Recycle effect on heat transfer enhancement in double-pass parallel-plate heat exchangers under asymmetric wall fluxes

A new design of conjugated heat transfer in double-pass parallel-plate laminar countercurrent operations subjected to asymmetric wall heat fluxes has been investigated theoretically, and the analytical results obtained with superposition model which introduces the an eigenfunction expansion in terms of power series for the homogeneous part and an asymptotic solution for the inhomogeneous part. The influences of the design parameters, the impermeable-sheet position (Δ), and the operating parameters, the mass-transfer Graetz number (Gz), wall heat flux ratio (Q_r) and recycle ratio (R), are examined. The results are represented graphically and compared with those in a single-pass parallel-plate heat exchanger (without inserting an impermeable sheet). Considerable improvement in heat transfer is obtainable by employing such a recyclic double-pass device, instead of using the single-pass one. A technical feasibility of the new double-pass device was investigated in terms of the Nusselt number and device performance improvement under the effect of variable ratio of heat fluxes on both sides. It concluded that a substantial heat-transfer efficiency improvement is achieved by employing such a recyclic device with suitable elections of impermeable-sheet position and recycle ratio.     

Recycle effect on heat-transfer efficiency improvement in a double-pass parallel-plate heat exchanger under uniform wall fluxes

The recycle concept was applied to a double-pass parallel-plate heat exchanger under uniform wall fluxes to enhance the device performance improvement. The mathematical statement of the conjugated Graetz problem was developed theoretically and the analytical solution was obtained by using an eigenfunction expansion in terms of power series for the homogeneous part and an asymptotic solution for the inhomogeneous part. The theoretical predictions of wall temperature and average Nusselt numbers are represented graphically with Graetz number and impermeable-sheet location as parameters. A substantial heat-transfer efficiency improvement is achieved by employing such a recyclic device with suitable adjustments of the impermeable-sheet position and recycle ratio, instead of using the single-pass device. The results indicate that the recyclic operation can effectively enhance the heat transfer efficiency, especially when the recyclic device was operated in large Graetz number.     

The influences of recycle on a double-pass laminar counterflow concentric circular heat exchangers

A new device of inserting an impermeable sheet with negligible thermal resistance to divide a circular tube into two subchannels with uniform wall temperature and external refluxes at the ends, resulting in substantially improving the heat transfer, has been designed. The mathematical formulation and theoretical analysis to such a conjugated Graetz problem of double-pass concentric circular heat exchangers have been developed by the use of an orthogonal expansion technique. The analytical results are represented graphically and compared with that in an open conduit of the same size without recycle. Considerable improvement in heat transfer is obtainable by employing double-pass operations with inserting an impermeable sheet instead of using single-pass operations without external refluxes. Two numerical examples in heat transfer efficiency by arranging the recycle effect as well as the power consumption were illustrated. The effects of the channel thickness ratio on the enhancement of heat transfer efficiency as well as on the power consumption increment have been also discussed.     

Heat transfer enhancement for the power-law fluids through a parallel-plate double-pass heat exchangers with external recycle

The conjugated Graetz problem of the double-pass heat transfer through a parallel-plate device with uniform wall temperature and external recycle in the outlet channel was solved analytically with the use of the orthogonal expansion technique for the power-law fluids. The mathematical formulation of the heat transfer problem was developed for fully developed laminar velocity profiles through the parallel-plate channels by ignoring axial conduction and assuming fluid properties of temperature independence. The constant outer wall temperature and continuous temperature and heat flux between the two subchannels with inserting impermeable sheet were considered for thermal boundary conditions. The analytical results show that the recycle ratio and impermeable sheet position play significant influences on the efficiencies of the heat transfer as compared to that in a single pass (without an impermeable sheet inserted and without recycle). The outlet temperature of the heat exchanger seems to be independent of the power-law index of the fluid, while the average Nusselt number could not be enhanced significantly with the lowering power index. The power consumption increment owing to the cross-sectional area reduction from single-pass to double-pass was also taken into account for comparisons.     

An analytical study of power-law fluids in double-pass heat exchangers with external recycle

The influence of the recycle effect on heat transfer to the power-law fluids from a double-pass parallel-plate heat exchanger with uniform wall temperature has been studied analytically. The governing equations are solved by an orthogonal expansion technique in terms of power series. The heat transfer problem is solved for fully developed laminar flow through parallel-plate channels by ignoring axial conduction, with fluid properties of temperature independence. The dependence of the average Nusselt number on the Graetz number has been studied in detail. Analytical results show that the recycle effect can enhance the heat transfer efficiency as compared with that in a single pass (without an impermeable plate inserted and without recycle). Considerable heat-transfer enhancement is obtained by introducing the recycle-effect concept in designing such double-pass operations. The effects of the impermeable-sheet position and the power-law index on the enhancement of device performance as well as the power consumption increment have also been delineated.     

Heat transfer of conjugated Graetz problems with laminar counterflow in double-pass concentric circular heat exchangers

A device of external recycle at the ends of double-pass concentric circular heat exchangers with uniform wall temperature, resulting in substantially improving the heat transfer, has been designed and studied theoretically. The theoretical analysis on heat transfer efficiency improvement has been developed using orthogonal expansion technique in power series. The analytical results are also represented graphically and compared with that in an open conduit (without an impermeable plate inserted and without recycle). Considerable improvement in heat transfer is obtainable by employing the external recycle at both ends with a suitable adjustment of the impermeable-sheet position and recycle ratio, instead of using an open conduit.     

The influence of recycle on a parallel-plate heat exchanger with insulation sheet inserted for double-pass operations

The influence of recycle on a parallel-plate heat exchanger of inserting in parallel an insulation sheet to divide an open duct into two channels for double-pass operations with uniform wall temperature has been studied analytically. The results are represented graphically and compared with those in an open duct (without an inserted insulation sheet) and a double-pass without recycle. Substantial improvement in heat transfer is obtainable by employing such a double-pass device with external refluxes, instead of using an open conduit with single-pass operations and using double-pass operations without recycle. The effect of insulation-sheet location on the enhancement of heat transfer efficiency as well as on the increment of power consumption, has been also discussed.     

Asymmetric wall heat fluxes boundary conditions in double-pass parallel-plate heat exchangers

Boundary conditions for asymmetric wall heat fluxes in double-pass parallel-plate laminar countercurrent operations are analyzed theoretically in this work by using an eigenfunction expansion in terms of power series for the homogeneous part and an asymptotic solution for the non-homogeneous part. Effects of variable ratio of heat fluxes on both sides and impermeable-sheet location are also studied. Quantitative and qualitative interpretations of theoretical predictions are utilized to investigate of heat-transfer efficiency enhancement of the double-pass model under consideration as compared to those in the single-pass operations without an impermeable sheet inserted. Results are presented in terms of Nusselt number and device performance improvement. The influence of the impermeable-sheet location on the heat-transfer efficiency enhancement as well as on the power consumption increment in double-pass operations has also been delineated.     

Buoyancy effects on laminar heat transfer in the thermal entrance region of horizontal rectangular channels with uniform wall heat flux for large prandtl number fluid

The Graetz problem for fully developed laminar flow in horizontal rectangular channels with uniform wall heat flux is extended by including buoyancy effects in the analysis for the case of large Prandtl number fluid. A general formulation valid for all Prandtl numbers is presented and the limiting case of large Prandtl number is approached by a numerical method. The typical developments of temperature profile, wall temperature and secondary flow in the thermal entrance region are presented for the case of square channel γ = 1. Local Nusselt number variations are presented for the aspect ratios γ = 0.2, 0.5, 1, 2 and 5 with Rayleigh number as parameter. Due to entry and secondary flow effects, a minimum Nusselt number occurs at some distance from the entrance, depending on the magnitude of Rayleigh number. This behavior is similar to that observed in the thermal entrance region where the transition from laminar to turbulent flow occurs. The effect of Rayleigh number is seen to decrease the thermal entrance length, and the Graetz solution, neglecting buoyancy effects, is found to be applicable only when Rayleigh number is less than about 10³. A study of the practical implications of large Prandtl number on heat transfer results for hydrodynamically and thermally fully developed case reveals that the present heat transfer results are valid for Prandtl number ranging from order 10 to infinity.     

Heat transfer flow in a parallel-plate channel by inserting in parallel impermeable sheets for multi-pass coolers or heaters

The influences of recycle at the ends on multi-pass coolers or heaters through a parallel-plate channel with constant wall temperature are studied and an exact solution of this problem is presented using an orthogonal expansion technique. Analytical results show that the external refluxes can enhance the heat transfer efficiency due to the desirable convective effect having more influence than the undesirable preheating effect for all Graetz numbers, leading to considerably improved device performance in heat transfer. The results are represented graphically and compared with the heat transfer efficiency by the adjustment of channel thickness ratio in a single-pass operation (without inserting impermeable sheets). The suitable selections of the design and operating parameters on considering of both the heat transfer improvement and power consumption increment are also discussed.     

Heat-transfer efficiency improvement of double-pass concentric circular heat exchangers under uniform wall fluxes

The new design of the double-pass operation with external recycle is proposed to apply to enhance the heat-transfer efficiency of concentric circular heat exchangers under uniform wall fluxes. The mathematical formulation was developed theoretically and the analytical solutions were achieved by using the orthogonal expansion technique with the eigenfunctions expanding in terms of an extended power series. The theoretical predictions were represented graphically and compared with those obtained from the single-pass device without external recycle and the previous work [C.D. Ho, S.C. Yeh, Improvement in device performance on laminar counterflow concentric circular heat exchangers with uniform wall flux, International Journal of Heat and Mass Transfer 49 (2006) 202–2032] under the different flow pattern. The results show that a considerable heat-transfer efficiency improvement was obtained with a suitable adjustment of the subchannel thickness ratio and recycle ratio. The power consumption increment due to the device with external recycle was also discussed in this study.     

Turbulence forced convection heat transfer over double forward facing step flow

Turbulent forced heat transfer for double forward facing step flow was studied numerically. The bottom wall of the channel is heated at uniform temperature and the flow temperature at the upstream is colder than the wall. Two adiabatic steps are located together with different lengths and heights. The solutions are done using commercial code FLUENT which uses finite volume method. The standard k − ε turbulence model is employed to obtain turbulence flow modeling for double forward step. Effects of step heights, step lengths and Reynolds numbers on heat transfer and fluid flow are investigated as main parameters. Results showed that the second step can be use as a control device for both heat transfer and fluid flow.     

Heat transfer over a nonlinearly stretching sheet with non-uniform heat source and variable wall temperature

In this paper we study the flow and heat transfer characteristics of a viscous fluid over a nonlinearly stretching sheet in the presence of non-uniform heat source and variable wall temperature. A similarity transformation is used to transform the governing partial differential equations to a system of nonlinear ordinary differential equations. An efficient numerical shooting technique with a fourth-order Runge–Kutta scheme is used to obtain the solution of the boundary value problem. The effects of various parameters (such as the power law index n, the Prandtl number Pr, the wall temperature parameter λ, the space dependent heat source parameter A¹ and the temperature dependent heat source parameter B¹) on the heat transfer characteristics are analyzed. The numerical results for the heat transfer coefficient (the Nusselt number) are presented for several sets of values of the parameters and are discussed. The results reveal many interesting behaviors that warrant further study on the effects of non-uniform heat source and the variable wall temperature on the heat transfer phenomena at the nonlinear stretching sheet.     

Numerical simulation of conjugate,turbulent mixed convection heat transfer in a vertical channel with discrete heat sources

This paper presents the results of a comprehensive numerical study to analyze turbulent mixed convection in a vertical channel with a flush-mounted discrete heat source in each channel wall. The conjugate heat transfer problem is solved to study the effect of various parameters like the thermal conductivity of the wall material (k_s), the thermal conductivity of the flush-mounted discrete heat source (k_c), Reynolds number (Re_s), modified Richardson number (Ri⁎) and the aspect ratio of the channel (AR). The standard k–ε turbulence model, modified by including buoyancy effects, without wall functions, has been used for the analysis. The two-dimensional governing equations are discretised on a semi-staggered, non-uniform grid, using the finite volume method. The asymptotic computational fluid dynamics (ACFD) technique has been then applied to obtain a correlation for the non-dimensional maximum temperature θ¯_max, which can be used for a wide range of parameters.     

Numerical study of hydrodynamic and heat transfer of nanofluid flow in microchannels containing micromixer

In this study heat transfer and fluid flow of Al₂O₃/water nanofluid in two dimensional parallel plate microchannel without and with micromixers have been investigated for nanoparticle volume fractions of ϕ = 0, ϕ = 4%  and base fluid Reynolds numbers of Re_f = 5, 20, 50. One baffle on the bottom wall and another on the top wall work as a micromixer and heat transfer enhancement device. A single-phase finite difference FORTRAN code using Projection method has been written to solve governing equations with constant wall temperature boundary condition. The effect of various parameters such as nanoparticle volume fraction, base fluid Reynolds number, baffle distance, height and order of arrangement have been studied. Results showed that the presence of baffles and also increasing the Re number and nanoparticle volume fraction increase the local and averaged heat transfer and friction coefficients. Also, the effect of nanoparticle volume fraction on heat transfer coefficient is more than the friction coefficient in most of the cases. It was found that the main mechanism of enhancing heat transfer or mixing is the recirculation zones that are created behind the baffles. The size of these zones increases with Reynolds number and baffle height. The fluid pushing toward the wall by the opposed wall baffle and reattaching of separated flow are the locations of local maximum heat transfer and friction coefficients.     

Mixed convection heat and mass transfer along a vertical wavy surface

A numerical study of mixed convection heat and mass transfer along a vertical wavy surface has been carried out numerically. The wavy surface is maintained at uniform wall temperature and constant wall concentration that is higher than that of the ambient. A simple coordinate transformation is employed to transform the complex wavy surface to a flat plate. A marching finite-difference scheme is used for present analysis. The buoyancy ratio N, amplitude-wavelength ratio α, and Richardson number (Gr/Re²) are important parameters for this problem. The numerical results, including the developments of skin-friction coefficient, velocity, temperature, concentration, Nusselt number as well as Sherwood number along the wavy surface are presented. The effects of the buoyancy ratio N and the dimensionless amplitude of wavy surface on the local Nusselt number and the local Sherwood number have been examined in detail.     

Natural convection heat and mass transfer along a vertical wavy surface

A numerical study of natural convection heat and mass transfer along a vertical wavy surface has been performed. The wavy surface is maintained at uniform wall temperature and constant wall concentration. A simple coordinate transformation is employed to transform the complex wavy surface to a flat plate. A marching finite-difference scheme is used for the analysis. The buoyancy ratio N, amplitude-wavelength ratio α, and Schmidt number Sc are important parameters for this problem. The numerical results, including the developments of skin-friction coefficient, velocity, temperature, concentration, Nusselt number as well as Sherwood number along the wavy surfaces are presented. The effects of the buoyancy ratio N and the dimensionless amplitude of wavy surface on the local Nusselt number and the local Sherwood number have been examined in detail.     

An Experimental Investigation of Heat Transfer Enhancement Mechanisms in Microencapsulated Phase-Change Material Slurry Flows

This article investigates laminar heat transfer characteristic of two-phase microencapsulated phase-change material (MPCM) suspension flows within minichannels under a constant wall heat flux boundary. Capsules containing paraffin wax with phase-change temperature between 36.1°C and 38.1°C are examined and found to be well suited for electronics cooling applications using liquid cold plate technologies. In particular, it is shown that the large thermal capacity of MPCM slurries around the phase-change temperature can lead toward greater isothermality of isoflux systems, a characteristic of significant interest to telecommunication, laser and biomedical applications. The principal focus of the study is to examine heat transfer characteristics within standard tube flow geometries, quantify the heat transfer augmentation/degradation observed, and finally, elucidate the mechanisms from which these result. Through the study volume concentrations of the MPCM slurry were varied between 0% and 30.2%. High-resolution local heat transfer measurements were obtained using infrared thermography and results presented in terms of local Nusselt number versus inverse Graetz parameter. These spanned both the thermal entrance and the fully developed flow regions with inverse Graetz number ranging from 10^?3 to 10⁰. Results show that significant heat transfer enhancements are attainable via the use of MPCM slurries over conventional single-phase coolants. Overall, the study highlights mechanisms that lead to significant heat transfer enhancements in heat exchange devices employing microencapsulated phase-change material slurries.     

Forced convection heat transfer in microchannel heat sinks

This paper presents an analysis of forced convection heat transfer in microchannel heat sinks for electronic system cooling. In view of the small dimensions of the microstructures, the microchannel is modeled as a fluid-saturated porous medium. Numerical solutions are obtained based on the Forchheimer–Brinkman-extended Darcy equation for the fluid flow and the two-equation model for heat transfer between the solid and fluid phases. The velocity field in the microchannel is first solved by a finite-difference scheme, and then the energy equations governing the solid and fluid phases are solved simultaneously for the temperature distributions. Also, analytical expressions for the velocity and temperature profiles are presented for a simpler flow model, i.e., the Brinkman-extended Darcy model. This work attempts to perform a systematic study on the effects of major parameters on the flow and heat transfer characteristics of forced convection in the microchannel heat sink. The governing parameters of engineering importance include the channel aspect ratio (α_s), inertial force parameter (Γ), porosity (ε), and the effective thermal conductivity ratio (k_r). The velocity profiles of the fluid in the microchannel, the temperature distributions of the solid and fluid phases, and the overall Nusselt number are illustrated for various values of the problem parameters. It is found that the fluid inertia force alters noticeably the dimensionless velocity distribution and the fluid temperature distribution, while the solid temperature distribution is almost insensitive to the fluid inertia. Moreover, the overall Nusselt number increases with increasing the values of α_s and ε, while it decreases with increasing k_r.