Unsteady Conjugate Research Articles

Unsteady conjugate mass transfer from a spherical drop in simple extensional creeping flow

This paper presents the detailed numerical investigation on the unsteady conjugate mass transfer from a spherical drop immersed in a simple extensional flow. By making use of the known Stokes velocity field at small Reynolds numbers, a finite difference method with the control volume formulation is adopted to solve the convection-diffusion transport equations. The interactive effects of Peclet number, viscosity ratio, diffusivity ratio and distribution coefficient, as well as flow direction on the conjugate transport process are examined in terms of numerical simulation. Simulation results show that the conjugate mass transport is significantly influenced by these four parameters and it approaches some limit cases if viscosity ratio, diffusivity ratio and distribution coefficient become far larger or less than unity. The flow direction, no matter uniaxial extensional or biaxial extensional flow, has no influence on the total transport rate but affects a lot the distribution of solute concentration.

Unsteady Conjugate Heat Transfer Analysis of an Immersed Particle Innovative Heat Exchanger

The improvement of both heat recovery Joule-Brayton cycles and closed cycle (externally fired) gas turbine plants is strongly limited by the availability of high efficiency heat exchangers. In such a scenario, a nonconventional heat exchanger was recently proposed; this device employs falling solid particles to perform heat transfer between two separate gas flows and was designed with a 1D model neglecting conduction within the particles. Although the experimental reliability of this assumption was already obtained for one particle size, there is no proof available of the quantitative effect introduced by the above mentioned simplification and, more importantly, no indication of when this assumption becomes unacceptable. In this work, direct numerical simulation (DNS) of a solid particle immersed in a gas flow has been performed in order to further validate the hypothesis of negligible conduction and to enhance the design of the proposed heat exchanger. Unsteady conjugate heat transfer has been used to predict the final temperature of the solid sphere for Reynolds numbers ranging from 30 to nearly 300, the computational grid being generated with the immersed boundary (IB) technique. A validation of the study is presented, together with grid independence and boundary independence assessment. The results fully confirmed the worthiness of the initial assumption, with a 1.4% maximum error for high Reynolds conditions (large diameter particles) with respect to the 1D model. Additionally, the code has been employed to explore the influence of the wake in the case of aligned particles, namely, the worst possible situation in terms of efficiency of the heat transfer mechanism. Finally, the discrepancy between the results obtained with an axisymmetric domain and a 3D domain, in terms of final temperature of the particle, have been investigated for the highest Reynolds number, when the flow is supposed to lose its axial symmetry.

Unsteady Conjugate Numerical Simulation of the Solar Chimney Power Plant System with Vertical Heat Collector

A new kind of solar chimney power plant system combining chimney and heat collector was designed. Paraffin was chosen as the material of energy storage layer and the unsteady conjugate numerical simulation of the system was done by Fluent software. The operation condition of the system was simulated when the solar radiation value was changed with time according to the actual situation. Simulation results showed that: with the increase of solar radiation, flow velocity of the air and the maximum output power increased. At twelve o'clock, the air velocity could reach 1.24 m/s and output power was 122W. Due to the energy storage effect of phase change materials, the system had output power of 1.3W at night. Moreover because of the continuous work of the heat storage layer, in the same condition of solar radiation, the air velocity and maximum output power increased with the system operation days extended.

Unsteady Conjugate Natural Convective Heat Transfer in a Saturated Porous Square Domain Generalized Model

Numerical unsteady predictions are carried out for two-dimensional natural convective heat transfer in a saturated porous square domain sandwiched between two finite wall thicknesses. The horizontal boundaries of the cavity are adiabatic and the vertical walls are maintained at fixed different temperatures T h and T c . In the core cavity (porous region), the extension of the Darcy model/Forchheimer–Brinkman-extended Darcy model with the Boussinesq approximation is used to solve the momentum equations as well as the energy and continuity equations. The conduction equation is employed to solve for the temperature distribution in the finite thickness wall layers. The nondimensional equations are solved by using the finite volume approach and the pressure velocity coupling is treated via the SIMPLE algorithm applicable in the porous media. The results are presented for different values of the nondimensional governing parameters, including the modified Rayleigh number (100 ≤ Ra* ≤ 1000), Darcy Number (10−7 ≤ Da ≤ 10−2), thermal conductivity ratio (0.1 ≤ Kr ≤ 10), and the ratio of wall thickness to height (0.1 ≤ D ≤ 0.4). A correlation to evaluate the average Nusselt numbers on the left wall interface of the porous cavity is proposed as a function of modified Rayleigh number, Darcy number, as well as a number of physical, geometrical and material property variables.

Unsteady conjugate thermogravitational convection in a cylindrical region with local energy source

The mathematical modelling of unsteady regimes of natural convection in a closed cylindrical region with a heat-conducting shell of finite thickness was carried out in the presence of a local heat source under the conditions of convective heat exchange with the ambient medium. The mathematical model was constructed in dimensionless variables “stream function — vorticity vector — temperature” in the cylindrical coordinate system. The influence of the Rayleigh number, 104 ≤ Ra ≤ 106, of the unsteadiness factor 0 < τ < 300, of the thermal conductivity ratio λ2,1 = 5.7·10−4, 4.3·10−2, and the energy source sizes on both local characteristics (streamlines and temperature fields) and on the integral complex (the mean Nusselt number on typical boundaries) was analysed in detail. Thermohydrodynamic peculiarities due to the geometry of the object of research were established.

A Simplified Model with a Hybrid Analytical-Numerical Solution for Predicting the Unsteady Conjugate Heat Transfer Process in Pipelines

This work presents a new, simplified and yet efficient model for studying the transient conjugate heat transfer process in pipelines. The simplified model consists of assuming the thermal transport by fluid flow in bulk form and the pipe–wall heat conduction as two-dimensional. The scale analysis of the dimensionless equations resulting from the simplified model allows for the identification of two predicting parameters useful in determining when axial diffusion in the pipe wall is important, ψ = Pe Γ/ξ < 1 and λ = 4 Nu E 2/ξ < 1, and when radial diffusion is important, ψ > 1 and λ > 1. When these criteria are satisfied, in which case the existing analytical solution becomes invalid, the simplified model proposed here becomes an efficient alternative to the full-scale numerical simulations required for solving the problem. The scale analysis predictions and the hybrid analytical-numerical solutions of the simplified model, involving the Laplace transform and the finite-volume method, are validated first by comparison against the existing analytical solution, and then by comparison against experimental results of turbulent flow, showing excellent agreement in both cases.

Unsteady Conjugate Heat Transfer Modeling

The primary requirement for high pressure turbine heat transfer designs is to predict blade metal temperature. There has been a considerable recent effort in developing coupled fluid convection and solid conduction (conjugate) heat transfer prediction methods. They are, however, confined to steady flows. In the present work, a new approach to conjugate analysis for periodic unsteady flows is proposed and demonstrated. First, a simple model analysis is carried out to quantify the huge disparity in time scales between convection and conduction, and the implications of this for steady and unsteady conjugate solutions. To realign the greatly mismatched time scales, a hybrid approach of coupling between the time-domain fluid solution and frequency-domain solid conduction is adopted in conjunction with a continuously updated Fourier transform at the interface. A novel semi-analytical harmonic interface condition is introduced, initially for reducing the truncation error in finite-difference discretization. More interestingly, the semi-analytical interface condition enables the unsteady conjugate coupling to be achieved without simultaneously solving the unsteady temperature field in the solid domain. This unique feature leads to a very efficient and accurate unsteady conjugate solution approach. The fluid and solid solutions are validated against analytical solutions and experimental data. The implemented unsteady conjugate method has been demonstrated for a turbine cascade subject to inlet unsteady hot streaks.

Heat-transfer analysis of indirect moxibustion using unsteady conjugate heat-transfer solutions

A conjugate heat-transfer problem in indirect moxibustion was analyzed by solving the problem of unsteady convective heat transfer coupled with conductive heat transfer. The interaction of a combustion-heated paper disk of moxa with the body and surrounding fluid was revealed by examining the body’s unsteady temperature distributions. From the grid- and time step-independent solutions to the present conjugate heat-transfer problem, the effective stimulation periods for four widths of paper disk, along with the depths of the effective stimulation zones, were obtained. Further, it was found that the effective stimulation zone becomes larger and lasts longer for the wider paper disks, whereas the depth of the effective stimulation zone is saturated beyond a certain size. Lastly, the streamline pattern and the history of the spatially averaged heat-transfer coefficient, which is related to the convective heat transfer between the body and the surrounding fluid, were determined.

Conjugate conduction-natural convection in an enclosure with time-periodic sidewall temperature and inclination

The unsteady conjugate conduction-natural convection in enclosure is of great theoretical significance and is widely encountered in engineering applications in the areas of fluid dynamics and heat transfer. However, there are relatively few efforts to investigate the unsteady flow physics and heat transfer characteristics in the inclined enclosure of finite thickness walls. In the present work, this problem is numerically investigated by a high accuracy multidomain temporal–spatial pseudospectral method. The enclosure is filled with Boussinesq fluid and is bounded by four finite thickness and conductive walls; one of the vertical sidewall is exposed to time-periodic temperature environment while the opposite sidewall holds constant temperature; the top and bottom walls are assumed to be adiabatic. Particular efforts are focused on the effects of three types of influential factors: the wall thermophysical properties, the time-periodic temperature patterns and the inclination, and the time-periodic flow patterns and heat transfer characteristics are presented. Numerical results reveal that within the present parameter range, the heat transfer rate increases almost linearly with the thermal conductivity ratio and thermal diffusivity ratio but decreases with the inclination angle. Moreover, the heat transfer could be enhanced or weakened by selecting different temperature pulsating period in the case of finite thickness wall, while it is always enhanced if the walls are zero thickness. The back heat transfer and heat transfer resonance phenomena are observed, and their relationships with the time-periodic flow patterns and temperature distributions are analyzed. The findings are helpful to the understandings of the fluid flow and heat transfer mechanisms in the related enclosure configurations, and may be of engineering use in thermal design improvement.

Unsteady conjugate natural convection in a square enclosure filled with a porous medium

Mathematical simulation of unsteady natural convection modes in a square cavity filled with a porous medium having finite thickness heat-conducting walls with local heat source in conditions of heterogeneous heat exchange with an environment at one of the external boundaries has been carried out. Numerical analysis was based on Darcy–Forchheimer model in dimensionless variables such as a stream function, a vorticity vector and a temperature. The special attention was given to analysis of Rayleigh number effect Ra = 10 4, 10 5, 10 6, of Darcy number effect Da = 10 −5, 10 −4, 10 −3, ∞, of the transient factor effect 0 < τ < 1000 and of the heat conductivity ratio k 2,1 = 3.7 × 10 −2, 5.7 × 10 −4, 6.8 × 10 −5 on the velocity and temperature fields. The influence scales of the defining parameters on the average Nusselt number have been detected.

Unsteady conjugate mixed convection phase change of a power law non-Newtonian fluid in a square cavity

Transient phase change of a power law non-Newtonian fluid inside an inner thin walled container caused by external mixed convection in a square cavity has been analyzed numerically. Air was chosen as external cooling fluid and modified non-Newtonian water as the phase change fluid. Fluid mechanics and conjugate convective heat transfer, described in terms of continuity, linear momentum and energy equations, were predicted by using the finite volume method. Solidification was treated in terms of a phase change function varying linearly with temperature. The effect of the external Reynolds number, for Re = 200 and 1000 on solidification was studied along the influence of the non-Newtonian power law index ( n = 0.5, n = 1.0). Results for the time evolution of streamlines, isotherms and freezing curves are analyzed. The effect of the Reynolds number on streamlines of the external fluid is remarkable, principally near the region close to the internal water filled container. Differences between cooling and freezing times are found for Newtonian ( n = 1.0) and non-Newtonian modified ( n = 0.5) water.

Unsteady conjugate forced convection heat/mass transfer in ensembles of Newtonian fluid spheres

The unsteady, conjugate, forced convection heat/mass transfer from ensembles of mono-size Newtonian fluid spheres to Newtonian fluids has been studied at moderate Peclet and Reynolds numbers. The cell model has been used to account for the spheres hydrodynamic interactions. The momentum and heat/mass balance equations were solved numerically in spherical coordinates system by a finite difference method. The values considered for the sphere exterior Reynolds number are Re 2 ⩽ 200 . The influence of the voidage and physical properties ratios on the heat/mass transfer rate was analysed for sphere Peclet numbers, Pe 1(2) ⩽ 10 4, and three fluid – fluid systems: gas–liquid, liquid–liquid and liquid–gas.

3D conjugate natural convection in a vertical cylinder on the assumption of heat transfer to the environment

Mathematical simulation of three-dimensional unsteady conjugate natural convection in a closed vertical cylinder having a local heat source in conditions of convective heat transfer to the environment in terms of dimensionless variables such as vector potential, vorticity vector, temperature has been carried out. Temperature and velocity fields and the average Nusselt number at the heat source surface as functions of key parameters, reflecting formation of different modes of mass transfer, momentum transport and energy transfer, have been obtained.

Unsteady conjugate water/air mixed convection in a square cavity

Transient natural convection inside an inner thin walled container caused by external mixed convection in a square cavity has been analyzed numerically. Air and water were chosen alternatively as internal and external working fluids. Fluid mechanics and conjugate heat transfer, described in terms of continuity, linear momentum and energy equations, were predicted by using the finite volume method. Streamlines, isotherms, velocity profiles and local Nusselt number time evolution are presented for external flows, of either air or water, with Ri = 1, in two cases: Re = 200 and 500.

CONJUGATE NATURAL CONVECTION IN AN ENCLOSURE WITH LOCAL HEAT SOURCES

The development of unsteady conjugate natural convection in an enclosure has been numerically studied. The decision region is common in many applications, such as environmental control (e.g., room), applied chemistry (e.g., storage reservoir), and electronics (e.g., cabinets). The enclosure considered has thick walls, two heat sources, and a zone with an elevated heat transfer intensity. The heat sources are isothermal. The governing unsteady, three-dimensional heat transfer equations, written in dimensionless terms of the vorticity vector, vector potential functions, and temperature, have been solved using an implicit finite-difference method. The conjugate heat transfer in the enclosure is investigated by means of a continuum model, which treats the fluid and solid constituents individually. The solution has the following parameters: the Grashof number Gr and the Prandtl number Pr. Results have been obtained for a Prandtl number of 0.702 and Grashof number ranged from10 4 to 10 7 .

Unsteady conjugate forced convection heat/mass transfer in ensembles of spherical particles with cell models

Numerical methods are used to investigate the transient, conjugate, forced convection heat/mass transfer in multiparticle systems at low to moderate Reynolds numbers. The interparticle interactions have been accounted for by using the simple cell models. The momentum and heat/mass balance equations were solved numerically in spherical coordinates system by a finite difference method. The values considered for the sphere Reynolds number are Re < 100. The computations were focused on the influence of the voidage and physical properties ratios on the heat/mass transfer rate for sphere Peclet number, 10 ⩽ Pe ⩽ 1000.

A level set embedded interface method for conjugate heat transfer simulations of low speed 2D flows

This study examines the use of a level set based embedded interface method to simulate fluid–solid heat transfer processes using Cartesian grids. The flow field is described by the incompressible 2D Navier–Stokes equations using a vorticity–streamfunction approach. A fluid–solid coupling formulation for the thermal and momentum fields is developed that is robust, computationally efficient and second-order accurate. Solutions for several example problems are presented for flow over stationary and moving cylinders to bench mark the current approach. Heat transfer for an isolated cylinder and two cylinders in series are then examined to explore the Nusselt number dependence on cylinder spacing and unsteady conjugate heat transfer processes.

Unsteady conjugate problem of a dissipative fluid in a horizontal channel with a periodic variation temperature

The unsteady two-dimensional transient heat transfer problem referring to a fully laminar flow developing in a parallel-plane channel exposed to a periodic variation surface temperature with distance is numerically studied. The effects of channel thickness, Peclet number, wall-to-fluid conductivity ratio, thermal diffusivity ratio, angular frequency and the viscous dissipation parameter are determined in the solutions. The non-linear equations are discretized by means an implicit finite difference scheme and the electric analogy to the resulting system is applied to convert these equations into a network-electrical model that was solved using a computer code (electric circuits simulator). In this scheme, only spatial discretization is necessary, while time remains as a real continuous variable, and its programming does not require manipulation of the sophisticated mathematical software that is inherent in other numerical methods. The network simulation method, which satisfies the conservation law for the heat flux variable and the uniqueness law for temperature, also permits the direct visualization of the local and/or integrated transport variables at any point or section of the medium.

Unsteady conjugate forced convection heat/mass transfer from a finite flat plate

Numerical methods are used to investigate the transient, conjugate, forced convection heat/mass transfer from a finite flat plate to a steady stream of viscous, incompressible fluid. The heat/mass balance equations were solved numerically in Cartesian coordinates by a finite difference method. The values considered for the plate Reynolds number and Prandtl number are Re = 100 and Pr = 0.1 , 1 and 10. The computations were focused on the influence of the physical properties ratios and aspect ratio on the heat/mass transfer rate.

Modelling of thermogravitation convection in closed volume with local sources of heat release

A mathematical model is presented for unsteady conjugate convective-conductive heat transfer in a closed volume with local sources of heat release under the conditions of a convective-radiation heat exchange on one of external faces of the solution region. The thermogravitation convection regime was analysed for moderate Grashof numbers. The typical temperature and velocity fields were obtained, and the fields of desired quantities were compared for the planar and three-dimensional models in one of the typical sections of the solution region.