Temperature field in a moving semi-infinite region with a prescribed wall heat flux

Steady state conduction of heat from a stationary wall to a medium moving at a uniform velocity is the subject herein. This medium can be a solid or a fluid moving at a constant velocity. The surface of this medium is insulated until a change in the surface heat flux occurs. The determination of temperature field is the main objective herein. The results show that the surface temperature begins to increase before its arrival to the heater’s location where there is an abrupt change in the surface heat flux. The application of this phenomenon to a moving wall with frictional heating at its surface and to classical heat transfer in ducts can lead to new information.     

Exact analytical solutions of moving boundary problems of one-dimensional flow in semi-infinite long porous media with threshold pressure gradient

The dimensionless mathematical models of one-dimensional flow in the semi-infinite long porous media with threshold pressure gradient are built for the two cases of constant flow rate and constant production pressure on the inner boundaries. Through formula deduction, it is found that the velocity of the moving boundary is proportional to the second derivative of the unknown pressure function with respect to the distance parameter on the moving boundary, which is very different from the classical heat-conduction Stefan problems. However, by introducing some similarity transformation from Stefan problems, the exact analytical solutions of the dimensionless mathematical models are obtained, which can be used for strict validation of approximate analytical solutions, numerical solutions and pore-scale network modeling for the flow in porous media with threshold pressure gradient. Comparison curves of the dimensionless pressure distributions and the transient dimensionless production pressure under different values of dimensionless threshold pressure gradient are plotted from the exact analytical solutions of problems of the flow in semi-infinite long porous media with and without threshold pressure gradient. It is shown that for the case of constant flow rate the effect of the dimensionless threshold pressure gradient on the dimensionless pressure distributions and the transient dimensionless production pressure is not very obvious; in contrast, for the case of constant production pressure the effect on the dimensionless pressure distributions is more obvious especially at the larger dimensionless distance near the moving boundary; and for the case of constant production pressure, the smaller the dimensionless threshold pressure gradient is, the larger the dimensionless pressure is, and the further the pressure disturbance area reaches.     

Time and space resolved wall temperature and heat flux measurements during nucleate boiling with constant heat flux boundary conditions

The lack of time and space resolved measurements under nucleating bubbles has complicated efforts to fully explain pool-boiling phenomena. In this work, time and space resolved temperature and heat flux distributions under nucleating bubbles on a constant heat flux surface were obtained using a 10 × 10 microheater array with 100 μm resolution along with high-speed images. A numerical simulation was used to compute the substrate conduction, which was then subtracted from the heater power to obtain the wall-to-liquid heat transfer. The data indicated that most of the energy required for bubble growth came from the superheated layer around the bubble. Microlayer evaporation and contact line heat transfer accounted for not more than 23% of the total heat transferred from the surface. The dominant heat transfer mechanism was transient conduction into the liquid during bubble departure. Bubble coalescence was not observed to transfer a significant amount of heat.     

Maximum heat flux in relation to quenching of a high temperature surface with liquid jet impingement

Experimental investigation has been conducted for quenching of hot cylindrical blocks made of copper, brass and steel with initial block temperature 250–400 °C by a subcooled water jet of diameter of 2 mm. The subcooling was from 5 to 80 K and the jet velocity was from 3 to 15 m/s. After impingement, the jet stagnates for a certain period of time in a small region near the centre and then the wetting front starts moving outwards. During this movement, when the surface temperature at the wetting front drops to 120–200 °C, the surface heat flux reaches its maximum value due to forced convection nucleation boiling. The maximum heat flux is a strong function of the position on the hot surface, jet velocity, block material properties and jet subcooling. A new correlation for maximum heat flux is proposed.     

Three-dimensional thermal boundary layer corrections for circular heat flux gauges mounted in a flat plate with a surface temperature discontinuity

Three-dimensional Navier–Stokes computational fluid dynamics (CFD) analysis has been performed in an effort to determine thermal boundary layer correction factors for circular convective heat flux gauges (such as Schmidt–Boelter and plug type) mounted flush in a flat plate subjected to a stepwise surface temperature discontinuity. Turbulent flow solutions with temperature-dependent properties are obtained for a freestream Reynolds number of 1E6, and freestream Mach numbers of 2 and 4. The effect of gauge diameter and the plate surface temperature have been investigated. The 3D CFD results for the heat flux correction factors are compared to quasi-2D results deduced from constant property integral solutions and also 2D CFD analysis with both constant and variable properties. The role of three-dimensionality and of property variations on the heat flux correction factors has been demonstrated.     

变热流条件下木材点燃时间与热流变化率关系的实验研究

实验研究了外加线性变化热流条件下木材点燃时间与热流变化率之间的关系,测量了不同种类木材在不同热流变化率下的点燃时间。通过分析实验数据发现,点燃时间和热流变化率之间符合很好的幂函数关系,而密度是影响木材着火的一个关键因素。     

Falkner-Skan problem for a static and moving wedge with prescribed surface heat flux in a nanofluid

An analysis is carried out to study the problem of the steady flow and heat transfer over a static or moving wedge with a prescribed surface heat flux in a nanofluid. The governing partial differential equations are transformed into a set of nonlinear ordinary differential equations using similarity transformation, before being solved numerically by the Keller box method and the Runge-Kutta-Fehlberg method with shooting technique. The features of the flow and heat transfer characteristics are analyzed and discussed. Three different types of nanoparticles are considered, namely copper Cu, alumina Al₂O₃ and titania TiO₂ with water as the base fluid. It is found that the skin friction coefficient and the heat transfer rate at the surface are highest for copper-water nanofluid compared to the alumina-water and titania-water nanofluids. Moreover, the heat transfer rate at the surface increases with the Falkner-Skan power law parameter m.     

Solutions for modelling moving heat sources in a semi-infinite medium and applications to laser material processing

This study describes the analytical and numerical solution of the heat conduction equation for a localised moving heat source of any type for use in laser material processing, as welding, layered manufacturing and laser alloying. In this paper, the analytical solution for a uniform heat source is derived from the solution of an instantaneous point heat source. The result is evaluated numerically and is compared to existing solutions for the moving point source and a semi-ellipsoidal source. Next, the result is used to demonstrate how such model can be used to study the effect of the heat source geometry. Besides, this solution reveals that a melting efficiency higher than 0.37 (= 1/e, a maximum value stated by Rykalin [N. Rykalin, A. Uglov, A. Kokora, O. Glebov, Laser Machining and Welding, Mir Publishers, Moscow, 1978]) can be obtained. To investigate the effect of the temperature dependence of the material parameters, in particular the latent heat of fusion, a finite difference model is implemented. It is shown that the enthalpy method is most suited to implement the latent heat of fusion. A numerical evaluation for Ti–6Al–4V, reveals that the effect of the latent heat is rather small, except when the conductivity is very low, e.g. when scanning in a loose powder bed. The results demonstrate that analytical and numerical solutions can be effectively used to calculate the temperature distribution in a semi-infinite medium for finite 3D heat sources. In this way, a tool to investigate the importance of different processing parameters in laser manufacturing is obtained.     

Natural convection boundary layer on a horizontal elliptical cylinder with constant heat flux and internal heat generation

In this paper the natural convection boundary layer on a horizontal elliptical cylinder with constant heat flux and temperature dependent internal heat generation is investigated. The mathematical problem is reduced to a pair of coupled partial differential equations for the temperature and the stream function, and the resulting nonlinear equations are solved numerically by cubic spline collocation method. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of heat generation parameters, Prandtl numbers and aspect ratios. An increase in the aspect ratio of the elliptical cylinder decreases the average surface temperature of the elliptical cylinder with blunt orientation, while it increases the average surface temperature of the elliptical cylinder with slender orientation. Moreover, an increase in the heat generation parameter for natural convection flow over a horizontal elliptic cylinder with constant heat flux leads to an increase in the average surface temperature of the elliptical cylinder.     

Control of the boundary heat flux during the heating process of a solid material

In this paper we apply the conjugate gradient method to solve the inverse problem of determining a time-dependent boundary heat flux in order to achieve a given temperature distribution at the final time. The derivation of sensitivity and adjoint equations in conjunction with the conjugate gradient algorithm are given in detail. The zeroth-order Tikhonov regularization is introduced to stabilize the inverse solution. Solutions by finite differences are obtained for various heat flux profiles. It is found that the time-dependent heat flux may be predicted only for a non-dimensional time of the order of 0.1 while the control problem can be satisfactorily solved for an arbitrary period of time.     

Scroll heat sink: A novel heat sink with the moving fins inserted between the cooling fins

In this paper, a new type of a fan-integrated heat sink named a scroll heat sink is proposed and demonstrated. The most striking feature of the scroll heat sink is that heat dissipation and fluid pumping occurs simultaneously in the whole cooling space without requiring any additional space for a fan module. In the scroll heat sink, the moving fins, which rotate with two eccentric shafts, are inserted between the fixed (cooling) fins. By a relative motion between the moving fins and the cooling fins, a coolant is drawn into the space between them, takes heat away from the cooling fins, and the heated coolant is discharged out of the heat sink. In the present study, an experimental investigation is performed in order to demonstrate the concept of the scroll heat sink. Average coolant velocities and thermal resistances of the scroll heat sink are measured for various rotating speeds of the moving fins from 200 rpm to 500 rpm. Experimental results show that measured flow rates of the coolant are almost linearly proportional to the rotating speed of the moving fins. A theoretical model is also developed to estimate the required pumping power and the thermal resistance, and validated using experimental results. The theoretical model shows that optimized scroll heat sinks have lower thermal resistances than optimized plate-fin heat sinks under the fixed pumping power condition.     

Effects of mass transfer on the transient free convection flow of a dissipative fluid along a semi-infinite vertical plate with constant heat flux

Effect of mass transfer on the transient free convection flow of a dissipative fluid along a semi-infinite vertical plate in presence of constant heat flux, is studied by solving coupled non-linear system of partial differential equations, using Crank-Nicolson technique which is stable and convergent. Transient temperature, concentration and velocity profiles, local and average skin-friction, Nusselt number and Sherwood number are shown graphically for air. The effects of ε, viscous dissipative parameter, Schmidt number, buoyancy ratio parameter on the transient state are discussed.     

Natural convection in a nanofluid-filled eccentric annulus with constant heat flux wall: A lattice Boltzmann study with immersed boundary method

A numerical investigation of natural convection in a Cu–water nanofluid-filled eccentric annulus with constant heat flux wall is presented. The governing equations of the flow and temperature fields are solved by lattice Boltzmann method (LBM), and the Dirichlet and Neumann boundary conditions are treated using the immersed boundary method (IBM). Influences of the Rayleigh number (10³ ≤ Ra ≤ 10⁷), eccentricity (ε = −0.625,0 and 0.625), nanoparticles volume fraction (0 ≤ ϕ ≤ 0.03) and radial ratio (rr = 2.33,2.6 and 3) on the streamlines, isotherms and Nusselt number are studied. It is found that the inclusion of the nanoparticles into pure fluid changes the flow pattern. And the Nusselt number has a positive relationship with nanoparticle volume fraction, Rayleigh number and radial ratio. Also, it can be confirmed that Nusselt number in the case with negative eccentricity (ε = −0.625) is larger than the others.     

Temperature distribution and local heat flux in the unidirectional freezing of antifreeze-protein solution

Experiments have been conducted on the unidirectional freezing of dilute aqueous solutions of winter flounder antifreeze protein, which are 0.02 mm thick, between two cover glasses on the stage of a microscope. The instantaneous temperature field has been obtained by measuring the intensity of near-infrared light with a near-infrared camera. In addition, the local protein concentration has been measured separately using the brightness of fluorescence emitted from molecules tagged to the protein. It is found that the temperature distribution in the ice region near the ice/water interface is similar to that predicted from the modified Neumann solution. Furthermore, the temperature measurement made using the near-infrared light with a specific wavelength is verified. In addition to this, in the case of antifreeze protein solutions, serrated interfaces are observed. The sum of the conduction heat flux of a protein solution near the front edge of the serrated interface and the heat flux for solidification is lower than the conduction heat flux of ice. On the other hand, the sum of the conduction heat flux of protein solution near the bottom edge of the serrated interface and the heat flux for solidification is higher than the conduction heat flux of ice. The balance of heat flux is obtained by taking account of heat convection due to high-concentration regions of protein. These regions move to the deepest parts of the interface and form narrow liquid regions inside the ice. The convection is maintained by the heat conduction in a direction perpendicular to the direction of ice growth. Not only protein adsorption to the interface but also the heat conduction/convection contributes to the modification of ice growth in the non-equilibrium state.