Boundary Temperature Difference Research Articles

Thermal field of large-diameter concrete filled steel tubular members under solar radiation

Concrete-filled steel tubular (CFST) members have been widely used in engineering, and their tube diameters have become larger and larger. But there is no research on the thermal field of large-diameter CFST structure. These studies focused on the thermal field of the large-diameter CFST structure under solar radiation. The environmental factors and the actual placement position were considered, and the finite element model (FEM) of the thermal field of CFST members under solar radiation (SR) was established. Then the FEM was verified by practical experiments. The most unfavorable temperature gradient model in the cross-section was proposed. The testing results showed that the temperature field of the large-diameter CFST member section was non-linearly distributed due to the influence of SR. The temperature field results of CFST members with different pipe diameters indicated that the larger the core concrete diameter was, the slower the central temperature changed, and there was a significant temperature difference between the center and the boundary. Based on the numerical model, the most unfavorable temperature gradient model in the section was proposed. The model showed that the temperature difference around the center of the circle is small, and the boundary temperature difference is significant. The maximum temperature difference is 15.22oC, which appeared in the southern boundary area of the specimen. Therefore, it is necessary to consider the influence of SR on the thermal field of the member for large-diameter CFST members in actual engineering, which causes a large temperature gradient in the member.

Buoyant flow and instability in a vertical cylindrical porous slab with permeable boundaries

The basic stationary buoyant flow in a vertical annular porous passage induced by a boundary temperature difference is investigated. The vertical cylindrical boundaries are considered both isothermal and permeable to external fluid reservoirs. There exists a stationary parallel velocity field with a zero flow rate and pure conduction heat transfer. Its linear stability is analysed with normal mode perturbations of the pressure and temperature fields. The transition to convective instability is caused by the basic horizontal temperature gradient. Hence, its nature differs from that of the usual Rayleigh–Bénard instability. The linear dynamics of the perturbed flow is formulated as an eigenvalue problem, solved numerically. Its solution provides the neutral stability curve at each fixed aspect ratio between the external radius and the internal radius. The critical Rayleigh number triggering the instability is evaluated for different aspect ratios. It is shown that the system becomes more an more unstable as the aspect ratio increases, with the critical Rayleigh number dropping to zero when the aspect ratio tends to infinity.

Thermal rectification mechanism of one-dimensional composite structure with interface thermal contact resistance

Thermal rectification refers to the phenomenon that heat fluxes or equivalent thermal conductivities are different under the same temperature difference when temperature gradient directions are different. The nature of the thermal rectification is that the structure has different effective thermal conductivities in different directions. Most of previous studies focused on thermal rectification of temperature-dependent thermal conductivity materials or variable cross section area structure, and the effect of thermal contact resistance at the interface was investigated very rarely. In the present paper we present the analytical and finite element numerical solution of temperature field and thermal rectification ratios of a composite structure with variable cross section area and thermal conductivity under different interface thermal contact resistances. The prescribed temperature boundary condition is introduced by penalty method, and the temperature jump condition at the interface is implemented by the definition of thermal contact resistance directly. The nonlinear heat conduction problem caused by temperature-dependent thermal conductivity and interface thermal contact resistance is then solved with a direct iteration scheme. Comparisons between experimental results and the present theoretical and numerical results show the feasibility of the proposed model. Then parameter investigations are also conducted to reveal the effect of some key geometric and material parameters. Numerical results show that thermal contact resistance plays an important role in the temperature field and thermal rectification ratio of the two-segment thermal rectifier. With the increase of the length ratio, thermal ratification ratio increases first and decreases then, and the optimal length ratio varies with both thermal contact resistance and cross-section radius change rate of the two segments. In general, the existence of thermal contact resistance can increase the total thermal resistance of the rectifier and magnify the distinction of the heat flux in forward and reverse cases. However, if the thermal contact resistance is too large, this distinction will decrease and correspondingly the thermal rectification ratio becomes low. With the increase of the boundary temperature difference, thermal rectification ratio increases due to the effect of temperature-dependent thermal conductivity. In the present study, we propose a theoretical and numerical approach to designing and optimizing the length ratio, cross-section radius change rate, thermal conductivity, boundary temperature difference and interface thermal contact resistance to obtain the maximal thermal rectification ratio of a bi-segment thermal rectifier, as well as the manipulation of thermal flux in engineering applications.

Instability of stationary two-dimensional mixed convection across a vertical porous layer

The two-dimensional and stationary mixed convection in a vertical porous layer is studied. This mixed convection flow is caused by the pressure and temperature difference between the parallel boundaries of the porous layer. In the limiting case where the boundary pressure difference is zero, the two-dimensional flow actually becomes the one-dimensional conduction regime of natural convection. On the other hand, when the boundary temperature difference tends to zero, the two-dimensional flow becomes a simple uniform horizontal through flow. The linear stability of the basic two-dimensional mixed convection is analysed. The growth rate and the angular frequency of the perturbations are evaluated numerically. The neutral stability curves are obtained by plotting the Rayleigh number versus the wave number, for different values of the Péclet number associated with the boundary pressure difference. The effect of the dynamic boundary conditions on the onset of the convective instability is discussed.

Extended Oberbeck–Boussinesq approximation study of convective instabilities in a porous layer with horizontal flow and bottom heating

A study of the onset of convective instabilities in a porous layer with a horizontal basic flow is performed by including the effects of viscous dissipation and pressure work in the energy balance. Firstly, the so-called extended Oberbeck–Boussinesq approximation, i.e. the model based on the enthalpy formulation of the energy balance, is adopted. Then, the results for the marginal stability condition are compared with those obtained by the so-called Chandrasekhar approximation, i.e. the model based on the internal-energy formulation of the energy balance. It is shown that a marked discrepancy occurs between the two approaches, that becomes specially evident for high values of the Gebhart number. According to the extended Oberbeck–Boussinesq approximation, the effects of the viscous dissipation and of the pressure work result in a stabilization of the basic flow. On the contrary, the Chandrasekhar approximation predicts a destabilization of the basic flow induced by the viscous dissipation. The destabilization can be so intense that the onset of convective rolls may occur even in the absence of a boundary temperature difference, i.e. with a vanishing Darcy–Rayleigh number.

Convective Roll Instabilities of Vertical Throughflow with Viscous Dissipation in a Horizontal Porous Layer

The vertical throughflow with viscous dissipation in a horizontal porous layer is studied. The horizontal plane boundaries are assumed to be isothermal with unequal temperatures and bottom heating. A basic stationary solution of the governing equations with a uniform vertical velocity field (throughflow) is determined. The temperature field in the basic solution depends only on the vertical coordinate. Departures from the linear heat conduction profile are displayed by the temperature distribution due to the forced convection effect and to the viscous dissipation effect. A linear stability analysis of the basic solution is carried out in order to determine the conditions for the onset of convective rolls. The critical values of the wave number and of the Darcy–Rayleigh number are determined numerically by the fourth-order Runge–Kutta method. It is shown that, although generally weak, the effect of viscous dissipation yields an increase of the critical value of the Darcy–Rayleigh number for downward throughflow and a decrease in the case of upward throughflow. Finally, the limiting case of a vanishing boundary temperature difference is discussed.

Convection with internal heat sources and thermal turbulence in the Earth's mantle

SUMMARY The influence of internal heat sources on mantle convection is investigated using numerical calculations of 2-D thermal convection in an infinite Prandtl number, incompressible fluid. The geometry is a cylindrical annulus with inner and outer radii in proportion to the whole mantle. Time-dependent calculations are made starting from random initial conditions, with Rayleigh numbers RaT (based on boundary-temperature difference) and Ra, (based on internal-heat production) in the range 1dsRaTs lo7 and OsRa,524RaT. At fixed RaT, increasing Ra, results in transitions in flow structure from steady cells, to a pattern of stationary cells with time-variable amplitude, and finally to thermally turbulent convection with a non-stationary cell count. For RaT 10' and Ra, >RaT approximately, the travelling plumes disrupt the large-scale circulation, producing turbulent convection. At Ra, = lo7 the flow is fully developed thermal turbulence, and for Ra, > 0, consists of a rapidly fluctuating, irregular flow driven by transient rising and sinking sheets of buoyant fluid. Large fluctuations in total kinetic energy occur in this regime, with periodicities ranging from 40 to 1400Myr. The transition to thermal turbulence occurs in these calculations at Rayleigh numbers well below the value estimated for subsolidus convection in the mantle, suggesting thermally turbulent convection may occur in the mantle, a consequence of internal heat sources. Thermal turbulence offers an explanation for long-term fluctuations in the rate of subduction, sea-floor spreading and global volcanic activity.

The stability of steady convective motion in a vertical slender slot with non-uniform volumetric energy sources and unequal surface temperatures

The problem of stability of a liquid layer contained between two vertical plates at different prescribed temperatures and subjected to an external radiation source penetrating its body is solved. Results for the effects of radiation and the boundary temperature difference are presented in graphical form in terms of two different critical Grashof numbers as functions of the Prandtl number, the optical thickness of the fluid and the wall reflectivities. A physical justification for the behavior of instability under wide range of each parameter is given. Conclusively, the effects of radiation parameters on the stability of liquids are found to be contrary with that reported on radiating gases under the same isothermal case.