The cooling of a plate by combined thermal radiation and convection

The cooling of a plate by a combination of thermal radiation and free or forced convection is a commonly occurring process for which no analytical solution exists. Elaborate numerical solutions are possible but there is an obvious need for a more accessible solution which may be used for engineering calculations such as the estimation of thermal stresses. This paper describes the development of such a solution using the heat balance integral technique. The accuracy is demonstrated to be acceptable for engineering purposes and the solution requires only simple arithmetic operations.     

Superficial heat transfer by forced convection and radiation in a horizontal channel

This paper presents a numerical investigation of turbulent forced convective flow in a horizontal channel. An exchanger isothermal test plate is embedded in the lower wall, in the fully developed region of the flow close to the exit of the channel. Above this isothermal plate, on the upper surface, a black coated isothermally heating resistance facing downwards is installed. This absorbing surface provides a controlled radiative heat flux on the lower test plate. In this study, custom-built tangential gradient fluxmeters (TGFM) are used to provide local measurements of convective heat transfer so as to validate the numerical predictions. Then, parametric studies are carried out. The profiles for the heat flux are presented for different Reynolds numbers in the flow direction along the cold isothermal lower plate. Then, the influence of the presence of an obstacle, located on the lower surface, on the heat flux is also investigated. All numerical predictions are carried out with Fluent, previously calibrated against benchmark problems and experimental measurements. In the paper, special emphasis is given in the systematic comparison between experimental and numerical results.     

Heating characteristics of convection reflow ovens

The inhomogeneous temperature distribution in the reflow oven can cause soldering failures. In this project, we investigate how the construction of a convection reflow oven has an affect on its heating characteristics. In the convection reflow oven itself, the heating capability is mainly dependent on the heat transfer coefficient, which in turn is mostly determined by the gas flow parameters. Therefore, we study how the construction of the reflow oven affects the flow of gas in the oven. Our conclusions are then verified with experimental results. During our experiments, temperature changes were measured at different points located around the centre of the processing area in the oven. From this data, the 3D directional characteristics of the heat transfer coefficient was calculated using the heat equation of the investigated reflow oven. We consider that our results are important for the effective thermal modelling of the reflow soldering process [B. Illés, G. Harsányi, 3D Thermal model to investigate component displacement phenomenon during reflow soldering, Microelectronics Reliability 48 (2008) 1062–1068] and are also useful when calibrating and designing reflow ovens. During our work, we examine the latest reflow ovens constructed with the nozzle-matrix blower system.     

Effects of convection and inertia on close contact melting

An analytical study was conducted in order to examine the role of convection and inertia on close contact melting of a phase change material (PCM) resting on a sliding heated plate. Results indicate that for high Prandtl substances, inertia has no effect on contact melting regardless of the magnitude of the melt layer Reynolds number Re. Convection however, enhances contact melting and its effect is increasingly perceptible for Re>10². Viscous dissipation may be ignored as long as Re<10⁴ and the Stefan number Ste0.001. On the other hand, for low Prandtl substances, both convection and inertia influence contact melting. Convection enhances melting while inertia hinders it. The effect of inertia is further accentuated as the Prandtl number becomes smaller. Viscous dissipation remains negligible as long as Re<10⁶ and Ste0.001.     

An experimental and numerical investigation of natural convection melting

The melting of a vertical ice cylinder in water is investigated in this paper. The experiments were carried out in a water-filled cylindrical Perspex barrel with adiabatic walls for Rayleigh numbers of 0.22x10⁸ and 0.475x10⁸. The ice crystal is suspended in the water and experimental images of the natural convection melting process were obtained using both shadowgraphy and particle image velocimetry (PIV) techniques. This data is compared with a numerical model which attempts to capture the melt-front on a fixed computational grid. The numerical model takes into account the density inversion effects in the water. The results show the applicability of PIV to this type of flow and demonstrate a simple numerical model to effectively resolve the melting phenomenon.     

单个相变微胶囊在湍流中的运动与融化特性

使用欧拉-拉格朗日方法研究了功能热流体中单个相变微胶囊颗粒在湍流场中的运动和融化特性,获得了相变颗粒在湍流场中运动轨迹以及温度沿轴线分布情况。结果表明,相变颗粒的粒径、密度以及入口位置对其运动和融化特性有较大影响。颗粒较小时跟随性好,但吸收能量能力较小,相变段较短;颗粒较大时跟随性差,但吸收能量能力较大,相变段增长;靠近圆管中心处颗粒温度较低,相变段较长且靠后,靠近壁面处颗粒温度高,相变段较短且靠前。     

Surface radiation effect on convection in a closed enclosure driven by a discrete heater

This paper is aimed at presenting the changes experienced by a convective flow in a closed square enclosure when surface radiation is taken into account. The flow is driven by a centrally placed discrete heater in an air filled two dimensional square enclosure. Symmetrically cooled isothermal vertical walls and insulated horizontal walls are considered. The governing coupled partial differential equations were solved using a finite volume method on a uniformly staggered grid system. The resulting augmentation of fluid velocities and the factors causing them are discussed.     

Visualization of the solid-liquid interface morphology formed by natural convection during melting of a solid from below

Experiments have been performed to obtain quantitative solid-liquid interface morphology data for melting of n-octadecane from below. Flow visualization experiments have revealed that natural convection flow was established as soon as the critical Rayleigh number was exceeded for the melt layer. For a given bottom temperature, the Benard-like, three-dimensional convection cells increased in size, merged with the neighboring ones and formed nearly two-dimensional rolls as the melting progressed. The mean diameter increased and the number of cells per unit projected area decreased with the melting time. The effect of initial subcooling of the solid was only to delay the development of the solid-liquid interface morphology.     

Analysis of the onset of buoyancy-driven convection in a water layer formed by ice melting from below

When an ice layer is melting from below, buoyancy-driven convection often appears in a thermally-unstable water layer. In this study, the onset of convection during time-dependent melting is investigated by using similarly transformed disturbance equations under the propagation theory. The critical Rayleigh numbers based on the water layer thickness are obtained for various conditions and compared with previous experimental and theoretical results. For a slowly melting system, the present prediction is quite close to that under the quasi-static assumption. However, for a rapidly melting system the critical condition deviates from the quasi-static one. With increasing the ratio of the depth of the unstable layer to the whole depth of the liquid layer the system becomes more unstable. But with increasing the phase change rate the system becomes more stable. With decreasing the phase change rate the present results approach the available critical conditions from the quasi-static model. The double cell pattern is predicted at the critical condition and the present results agree reasonably well with existing experimental data.     

Numerical and experimental investigation of melting of ice involving natural convection

Two‐dimensional transient melting of ice in a rectangular enclosure was numerically and experimentally investigated. Natural convection in the liquid phase due to the temperature dependency of water density was considered in the numerical model. The implicit finite difference method with fixed staggered grid approach was utilized. The SIMPLER algorithm was followed for the solution of pressure and velocity fields in the liquid phase. The prediction of the model was found to be satisfactory through preliminary experimentation. Copyright © 2002 John Wiley & Sons, Ltd.     

Heat transfer by radiation and natural convection through a vertical annulus embedded in porous medium

The effect of radiation and natural convection in a saturated porous medium embedded in a vertical annular cylinder has been investigated. Finite element method has been used to solve the governing equations. Influence of aspect ratio (A) and radius ratio (R) on Nusselt number is presented. The effect of radiation on heat transfer behavior is discussed. Results for two limiting cases of vertical cylinder and vertical plate embedded in saturated porous medium are presented. It is seen that average Nusselt number (N¯u) increases significantly with radiation parameter (Rd). N¯u attains maximum value at an aspect ratio of around one. N¯u always decreases with decrease in radius ratio.     

Free convection heat and mass transfer during pool penetration into a melting miscible substrate

A theoretical investigation is made of the process of free convection melting of a solid slab by an overlying hot liquid pool. The solid, when molten, is lighter than and miscible with the pool material. Systematic mathematical approximations to the Boussinesq equations of motion are performed to determine the behavior of the temperature and the concentration fields in two different flow regions. These are the boundary layer region at the melting interface and the turbulent core region in the bulk pool. The dependence of the melting rate on various controlling parameters, including the Grashof number based on the pool-to-substrate density ratio, the external Stefan number based on the pool-to-substrate temperature difference, and the internal Stefan number based on the freezing-point depression, is obtained by matching the boundary layer solution and the turbulent core solution in the region of overlap. Comparison of the present theory is made with existing experiments and found to be good.     

Combined radiation and convection heat transfer in a porous channel bounded by isothermal parallel plates

Combined radiation and convection heat transfer in a porous medium confined between gray isothermal parallel plates is investigated. The medium is absorbing, emitting and scattering. Cases of boundaries at temperatures higher or lower than the medium are considered. In the porous medium, the boundary effect on the fully developed laminar velocity field as proposed by Kaviany is accounted for. For various values of the extinction coefficient, the scattering albedo, the conduction-radiation parameter and the boundary emissivity, Nusselt number, temperature and heat flux distributions are found for the range of values including the extreme limits of the porous medium shape parameter (PMSP), γ=(W²φ/K)^1/2, where W is the channel width, φ the porosity and K the permeability. For the lower limiting value of the PMSP γ, the effect of the porous medium is negligible and the situation approaches that of Poiseuille flow. For this limiting case, results from the present work are compared with those available in the literature. For medium to high values of the PMSP γ, for the purpose of comparison, some results are presented in tabular form. Radiation is found to have a significant effect on various parameters studied. The discrete transfer method was used for the solution of the radiative part of the energy equation. An iterative finite difference scheme was used to solve the energy equation.     

Mixed convection of transient MHD stagnation point flow over a stretching sheet with quadratic convection and thermal radiation

This study investigates the influence of quadratic (nonlinear) convection in transient magnetohydrodynamic (MHD) combined convection over a two-dimensional stretching sheet. It explores the effects of thermal radiation, suction, and heat sources or sinks. The Crank–Nicholson implicit finite difference method is employed for numerical computations. The significance lies in considering secondary convection, which is crucial in understanding nonlinear convective effects affecting flow and heat transfer properties. The study aims to advance our comprehension of how secondary convection impacts the overall system behavior. Through numerical calculations validated against existing literature, strong agreement is demonstrated. The study evaluates secondary convection effects, magnetic, buoyancy, gravitational parameters, Prandtl number, and radiation parameters. Notably, strong quadratic convection alters flow patterns, affecting velocity and temperature profiles. Moreover, it is observed that when increasing the nonlinear (quadratic) convective factors, the temperature profile increases for $$ and decreases for $$. The prevalence of nonlinear or second-order convection highlights magnetic dominance. In essence, this research enhances our understanding of complex convection interactions in MHD flow, shedding light on the role of secondary convection in shaping system behavior.     

Computation of surface radiation and natural convection in a heated horticultural greenhouse

This study analyses the effects of the radiation exchange inside a horticultural greenhouse, under winter climatic conditions, according to the number of squared heating tubes used. These ones, hot and isothermal, are equidistant inside the greenhouse volume. The governing differential equations are discretized using a finite volume method and the coupling pressure–velocity problem is carried out by the SIMPLER algorithm. The algebraic systems obtained are solved by a conjugate gradient method. Results are reported in terms of isotherms, streamlines and average Nusselt number for Rayleigh number of 10³–10⁶. The contour lines show that the radiative effects are noted near the solid surfaces, and become increasingly important when the Rayleigh number increases. As a result, the rise in the value of Rayleigh number leads to an increase of the overall heat transfer within the greenhouse.     

Heat transfer from a horizontal fin array by natural convection and radiation—A conjugate analysis

The problem of natural convection heat transfer from a horizontal fin array is theoretically formulated by treating the adjacent internal fins as two-fin enclosures. A conjugate analysis is carried out in which the mass, momentum and energy balance equations for the fluid in the two-fin enclosure are solved together with the heat conduction equations in both the fins. The numerical solutions by using alternating direction implicit (ADI) method yield steady state temperature and velocity fields in the fluid, and temperatures along the fins. Each end fin of the array is exposed to limited enclosure on one side and to infinite fluid medium on the other side. Hence a separate analysis is carried out for the problem of end fin exposed to infinite fluid medium with appropriate boundary conditions. From the numerical results, the heat fluxes from the fins and the base of the two-fin enclosure, and the heat flux from the end fin are calculated. Making use of the heat fluxes the total heat transfer rate and average heat transfer coefficient for a fin array are estimated. Heat transfer by radiation is also considered in the analysis. The results obtained for a four-fin array are compared with the experimental data available in literature, which show good agreement. Numerical results are obtained to study the effectiveness for different values of fin heights, emissivities, number of fins in a fixed base, fin base temperature and fin spacing. The numerical results are subjected to non-linear regression and equations are obtained for heat fluxes from the two-fin enclosure and single fin as functions of Rayleigh number, aspect ratio and fin emissivity. Also regression equations are obtained to readily calculate the average Nusselt number, heat transfer rate and effectiveness for a fin array.     

Effect of radiation in a radial heat sink under natural convection

A radial heat sink was investigated, considering both natural convection and radiation. Experiments were performed to validate numerical results and a close agreement was found. The effect of radiation on total heat transfer was examined by varying emissivity, and it was found that the maximum radiation contribution was 27%. The radial heat sink was optimized to maximize thermal performance. The thermal performance was enhanced by 12.3% while the mass increased by 20%. Radiation (emissivity) had a significant effect on the optimum long fin length when only thermal performance was considered. The average thermal resistance decreased by 8.7% for the optimized model with the same mass as the reference model, and the effect of radiation on total heat transfer was greater than the effect of natural convection.     

Influence of natural convection on the melting of ice block surrounded by water on all sides

The ice block at initial temperature T_is = 0 °C is fixed at the center of a long, prismatic enclosure with isothermal vertical walls and insulated horizontal walls. The enclosure is completely filled with water at initial temperature T_il = 0 °C. Six numerical simulations were performed by varying vertical wall temperatures from T_W = 2 to 12 °C (range of Rayleigh number from 4.22 × 10⁶ to 2.28 × 10⁷). In the case of T_W > 8 °C the ice melts faster from above and for T_W < 8 °C from below. In the case of T_W = 8 °C, two vortices are separated by nearly vertical 4 °C isotherm and the average Nusselt number remains constant during the convection dominated regime.     

A simplified numerical model for melting of ice with natural convection

Ice in a rectangular enclosure is melted by heating from the top, while maintained at its melting point at the bottom. The other surfaces are insulated. In the enclosure near the hot region, liquid phase starts forming as temperatures reach values higher than the melting point of ice. This phenomenon is first modeled by ignoring the effect of natural convection in the liquid phase. The resulting equations of conservation of energy are solved in each phase. The motion of melting front is governed by an energy balance at the interface. This conduction model is verified by applying it on a system for which an analytical solution is available. The model is then extended to include convective heat transfer in such a way that the liquid phase is assumed to be a mixed body subjected to natural convection from the top surface and the liquid-solid interface. The flux at the interface is obtained by finding a heat transfer coefficient for natural convection with a cold plate facing upward. Comparison of the results of the numerical work with experiments performed on water/ice system shows a strong effect of natural convection on melting of ice. The model involving natural convection in the liquid phase agrees well with the experimental work.     

Inverse radiation analysis of a one-dimensional participating slab by stochastic particle swarm optimizer algorithm

A stochastic particle swarm optimizer (SPSO) algorithm, which can guarantee the convergence of the global optimization solution with probability one, is adopted to estimate the parameters of radiation system. To illustrate the performance of this algorithm, three cases are investigated, in which the source term, the extinction coefficient, the scattering coefficient, and the non-uniform absorption coefficients in a one-dimensional slab are retrieved. The directional radiative intensity, reflectance and transmittance, radiative flux simulated by discrete ordinate method (DOM) are served as input for the inverse analysis, respectively. By SPSO algorithm presented, all these radiative parameters could be estimated accurately, even with noisy data. In conclusion, the SPSO algorithm is proved to be fast and robust, which has the potential to be implemented in various fields of inverse radiation problem.