The conjugate heat transfer from an internal heated small strip in a forced laminar flow

 An asymptotic and numerical investigation was conducted for the cooling process, by a forced laminar flow, of a small strip with a non-uniform heat source. The nondimensional temperature distribution in the strip has been obtained as a function of the following parameters: (a) the intensity and distribution of the internal heat sources, (b) the aspect ratio of the strip, (c) the longitudinal heat conductance of the strip and (d) the Prandtl number of the fluid. Both the thermally thin as the thick wall approximations were considered in this paper. The total thermal energy or averaged temperature of the strip is found to decrease as the influence of the longitudinal heat conduction effects in the strip decreases in the thermally thin wall regime. After reaching a minimum, it increases again in the thermally thick wall regime. Received on 19 May 2000     

Conjugate free convection along a thin vertical plate with internal nonuniform heat generation in a porous medium

 The steady state heat transfer characteristics of a thin vertical strip with internal heat generation placed in a porous medium is studied in this work. The non-dimensional temperature distribution in the strip is obtained as a function of the intensity and distribution of the internal heat sources. Both the thermally thin as the thick wall approximations are considered in this paper. The mass flow rate of fluid induced by heating the strip decreases as the longitudinal heat conduction effects along the strip decreases. Received on 22 November 2000 / Published online: 29 November 2001     

Natural convection in a vertical strip immersed in a porous medium

In this work, the conjugated heat transfer characteristics of a thin vertical strip of finite length, placed in a porous medium has been studied using numerical and asymptotic techniques. The nondimensional temperature distribution in the strip and the reduced Nusselt number at the top of the strip are obtained as a function of the thermal penetration parameter s, which measures the thermal region where the temperature of the strip decays to the ambient temperature of the surrounding fluid. The numerical values of this nondimensional parameter permits to classify the different physical regimes, showing different solutions: a thermally long behaviour, an intermediate transition and a short strip limit.     

The 1-D heat transfer through a flat plate exposed to out of phase step changes in the free stream temperatures

 The thermal response of an infinite flat plate is considered, when the temperatures of both the surrounding fluids undergo step changes. The configuration is a simplified model for the heat transfer through the separating wall in the isochoric countercurrent heat exchanger (ICHE). The step changes appear with a time delay. The plate temperature, surface heat fluxes and accumulated energy perturbations are evaluated for both the thermally thick and thin cases and the corresponding results are compared. The results show a significant influence of the delay time and a smaller one for the Biot numbers, especially when their sum exceeds the value of 0.1. Received on 19 December 2000 / Published online: 29 November 2001     

Effect of wall emissivities on radiation heat transfer in glass tank forehearths

In an earlier work, we had proposed a two-band, nongrey radiative transfer model for heat transfer in forehearths with simultaneous optically thick and thin approximations for molten glass interiors and at boundaries. Here using the same model, the radiative interaction of the top-crown and bottomrefratory walls with interior layers of shallow molton glass is studied by varying the wall emissivities. The forehearth exit temperature profiles for higher wall emissivities (0.9) show better conditioning of the glass for white flint glasses (optically thin).     

Flow and heat transfer characteristics behind vortex generators - A benchmark dataset

The velocity field and wall heat transfer distributions for internal flows in the presence of longitudinal vortices have been experimentally investigated. A transient method based on temperature measurement with thermochromic liquid crystals was used to obtain the heat transfer distribution behind a tetrahedral, full-body vortex generator. With the focus on the longitudinal vortices, the flow field was captured by a three-component particle image velocimetry system. Mean values as well as velocity fluctuations have been assessed. The combined investigation of heat transfer and flow field describes in detail the physical conditions. For a channel Reynolds number of 300,000 a dataset has been obtained, which can be used for validation of numerical models.     

Buoyant flow in long vertical enclosures in the presence of a strong horizontal magnetic field. Part 2. Finite enclosures

Numerical computations and experiments were carried out for a buoyant flow of liquid metal (mercury in the experiments) in a long vertical enclosure of square cross-section, in the presence of a uniform horizontal magnetic field. A strong emphasis is put on the case of a magnetic field perpendicular to the applied temperature gradient for two reasons: (1) the MHD damping is smaller than with any other orientation, and (2) the quasi-two-dimensionality of the flow in this case yields a quite efficient velocity measurement technique. The enclosure is heated by a thermally controlled flow of water from one of the vertical walls and cooled by a similar technique from the facing wall. Those two walls are good thermal conductors (thick copper plates in the experiments), whereas the four other walls are thermally insulating. All walls are electrically insulated from the fluid. In this paper, as well as in the companion paper by Tagawa et al. (Eur. J. Mech. B Fluids 21 (4) (2002) 383–398), we model analytically the Hartmann layers present along the walls perpendicular to the magnetic field. This modeling, which yields boundary conditions for the core flow without any meshing of the thin layers, is quite accurate when Hartmann layers are stable. The numerical results are in fairly good agreement with the experimental data. They namely reveal how the heat flux and the fluid flow organization depend on the magnetic field.     

Conjugate Phase Change Heat Transfer in an Inclined Compound Cavity Partially Filled with a Porous Medium: A Deformed Mesh Approach

In this paper, the melting process of a PCM inside an inclined compound enclosure partially filled with a porous medium is theoretically addressed using a novel deformed mesh method. The sub-domain area of the compound enclosure is made of a porous layer and clear region. The right wall of the enclosure is adjacent to the clear region and is subject to a constant temperature of T_c. The left wall, which is connected to the porous layer, is thick and thermally conductive. The thick wall is partially subject to the hot temperature of T_h. The remaining borders of the enclosure are well insulated. The governing equations for flow and heat transfer, including the phase change effects and conjugate heat transfer at the thick wall, are introduced and transformed into a non-dimensional form. A deformed grid method is utilized to track the phase change front in the solid and liquid regions. The melting front movement is controlled by the Stefan condition. The finite element method, along with Arbitrary Eulerian–Lagrangian (ALE) moving grid technique, is employed to solve the non-dimensional governing equations. The modeling approach and the accuracy of the utilized numerical approach are verified by comparison of the results with several experimental and numerical studies, available in the literature. The effect of conjugate wall thickness, inclination angle, and the porous layer thickness on the phase change heat transfer of PCM is investigated. The outcomes show that the rates of melting and heat transfer are enhanced as the thickness of the porous layer increases. The melting rate is the highest when the inclination angle of the enclosure is 45°. An increase in the wall thickness improves the melting rate.

     

Ultra fast cooling of hot steel plate by air atomized spray with salt solution

In the present study, the applicability of air atomized spray with the salt added water has been studied for ultra fast cooling (UFC) of a 6 mm thick AISI-304 hot steel plate. The investigation includes the effect of salt (NaCl and MgSO₄) concentration and spray mass flux on the cooling rate. The initial temperature of the steel plate before the commencement of cooling is kept at 900 °C or above, which is usually observed as the “finish rolling temperature” in the hot strip mill of a steel plant. The heat transfer analysis shows that air atomized spray with the MgSO₄ salt produces 1.5 times higher cooling rate than atomized spray with the pure water, whereas air atomized spray with NaCl produces only 1.2 times higher cooling rate. In transition boiling regime, the salt deposition occurs which causes enhancement in heat transfer rate by conduction. Moreover, surface tension is the governing parameter behind the vapour film instability and this length scale increases with increase in surface tension of coolant. Overall, the achieved cooling rates produced by both types of salt added air atomized spray are found to be in the UFC regime.     

Effects of viscous dissipation on laminar forced convection with axially periodic wall heat flux

The laminar forced convection in a circular duct is investigated in the case of a sinusoidal axial variation of the wall heat flux. The axial heat conduction in the fluid is neglected, while the effect of viscous dissipation is taken into account. The heat transfer in the thermally developed region, where the temperature is the sum of a linear function and a periodic function of the axial coordinate, is analysed. Both the temperature field and the local Nusselt number are evaluated analytically. Comparisons with the solution in the absence of viscous heating are performed. It is shown that the effect of viscous dissipation on the temperature field may be relevant especially in the case of a sinusoidal wall heat flux distribution with a vanishing mean value. Received on 24 July 1998     

On the thermal boundary layer on an electrode

In the present paper we consider the approximate calculation of the temperature distribution in a MHD channel operating in the accelerator regime with account for the dependence of the electrical conductance and thermal conductance coefficients on the temperature and with account for Joule dissipation. If the plasma temperature in the channel is about 10⁴ K, then the Prandtl number is much less than unity. Therefore the length of the inlet dynamic segment is much greater than the inlet thermal segment, and we can neglect the transverse velocity component. This permits solving the problem without imposing any constraint on the longitudinal velocity and density. Moreover, under certain conditions we can neglect the term with the pressure gradient in comparison with the Joulean dissipation in the heat transport equation, which permits separation of the thermal problem from the dynamic. In the study we investigate the length of the inlet thermal segment, the heat exchange at the channel wall as a function of the wall temperature, and we also analyze the applicability of the suggested method of calculation.     

A heat transfer measurement of jet impingement with high injection temperature

Local heat transfer from an impinging high temperature jet is studied using a method based on the heat thin foil technique and on the infrared thermography. Heat thin foil technique is used to impose several heat fluxes. For each flux, the temperature distribution is recorded using infrared imaging. Local heat transfer coefficients and adiabatic wall temperatures are determined by means of a linear regression method. This procedure is validated for a single round jet impinging on a flat plate for a range of injection temperatures. To cite this article: M. Fénot et al., C. R. Mecanique 333 (2005).     

Certain optimum forms of radiating bodies in supersonic gas flow

We solve two variational problems on determining the optimum form of a radiating body of given dimensions in a gas flow at high supersonic velocity with a laminar flow regime in the boundary layer. We consider the case in which two heat transfer processes are significant: convective heat transfer from the gas to the body and radiation from the body surface. The first problem involves finding the contour of the body which receives the minimal thermal flux. In the solution of the second problem we seek that form of the thermally isolated body for which its surface temperature will be minimal for given parameters of the approaching stream or for which the motion velocity will be maximal for a given wall temperature and flight altitude.     

Mixed convection in non-Newtonian fluids along nonisothermal horizontal surfaces in porous media

A nonsimilar boundary layer analysis is presented for the problem of mixed convection in power-law type non-Newtonian fluids along horizontal surfaces with variable wall temperature distribution. The mixed convection regime is divided into two regions, namely, the forced convection dominated regime and the free convection dominated regime. The two solutions are matched. Numerical results are presented for the details of the velocity and temperature fields. A discussion is provided for the effect of viscosity index on the surface heat transfer rate. Received on 11 March 1997     

Quantification of ignition time uncertainty based on the classical ignition theory and Fourier analysis

This study aims at modeling the effect of incoming heat flux fluctuations, on solid material ignition. In order to propose a general methodology based on the classical ignition theory that can be applied to any kind of solid target, kernels accounting for the target temperature response regarding an incoming heat flux are considered for thermally thick and thin solids with low or high thermal inertia. A Fourier decomposition of the incoming heat flux is then used to calculate the target response to harmonic heat fluxes. Finally, effects of harmonic fluctuations on ignition are discussed based on the previous analytical results, allowing us to discriminate situations where ignition time is expected to be rather predictable from situations where ignition time is expected to be less predictable thanks to an uncertainty quantification of the ignition time.     

Heat transfer for non-Newtonian laminar flow in internally finned pipes with uniform temperature

An analysis is presented for fully developed laminar convective heat transfer of non-Newtonian power-law fluids in pipes with internal longitudinal fins and uniform outside wall temperature. The governing momentum and energy equations have been solved numerically, with the influence of fin conductance. The distributions of fin temperature, fluid temperature and local heat flux (both at finned and unfinned surfaces) are presented. These are shown to be strongly dependent on finned pipe geometry, fluid flow behavior index and the fin conductance. Values of overall Nusselt number indicated significant heat transfer enhancement over finless pipes. The flow behavior index affects the no. of fins which maximizes the overall Nusselt number.     

Thermally developing flow in curved square ducts with internal fins

The laminar incompressible hydrodynamically fully developed and thermally developing flow is studied in a curved square duct with four longitudinal fins. The duct is successively subjected to constant wall temperature, to circumferentially uniform temperature and axially linearly or exponentially varying temperature. The local and fully developed Nusselt numbers are examined for various values of the Dean number and it is found that the heat transfer rate increases for high fins. The parameters that affect the entry length are studied and the fluctuations of the local Nu that appear in the entrance region are investigated. Temperature contour plots are presented for the visualization of the temperature field and functional relations for the Nusselt number are proposed in terms of the Dean and Prandtl numbers.     

Effect of longitudinal surface curvature on heat transfer

The effect of longitudinal surface curvature on heat transfer has been analysed for laminar forced convection by the method of matched asymptotic expansions. Utilizing the classical solution of boundary layer equations as the first order approximations, the second order perturbation for the velocity and temperature field has been calculated by a similarity analysis. The analysis permits the wall temperature to vary as a power function of distance from the stagnation point. Numerical solutions have been obtained for the resulting coupled ordinary differential equations. The results for the variation in the second order temperature profile and the second order wall temperature gradient due to surface curvature parameter, Prandtl number, wall temperature distribution parameter, and pressure gradient parameters are presented graphically. The variation in a typical temperature profile due to curvature, and percentage variations from the first order theory due to longitudinal surface curvature are also presented graphically.     

Heat transfer to non-newtonian laminar falling liquid films with smooth wave free gas—liquid interface

The present paper investigates analytically the problem of heat transfer to a non-Newtonian laminar falling liquid film flowing along an inclined wall for the thermally developing and thermally developed regions. In the developing region of the temperature profile, the Nusselt number decreases monotonically until the thermal boundary layer touches the interface. But immediately after this point, the liquid film thickness decreases as well as the temperature difference in the film. The influence of parameters such as α (i.e. Fr/Re_mod ratio), γ (i.e. modified form of ?μ), modified Prandtl number and the flow behaviour index “n’ on heat transfer results is also presented.