannot be learned from such experiments. The nonuniformity of temperature and moisture content tends to cause nonuniform deformation. The stresses set up are computed for a homogeneous, isotropic plate. These self-equilibrating stresses first increase with time and then die out. For some combinations of material constants, the stresses undergo a reversal. For example, in some cases the surface stresses initially become compressive as moisture begins diffusing into the plate. Subsequently, as the interior of the plate increases in temperature due to the coupling effect, the surface stresses become tensile before eventually subsiding to zeroPublished in Mekhanika Kompozitnykh Materialov, No. 1, pp. 53–61, January–February, 1980.     

Approximate analytic solution of heat conduction problems with a mismatch between initial and boundary conditions

We consider a heat conduction problem for an infinite plate with a mismatch between initial and boundary conditions. Using the method of integral relations, we obtain an approximate analytic solution to this problem by determining the temperature perturbation front. The solution has a simple form of an algebraic polynomial without special functions. It allows us to determine the temperature state of the plate in the full range of the Fourier numbers (0≤F<∞) and is especially effective for very small time intervals.     

Magnetohydrodynamic free convection flow about a semi-infinite plate at whose surface the heat flux is uniform

Summary The magnetohydrodynamic free convection flow of an electrically conducting fluid past a vertical, semi-infinite plate in a strong cross field has been examined when a uniform heat flux is present at the plate. Formulation in terms of a characteristic length has enabled a full numerical solution to be obtained providing details of skin friction and heat transfer at all stations along the plate for a range of Prandtl numbers appropriate to liquid metal coolants. Series solutions are also presented which give good estimates of the skin friction and heat transfer coefficients.

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Zusammenfassung Die magneto-hydrodynamische Strömung mit freier Konvektion in einer elektrisch leitenden Flüssigkeit entlang einer vertikalen halbunendlichen Platte mit einem gleichförmigen Wärmefluß ist in einem starken Querfeld untersucht worden. Die Einführung einer charakteristischen Länge hat eine vollständige numerische Lösung ermöglicht, die die Reibungskraft und den Wärmeübergang entlang der Platte ergibt, für einen Bereich von Prandtlzahlen geeignet für Flüssigmetallkühler, Reihenlösungen, die gute Schätzungen von Reibungskraft und Wärmeübergangs-Koeffizienten ermöglichen.

     

Computational treatment of free convection effect on flow of elastico-viscous fluid past an accelerated plate with constant heat flux

Effect of free convection on the visco-elastic fluid (Walter - B’ type) flow past an infinite vertical plate accelerating in its own plane with constant heat flux is examined analytically. It is found that for given values of Grashof number, Prandtl number and Newtonian parameter; flow velocity at any point increases with the increase in time and non-Newtonian parameter, however, it decreases with both, the heating and cooling of the plate.     

Inverse modeling of a solar collector involving Fourier and non-Fourier heat conduction

This article applies the golden section search method (GSSM), simplex search method (SSM) and differential evolution (DE) for predicting the unknown Fourier number (Fo), Vernotte number (Ve) and non-dimensional solar heat flux (S¹) in a flat-plate solar collector when subjected to a given temperature requirement. The required temperature field is calculated using an analytical forward method by considering Fourier and non-Fourier heat conduction, and using this, the inverse problem is solved to predict the Fo, Ve and S¹ which are assumed to be the unknown parameters. The study reveals that the temperature field is highly sensitive to the Fo, thus even a small error in the temperature measurement can result in an unrealistic estimation of heating time of the collector. The present study is proposed to be useful in determining the time, the time lag and solar heat flux for controlled heating of an absorber plate within a stipulated time, which will be required to attain a prescribed/desired temperature distribution. Additionally, the study also shows that subjected to different time levels, the same temperature distribution is possible through different absorber plate materials. It has been observed from the present study that apart from SSM and DE, GSSM fails to estimate the unknown parameters at large value of Ve and small value of Fo, due to the associated fluctuation in the measured temperature field. The present study further discusses the computational performance of direct search method (e.g. GSSM and SSM) with that of the evolutionary method (DE) in terms of the maximum number of iteration and CPU time required to achieve the desired objective.     

Numerical study of heat transfer enhancement in mixed convection flow along a vertical plate with heat source/sink utilizing nanofluids

Steady, mixed convection laminar boundary layer flow of incompressible nanofluid along the vertical plate with temperature dependent heat source/sink has been investigated numerically. The resulting non-linear governing equations (obtained with the Boussinesq approximation) are solved, using a robust, extensively validated, variational finite element method (FEM) for both spherical and cylindrical shaped nanoparticles with volume fraction ranging up to 4%, with associated boundary conditions and the effect of the parameters governing the problem are discussed. Different water-based nanofluids containing Cu, Ag, CuO, Al₂O₃, and TiO₂ are taken into consideration. The results show that the average Nusselt number is found to decrease for Ag, Cu, CuO, Al₂O₃, and TiO₂. The present study is of immediate interest in next-generation solar film collectors, heat exchangers technology, materials processing exploiting vertical surfaces, geothermal energy storage and all those processes which are highly affected with heat enhancement concept.     

Optimization of vertical axisymmetric thermal displacements in a round plate using heat sources

We consider the problem of using heat sources for optimal control of the distribution of the vertical axisymmetric thermal displacements of a thin round plate with edge clamped at an angle of revolution. On the basis of the method of the inverse thermoelasticity problem we construct a solution of the control problem. For specific cases of heating the plate we carry out a numerical analysis of the behavior of the optimal control.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Poly a, Issue 36, 1992, pp. 105–110.     

On generalised MHD couette flow with heat transfer

In the case of short-circuited generalised MHD Couette flow the rate of heat transfer, in general, increases with the increase in the value of both the Hartmann number and the pressure gradient. Especially, at the lower stationary plate it is affected by the magnetic field, which is not observed in the case of plane MHD Couette flow.     

Inverse heat conduction problem in a thin circular plate and its thermal deflection

An inverse problem of transient heat conduction in a thin finite circular plate with the given temperature distribution on the interior surface of a thin circular plate being a function of both time and position has been solved with the help of integral transform technique and also determine the thermal deflection on the outer curved surface of a thin circular plate defined as 0 ? r ? a, 0 ? z ? h. The results, obtained in the series form in terms of Bessel’s functions, are illustrated numerically.     

Flow,heat, and species transfer over a stretching plate considering coupled Stefan blowing effects from species transfer

In this paper, we investigate the flow, heat and mass transfer of a viscous fluid flow over a stretching sheet by including the blowing effects of mass transfer under high flux conditions. Mass transfer in this work means species transfer and is different from mass transpiration for permeable walls. The new contribution from this work is, for the first time, to consider the coupled blowing effects from massive species transfer on flow, heat, and species transfer for a stretching plate. Based on the exact solutions of the momentum equations, which are valid for the whole Navier–Stokes equations, the energy and mass transfer equations are solved exactly and the effects of the blowing parameter, the Schmidt number, and the Prandtl number on the flow, heat and mass transfer are presented and discussed. The solution is given in terms of an incomplete Gamma function. It is found the coupled blowing effects due to mass transfer can have significant influences on velocity profiles, drag, heat flux, as well as temperature and concentration profiles. These solutions provide rare results with closed form analytical expressions and can be used as benchmark problem for numerical code validation.     

Influence of eddies on heat transfer in Couette flow

Under creeping flow conditions, we consider the steady Couette flow of a Newtonian fluid between two plates, one of them planar, the other one with a sinusoidal profile. Recent analytical studies on the velocity field revealed the formation of kinematically induced eddies in the valleys of the plate topography and the influence of these eddies on drag force and flow rate. The influence of these eddies on the convective heat transfer is the subject of our paper. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hyperbolic heat conduction in a circular plate from green’s function

We show the existence and uniqueness of Green’s function of the Neumann problem for the axisymmetric hyperbolic heat conduction equation in a circular plate and present its explicit and rigorous computation. As an application, we use this function in order to compute the temperature profile in a circular plate irradiated by a continuous Gaussian laser source.