Freezing around a finite heat sink immersed in an infinite phase change medium

Freezing around a spherical heat sink immersed in an infinite phase change medium — a free boundary problem involving growth and decay of the free boundary — is analysed here. A one-dimensional conduction model is formulated and the resulting partial differential equations are solved by finite difference methods. The energy discharged from the phase change medium during the heat transfer process is analysed for latent heat thermal energy storage applications. Results are presented for a wide range of parameters that are encountered in energy storage devices. The cases of slab/cylindrical heat sink are reexamined for a range of parameters not covered by the earlier investigators     

Migration of salts in the unsaturated zone caused by heating

Heat-transfer phenomena as well as moisture movement in unsaturated soils due to thermal gradients, have been extensively studied during the last four decades. Less attention has been devoted to the transport and redistribution of solutes caused by heating.Solar radiation, radioactive waste repositories, underground energy storage, buried electric cables and steam pipes, disposal of waste heat from power plants are examples of heat sources in the soil.Soil-water properties, such as surface tension, viscosity, density, as well as the equilibrium composition of phases, depend on temperature. Hence, nonuniform heating of a soil partially saturated by saline water has an effect on such processes as water flow under capillary and gravitational forces, evaporation, condensation and diffusion of vapor and transport and precipitation of salts.A mathematical model is presented for the migration of salts in the vadoze zone in the soil under nonisothermal conditions, taking into account the above-mentioned phenomena. The physical assumptions underlying the model are briefly discussed.The study of a particular case shows that under certain conditions, a heat source may attract dissolved salts, and cause their precipitation in the hot area.     

Exact solution of conductive heat transfer in cylindrical composite laminate

This paper presents an exact solution for steady-state conduction heat transfer in cylindrical composite laminates. This laminate is cylindrical shape and in each lamina, fibers have been wound around the cylinder. In this article heat transfer in composite laminates is being investigated, by using separation of variables method and an analytical relation for temperature distribution in these laminates has been obtained under specific boundary conditions. Also Fourier coefficients in each layer obtain by solving set of equations that related to thermal boundary layer conditions at inside and outside of the cylinder also thermal continuity and heat flux continuity between each layer is considered. In this research LU factorization method has been used to solve the set of equations.     

Pool boiling performance of finned surfaces in R-113

Performance of horizontal copper heaters with a transverse fin structure was investigated for pool boiling heat transfer and critical heat flux limits. Data were obtained for 5.1 and 7.6 cm diameter structured cooper and brass heaters in saturated R-113 boiling at pressures ranging between 0.037 and 1 atm. The fin structure consisted of 0.16 cm×0.16 cm×0.32 cm high square fins with an interfin spacing of 0.16 cm. Following a similar methodology to Haley and Westwater¹, a numerical analysis of the heat transfer phenomenon was performed by solving the one-dimensional fin conduction equation with a non-linear heat transfer boundary condition obtained from the previously reported data for R-113 boiling on plain surfaces. The predictions agreed with the data at the 1 atm pressure levels but showed deviations at the low pressure levels. The results showed that, compared with plain surface heaters of the same diameters the finned structured surfaces investigated: (a) decreased the wall temperature differences for a given heat flux and saturated pool boiling conditions, thus improving the nucleate boiling heat transfer coefficients, and (b) increased the critical heat flux limits, calculated as the power input divided by the heater projected area, by a factor of 2–2.5.     

Parametric study of thermal constriction resistance

Thermal contact resistance is due to imperfect contact of two bodies at the interface. It plays an important role in the dissipation of heat from electronic devices. The concept of individual heat flux tubes consisting of a single contact area and the corresponding gap which extends far in either solid was used in this study. The three dimensional conduction equation in the contact region was solved numerically for different shapes of gap and contact area and various thermal boundary conditions at locations far from the contact area. Constriction resistance defined as the ratio of the temperature difference across the contact surface to the rate of heat transfer through a heat flux channel was calculated for each case. The results have indicated that constriction resistance is strongly affected by the gap geometry, shape of contact area and certain end surface boundary conditions. The geometry dependence becomes more significant as the ratio of contact to total area becomes smaller. Given the fact that the shape of the contact region is highly unpredictable, the heat flux tube approach can hardly provide a reasonable estimate of the thermal contact resistance, unless the geometry of the contact region is properly modeled. Received on 5 January 1999     

On the relative impact of subgrid‐scale modelling and conjugate heat transfer in LES of hot jets in cross‐flow over cold plates

This work describes numerical simulations of a hot jet in cross‐flow with applications to anti‐ice systems of aircraft engine nacelles. Numerical results are compared with experimental measurements obtained at ONERA to evaluate the performances of LES in this industrial context. The combination of complex geometries requiring unstructured meshes and high Reynolds number does not allow the resolution of boundary layers so that wall models must be employed. In this framework, the relative influence of subgrid‐scale modelling and conjugate heat transfer in LESs of aerothermal flows is evaluated. After a general overview of the transverse jet simulation results, a LES coupled with a heat transfer solver in the walls is used to show that thermal boundary conditions at the wall have more influence on the results than subgrid scale models. Coupling fluid flow and heat transfer in solids simulations is the only method to specify their respective thermal boundary conditions. Copyright © 2011 John Wiley & Sons, Ltd.     

Planar solidification of a warm flowing-liquid under different boundary conditions

Planar solidification of a warm flowing liquid with the convective heat transfer to the growing solid layer, has been analysed for the boundary conditions of constant temperature, constant heat flux and convective heat flux at the surface respectively. The mathematical formulation of the problem resulted in a coupled set of two differential equations in temperature and solid thickness as function of position, time and the problem parameters. Analytical expressions for the temperature distribution within the growing solid layer, the rate of solidification and the solidification time are obtained. The perturbation techniques employed here is simple and straight forward in contrast with the earlier techniques. Good agreement between the experimental results and the present solutions is obtained for the convective heat flux boundary condition. The results of this analysis are useful in the design and analysis of experiments dealing with freezing/melting in one dimension. The role of the parameter Stefan number which is small for phase change materials, is discussed in context with the storage of thermal energy.     

Einfluß der thermischen Randbedingung auf den laminaren Wärmeübergang im Kreisrohr bei hydrodynamischer Einlaufströmung

Heat transfer characteristics of hydrodynamically developing laminar flow in a circular duct with different thermal boundary conditions were calculated by solving the equations of continuity, motion and energy in finite difference form. Results are presented for linear, sinusoidal and exponential variations of the prescribed wall heat flux along the duct length. A comparison shows that the influence of the thermal boundary condition on heat transfer increases with increasing development of velocity and temperature profiles. As a side result an improved correlation for heat transfer with constant wall heat flux in hydrodynamically developing flow is presented.     

Thermal stresses induced by a point heat source in a circular plate by quasi-static approach

The present paper deals with the determination of quasi-static thermal stresses due to an instantaneous point heat source of strength g_pi situated at certain circle along the radial direction of the circular plate and releasing its heat spontaneously at time t = τ. A circular plate is considered having arbitrary initial temperature and subjected to time dependent heat flux at the fixed circular boundary of r = b. The governing heat conduction equation is solved by using the integral transform method, and results are obtained in series form in terms of Bessel functions. The mathematical model has been constructed for copper material and the thermal stresses are discussed graphically.     

COUPLING BETWEEN LAMINAR FILM CONDENSATION AND NATURAL CONVECTION ON OPPOSITE SIDES OF A VERTICAL PLATE

Theoretical analyses which incorporate one-dimensional heat conduction along a plate and transverse heat conduction approximations are presented to predict the net heat transfer between laminar film condensation of a saturated vapour on one side of a vertical plate and boundary layer natural convection on the other side. It is assumed that countercurrent boundary layer flows are formed on the two sides. The governing boundary layer equations of this problem and their corresponding boundary conditions are all cast into dimensionless forms by using a non-similarity transformation. Thus the resulting system of equations can be solved by using the local non-similarity method for the boundary layer equations and a finite difference method for the heat conduction equation of the plate. The plate temperature and the heat flux through the plate are repetitively determined until the solutions for each side of the plate match. The predicted results show that the effect of Pr_c is not negligible for larger values of A* (thermal resistance ratio between natural convecti on side and condensing film side) and the approximation of transverse heat conduction overpredicts the plate temperature for lower values of R_t (thermal resistance ratio between plate and condensing film). However, no significant differences are observed between the two different approximations for higher values of R_t. © by 1997 John Wiley & Sons, Ltd.     

Heat flux sensor with minimal impact on boundary conditions

A technique for determining the heat transfer on the far surface of a wall based on measuring the heat flux and temperature on the near wall is presented. Although heat transfer measurements have previously been used to augment temperature measurements in inverse heat conduction methods, the sensors used alter the heat flow through the surface, disturbing the very quantity that is desired to be measured. The ideal sensor would not alter the boundary condition that would exist were the sensor not present. The innovation of this technique in that it has minimal impact on the wall boundary condition. Since the sensor is placed on the surface of the wall, no alteration of the wall is needed. The theoretical basis for the experimental technique as well as experimental results showing the heat flux sensor performance is presented.     

Effects of boundary reflection on radiative heat transfer in participating media

Radiative heat transfer through a non-isothermal grey participating medium between two parallel surfaces kept at fixed temperature has been investigated. The integro-differential transfer equations for surface reflection were solved in semi-analytical form by projectional methods; conduction and convection were neglected. It was assumed that reflection from the cold wall was diffuse, while that from the hot wall was either diffuse or specular. The heat flux and the temperature distribution in the participating medium were calculated in each physical condition, in order to compare the effects of different reflection modes on heat transfer. The results show that temperature distributions and heat fluxes are only slightly affected by the particular reflection law, the relative difference being less than 1%. This suggests that diffuse reflection only could be considered for practical applications, since it requires a much simpler computational procedure.     

INTERVAL ANALYSIS OF FUZZY-RANDOM HEAT CONDUCTION IN COMPOSITE TUBES

IntroductionThere are a lot of uncertainties such as fuzziness and random in the design andmanufacture in engineering.In generally speaking,methods to deal with the fuzzy-randomproblems are first to transfer the fuzzy set to real number set,and then the p…     

Momentum and heat transfer of a special case of the unsteady stagnation-point flow

This paper investigates the unsteady stagnation-point flow and heat transfer over a moving plate with mass transfer,which is also an exact solution to the unsteady Navier-Stokes(NS)equations.The boundary layer energy equation is solved with the closed form solutions for prescribed wall temperature and prescribed wall heat flux conditions.The wall temperature and heat flux have power dependence on both time and spatial distance.The solution domain,the velocity distribution,the flow field,and the temperature distribution in the fluids are studied for different controlling parameters.These parameters include the Prandtl number,the mass transfer parameter at the wall,the wall moving parameter,the time power index,and the spatial power index.It is found that two solution branches exist for certain combinations of the controlling parameters for the flow and heat transfer problems.The heat transfer solutions are given by the confluent hypergeometric function of the first kind,which can be simplified into the incomplete gamma functions for special conditions.The wall heat flux and temperature profiles show very complicated variation behaviors.The wall heat flux can have multiple poles under certain given controlling parameters,and the temperature can have significant oscillations with overshoot and negative values in the boundary layers.The relationship between the number of poles in the wall heat flux and the number of zero-crossing points is identified.The difference in the results of the prescribed wall temperature case and the prescribed wall heat flux case is analyzed.Results given in this paper provide a rare closed form analytical solution to the entire unsteady NS equations,which can be used as a benchmark problem for numerical code validation.     

Buckling analysis of functionally graded nanobeams under non-uniform temperature using stress-driven nonlocal elasticity

In this work, the size-dependent buckling of functionally graded(FG)Bernoulli-Euler beams under non-uniform temperature is analyzed based on the stressdriven nonlocal elasticity and nonlocal heat conduction. By utilizing the variational principle of virtual work, the governing equations and the associated standard boundary conditions are systematically extracted, and the thermal effect, equivalent to the induced thermal load, is explicitly assessed by using the nonlocal heat conduction law. The ...     

Numerical and experimental investigation of convective drying in unsaturated porous media with bound water

The heat and mass transfer in an unsaturated wet cylindrical porous bed packed with quartz particles was investigated theoretically for relatively low convective drying rates. Local thermodynamic equilibrium was assumed in the mathematical model describing the multi-phase flow in the unsaturated porous media using the energy and mass conservation equations to describe the heat and mass transfer during the drying. The drying model included convection and capillary transport of the free water, diffusion of bound water, and convection and diffusion of the gas. The numerical results indicated that the drying process could be divided into three periods, the temperature rise period, the constant drying rate period and the decreasing drying rate period. The numerical results agreed well with the experimental data verifying that the mathematical model can evaluate the drying performance of porous media for low drying rates. The effects of drying conditions such as the ambient temperature, the relative humidity, and the velocity of the drying air, on the drying process were evaluated by numerical solution.     

Heat transfer in tube assemblies under conditions of laminar axial,transverse and inclined flow

This paper considers laminar flow heat transfer in tube assemblies. The main interest is focused on the virtually unexplored cases of heat transfer under conditions of fully-developed flow inclined to the axes of the tubes and of purely transverse developing flow. The limiting cases of purely axial or purely transverse fully-developed flow are also examined. In all cases, the thermal boundary condition on the tubes is constant heat flux. Governing differential equations are expressed in terms of curvilinear-orthogonal coordinates and solved using finite-differences. Results are compared with available theoretical and experimental data. The effect of the transverse component of the flow on the temperature distribution is found to remain very strong even in nearly-axial flows and therefore considerably higher heat transfer coefficients are exhibited by a nearly-axial flow than a purely axial one.     

Combined interface boundary condition method for coupled thermal simulations

A new procedure for modeling the conjugate heat‐transfer process between fluid and structure subdomains is presented. The procedure relies on higher‐order combined interface boundary conditions (CIBC) for improved accuracy and stability. Traditionally, continuity of temperature and heat flux along interfaces is satisfied through algebraic jump conditions in a staggered fashion. More specifically, Dirichlet temperature conditions are usually imposed on the fluid side and Neumann heat‐flux conditions are imposed on the solid side for the stability of conventional sequential staggered procedure. In this type of treatment, the interface introduces additional stability constraints to the coupled thermal simulations. By utilizing the CIBC technique on the Dirichlet boundary conditions, a staggered procedure can be constructed with the same order of accuracy and stability as those of standalone computations. Using the Godunov–Ryabenkii normal‐mode analysis, a range of values of the coupling parameter is found that yields a stable and accurate interface discretization. The effectiveness of the method is investigated by presenting and discussing performance evaluation data using a 1D finite‐difference formulation for each subdomain. Copyright © 2007 John Wiley & Sons, Ltd.     

Formulation of thermo-hydro-mechanical coupling behavior of unsaturated soils based on hybrid mixture theory

Thermo-Hydro-Mechanical （THM） coupling pro- cesses in unsaturated soils are very important in both theoretical researches and engineering applications. A coupled formulation based on hybrid mixture theory is derived to model the THM coupling behavior of unsaturated soils. The free-energy and dissipative functions for different phases are derived from Taylor＇s series expansions. Constitutive relations for THM coupled behaviors of unsaturated soils, which include deformation, entropy change, fluid flow, heat conduction, and dynamic compatibility conditions on the interfaces, are then established. The number of field equations is shown to be equal to the number of unknown variables; thus, a closure of this coupling problem is established. In addition to modifications of the physical conservation equations with coupling effect terms, the constitutive equations, which consider the coupling between elastoplastic deformation of the soil skeleton, fluid flow, and heat transfer, are also derived.     

Calculation of Radiation Heat Transfer in Problems of Flow past Bodies with Account for Heat-Shield Coating Mass Loss

Flow past bodies with account for radiation heat transfer near the body nose is considered in connection with the problem of thermal protection of spacecraft entering planetary atmospheres. An approach based on the spherical harmonics method is used for taking radiation into account. The heating and ablation of the heat-shield coating is determined by numerically solving the heat conduction equation with a moving boundary. The thermal problem is solved together with the calculation of the vehicle trajectory, which makes it possible to estimate the effect of the coating mass loss on the trajectory parameters. The approach formulated is realized under the conditions of entry of a spherical segment and a spherically-blunted cone with equal mid-section radii into the Venusian atmosphere. Comparing the results makes it possible to choose the vehicle shape optimal with respect to the thermal regime.