Numerical 2-D Modeling of a Coaxial Scraped Surface Heat Exchanger Versus Experimental Results Under the Laminar Flow Regime

Scraped surface heat exchangers (SSHEs) provide a versatile solution in the process industry for treating highly viscous fluids that may also contain particulate matter. Although SSHEs are frequently used in industrial applications, literature on this topic, particularly on the laminar flow regime, is limited. Moreover, due to the specificity of each product, it is difficult to generalize the few data available, and this makes the thermal design of this type of apparatus a critical point. Regarding the numerical approach, several studies based on a two-dimensional (2-D) approximation are available in the open scientific literature, but there is a lack of experimentally validated models. To test the numerical modeling approach, an experimental investigation that focused on the behavior of a coaxial SSHE in the presence of laminar flow was conducted. The appropriateness of the 2-D numerical approach is discussed here. Comparison of the numerical results with the experimentally measured Nusselt number values demonstrates the limits of the 2-D approach in describing the behavior of this type of apparatus.     

Investigation of a Confined Laminar Impinging Jet on a Plate with a Porous Layer Using the Preconditioned Density-Based Algorithm

The preconditioned density-based algorithm and two-domain approach were used to investigate the fluid flow and heat transfer characteristics of a confined laminar impinging jet on a plate covered with porous layer. In the porous zone, the momentum equations were formulated by the Darcy-Brinkman-Forchheimer model; the thermal nonequilibrium model was adopted for the energy equation. At the porous/fluid interface, the applicability and influence of different hydrodynamic and thermal interfacial conditions were analyzed for the problem. The governing equations were solved by the preconditioned density-based finite-volume method, with preconditioning matrix for equations of porous domain adopted, aiming to eliminate the equation stiffness of porous seepage flows. The effects of Reynolds number, porosity, Darcy number, thermal conductivity ratio, Biot number, and porous layer thickness on the flow pattern and local heat transfer performance were studied. Results indicate that the Reynolds number and porosity don't strongly influence the flow pattern of porous channel, while the Darcy number and porous layer thickness have obvious influence on the flow pattern. The heat transfer performance are greatly influenced by the parameters studied.     

Combined Experimental and Numerical Study for a Multiple-Microchannel Heat Transfer System

Multiple microchannel heat sinks for potential use for heat removal from localized thermal sources such as electronic chips are studied experimentally and numerically to characterize their thermal performance. An approach based on combined experimental and numerical modeling is presented. The numerical simulation is driven by experimental data, which are obtained concurrently, to obtain realistic, accurate, and validated numerical models. The ultimate goal is to design and optimize such thermal systems.

The experimental setup was established and liquid flow in the multiple microchannels was studied under different flow rates and heat influx. The temperature variation versus time was recorded by thermocouples, from which the time needed to reach steady state was determined. The measured temperatures under steady-state conditions were compared with those from three-dimensional steady-state numerical simulations for the same boundary and initial conditions. The experimental data were employed for the validation of the numerical model. In case of significant discrepancy, the numerical model was improved, starting initially with a relatively simple model. Fairly good agreement between the experimental and simulation results was finally obtained, indicating the main considerations for an accurate model. The numerical model also served to provide inputs that could be employed to improve and modify the experimental arrangement.

The main focus of this work is on the combined experimental and numerical approach to model and simulate thermal systems, such as the one considered here, particularly in regions where additional transport mechanisms are important. Consequently, low flow rates are employed to consider other transport mechanisms and make this combined experimental-numerical approach useful for design and optimization.     

Thermal state of an incompressible pseudo-plastic fluid and Nusselt number at the interface fluid–die wall

An experimental and numerical study was made of the steady laminar convective heat transfer to polyethylene Dowlex 2042E described by the Cross model flowing through an extrusion die. The inverse heat transfer problem is formulated to reconstruct the thermal history of the melted polymer in the channel die. Local Nusselt number distributions are presented for different flow rate and thermal boundary conditions. The effect of viscous dissipation combined with the flow rate on heat transfer is discussed. It is shown that an increasing flow rate leads to different Nusselt number and correlation is proposed to compute the heat transfer.     

Laminar heat transfer in a moving porous bed reactor simulated with a macroscopic two-energy equation model

This work investigates the influence of physical properties on heat transfer between the solid and fluid phases in a porous reactor, in which both the permeable bed and the working fluid move in the same direction with respect to fixed bounding walls. For simulating laminar flow and heat transfer, a two-energy equation model is applied in addition to a mechanical model. Transport equations are discretized using the control-volume method and the system of algebraic equations is relaxed via the SIMPLE algorithm. The effects of Reynolds number, solid-to-fluid velocity ratio, permeability, porosity, ratio of solid-to-fluid thermal capacity and ratio of solid-to-fluid thermal conductivity on flow and heat transport are analyzed. The laminar model is validated by means of an analytical solution. Results for concurrent laminar flow indicate that, when the speed of the solid approaches that of the fluid, the strong axial convection of the solid, as well as the reduction of the relative velocity, cause an increase in the axial length needed for thermal equilibrium between phases to occur. Longer thermal developing lengths are also found for higher permeabilities and higher porosities. For higher solid-to-fluid thermal capacities and higher solid-to-fluid thermal conductivity ratios, the temperature of the solid phase shows less axial variation regardless of its velocity in relation to the fluid phase.     

Numerical simulation and optimization of nanofluid in a C-shaped chaotic channel

ABSTRACT

In this study, numerical calculations using single- and two-phase models of CuO/water nanofluid forced convection in a three-dimensional C-shaped channel with constant heat flux are investigated. The laminar heat transfer enhancement using a nanofluid in a chaotic flow is first validated with the available data in the literature and the maximum discrepancy is within 3%; then further it is extended to design the C-shaped geometry. In addition, after comparisons of the numerical results with single- and two-phase models, the multiparameter constrained the optimization procedure integrating the design of experiments (DOE), response surface methodology (RSM), genetic algorithm (GA), and computational fluid dynamics (CFD) is proposed to design the nanofluid laminar convection of three-dimensional C-shaped channels. The thermal performance factors predicted by the regression function for the C-shaped channel case are in good agreement with the numerical results of CFD, with the difference being within 10%.     

Numerical investigation of two-phase laminar pulsating nanofluid flow in a helical microchannel

ABSTRACT

Numerical investigations on the thermal and hydraulic characteristics of pulsating laminar flow in a three-dimensional helical microchannel heat sink (HMCHS) model are performed using Al₂O₃-water-based nanofluid. The simulation is performed in the laminar regime for Reynolds number ranging from 6 to 25. The two-phase mixture model with modified effective thermal conductivity and viscosity equations is employed to solve the problem numerically. The detailed results for thermal and flow fields are reported for the effects of amplitude (1–3), frequency (5–20 rad/s), and nanoparticle concentration (1%–3%). The results indicate that the heat transfer performance improves significantly for sinusoidal velocity inlet conditions compared with steady flow conditions.     

Pressure loss and forced convective heat transfer in an annulus filled with aluminum foam

This experimental study investigates non-Darcy flow and heat transfer in an annulus with high porosity aluminum foams to attain the miniaturization of thermal systems. The local wall temperature distribution, inlet and outlet pressures, and temperatures and heat transfer coefficient were measured for heat flux of 13.6–31.4 kW/m². The results show that aluminum foam enhances heat transfer from a surface compared with that of laminar flow in a clear annulus. Correlations for the friction factor and the Nusselt number are proposed and used for design of thermal applications.     

Experiments and Simulations of Laminar Forced Convection With Water–Alumina Nanofluids in Circular Tubes

This work reports fundamental experimental-theoretical research related to heat transfer enhancement in laminar channel flow with nanofluids, which are essentially modifications of the base fluid with the dispersion of metal oxide nanoparticles. The nanofluids were synthesized by a two-step approach, using a dispersant and an ultrasound probe or a ball mill for alumina nanoparticles dispersion within the aqueous media. The theoretical work involves the proposition of an extension of the thermally developing flow model that accounts for the temperature variation of all the thermophysical properties, including viscosity and the consequent variation of the velocity profiles along the thermal entry region. The simulation was performed by making use of mixed symbolic-numerical computation on the Mathematica 7.0 platform and a hybrid numerical-analytical methodology (generalized integral transform technique, GITT) in accurately handling the governing partial differential equations for the heat and fluid flow problem formulation with temperature dependency in the thermophysical properties. Experimental work was also undertaken based on a thermohydraulic circuit built for this purpose, and sample results are presented to verify the proposed model. The aim is to confirm that both the constant properties and temperature-dependent properties models, besides available correlations previously established for ordinary fluids, provide adequate prediction of the heat transfer enhancement observed in laminar forced convection with such nanofluids and within the experimented Reynolds number range.     

Laminar forced convection heat transfer with phase change material suspensions

This paper presents results related to laminar forced convection heat transfer to a phase change material suspension in a circular duct with constant wall heat flux. An effective specific heat approach has been used to model the heat transfer process for a flow with a fully developed velocity profile. The model has been verified by comparing its numerical predictions with previous theoretical results as well as well as experimental data. A simple correlation for wall temperature rise as a function of the tube length that can be used for future design has been developed based on a parametric study.     

A way to explain the thermal boundary effects on laminar convection through a square duct

A way using the reformulation of the energy conservation equation in terms of heat flux to explain the thermal boundary effects on laminar convective heat transfer through a square duct is presented. For a laminar convection through a square duct, it explains that on the wall surface, the velocity is zero, but convection occurs for uniform wall heat flux (UWHF) boundary in the developing region due to the velocity gradient term; for uniform wall temperature (UWT) boundary, only diffusion process occurs on the wall surface because both velocity and velocity gradient do not contribute to convection; for UWHF, the largest term of the gradient of velocity components (the main flow velocity) on the wall surface takes a role in the convection of the heat flux normal to the wall surface, and this role exists in the fully developed region. Therefore, a stronger convection process occurs for UWHF than for UWT on the wall surface. The thermal boundary effects on the laminar convection inside the flow are also detailed.     

A preliminary model for phase change thermal energy storage in a shell and tube heat exchanger

A preliminary model for estimating possible thermal energy storage in a phase change shell and tube heat exchanger is presented. Effect of various parameters such as thermal and physical properties of PCM and convective fluid, heat exchanger dimensions and heat transfer fluid flow rates both in laminar and turbulent regime on energy storage times are discussed. The model is illustrated for specific cases.     

Numerical Analysis of Flow and Thermal Performance of Liquid-Cooling Microchannel Heat Sinks with Bifurcation

Single-phase liquid-cooling microchannels have received great attention to remove the gradually increased heat loads of heat sinks. Proper changes of the flow path and/or heat transfer surface can result in much better thermal performance of microchannel heat sinks. In this study, a kind of rectangular straight microchannel heat sink with bifurcation flow arrangement has been designed, and the corresponding laminar flow and heat transfer have been investigated numerically. Four different configurations are considered. The effects of the bifurcation ratio (the initial channel number over the bifurcating channel number) and length ratio (the channel length before bifurcation over the bifurcation channel length) on laminar heat transfer, pressure drop, and thermal resistance are considered and compared with those of the traditional straight microchannel heat sink without bifurcation flow. The overall thermal resistances subjected to inlet Reynolds number and pumping power are compared for the five microchannel heat sinks. Results show that the thermal performance of the microchannel heat sink with bifurcation flow is better than that of the corresponding straight microchannel heat sink. The heat sinks with larger bifurcation ratio and length ratio provide much better thermal performance. It is suggested to employ bifurcation flow path in the liquid-cooling microchannel heat sinks to improve the overall thermal performance by proper design of the bifurcation position and number of channels.     

Effects of a Thick Plate on the Excess Temperature of Iso-Heat Flux Heat Sources Cooled by Laminar Forced Convection Flow: Conjugate Analysis

A conjugate analysis via the finite volume approach is performed to study the effects of a thick plate on the excess (peak) temperature of an iso-heat flux heat source cooled by laminar forced convection flow. A thick plate of temperature-dependent thermal conductivity is placed between the heat sources and the cooling fluid. A cooling fluid flows over the thick plate and removes the heat by laminar forced convection. On account of the two-dimensional heat redistribution in the finite thick plate with one face subjected to iso-heat flux and the other face exposed to forced flow, the interface ceases to be an iso-heat flux and, consequently, reduces the excess temperature of the heat sources. In the numerical analysis, the thickness of the plate is relaxed one by one to search for the optimal thickness that minimizes the excess temperature. It is shown that the reduction in the excess temperature due to the insertion of the thick plate with optimal thickness depends upon the Reynolds number of the fluid flow and the fluid-to-solid thermal conductivity ratio.     

Physical Effects of Variable Fluid Properties on Laminar Gas Microconvective Flow

The physical effects of variable fluid properties on heat transfer and frictional flow characteristics of laminar gas microconvective flow are investigated in this research. The fully developed flow through a microtube is studied numerically by using 2D continuum‐based governing equations. The physical effects induced due to variations in gas density with pressure and temperature, and gas viscosity, thermal conductivity, and specific heat with temperature are analyzed. Numerical results reveal that the heat transfer and frictional flow characteristics of laminar gas microflow are drastically affected by these physical effects. Hence, this research suggests that these physical effects need to be well considered in the applications of laminar gas microconvection based on large temperature gradients, for example, the design of microchannel heat sinks, and the flow cannot be generally considered as a constant property flow, as in conventional channels.     

Laminar Flow Forced Convection Heat Transfer Behavior of a Phase Change Material Fluid in Finned Tubes

The heat transfer behavior of phase change material fluid (PCM) under laminar flow conditions in circular tubes and internally longitudinal finned tubes was studied. An effective specific heat technique was used to model the phase change process. Heat transfer results for a smooth circular tube with PCM fluid were obtained under hydrodynamically and thermally fully developed conditions. Results for the finned tube were obtained using the H2 and T boundary conditions. It was determined that the Nusselt number was strongly dependent on the Stefan number, fin thermal conductivity value, and height of the fins.     

Transient Analysis of Slip Flow and Heat Transfer in Microchannels

Hybrid analytical-numerical solutions for transient flow and transient convective heat transfer within microchannels are presented. Analytical solutions for flow transients in microchannels are obtained by making use of the integral transform approach. The proposed model involves the transient fully developed flow equation for laminar regime and incompressible flow with slip at the walls in simple channel geometries. The solution is constructed so as to account for any general functional form of the time variation of the pressure gradient along the duct. Then, the transient-state convection heat transfer is solved for laminar slip flow inside microchannels formed by parallel-plates, making use of the generalized integral transform technique (GITT) and the exact analytical solution of the corresponding eigenvalue problem in terms of confluent hypergeometric functions so as to eliminate the transversal coordinate. The resulting system of transformed partial differential equations in the longitudinal coordinate is numerically solved by the Method of Lines as implemented in the routine NDSolve of the Mathematica system. Mixed symbolic-numerical algorithms are developed under the Mathematica platform.     

An inverse heat transfer problem for restoring the temperature field in a polymer melt flow through a narrow channel

An important problem in polymer processing is to provide suitable thermal conditions for polymer melt flows through narrow channels during extrusion or injection. Due to various thermal effects (e.g., viscous dissipation, chemical reactions) the temperature profile of the melt could be quite sharp. In order to numerically simulate polymer flows and heat transfer through a narrow channel, the inlet boundary conditions, which are generally unknown, have to be specified. For such a creeping flow, the area where the velocity field develops is very short. In contrast, the inlet temperature profile develops quite slowly and affects the temperature field far downstream. An approach is suggested for restoring the inlet temperature profile by solving an inverse heat transfer problem using Cauchy data at the channel wall. The polymer flow is assumed to be a steady, laminar and incompressible flow of a non-Newtonian pseudo-plastic fluid, which is governed by the Navier–Stokes equations and a constitutive “power law” model for viscosity. This non-linear inverse problem is solved by a sequential approximation method combined with Tikhonov's regularization method. Notably, this approach has been found to be efficient for field observation problems, when the magnitude of non-linearity is not too large. The results of numerical simulation are presented and questions regarding accuracy are discussed.     

Heat flux and slip effects on liquid flow in a microchannel

In this study, the liquid flow with the slip boundary condition in a microchannel between two parallel plates with imposed heat flux was numerically investigated. The combined effect of pressure-driven flow and electro-osmosis was taken into account. Electric potential, liquid flow and thermal characteristics were determined using the Poisson–Boltzmann, the modified Navier–Stokes and the energy equations for a hydrodynamical and thermal steady fully developed laminar flow for an incompressible liquid. The results demonstrate the influence of the slip coefficient, the heat flux and the pressure difference on flow velocity, local temperature and Nusselt number. A comparison of the developed model results with those in a previous study was made.