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.     

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.     

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.     

Improvement in device performance on laminar counterflow concentric circular heat exchangers with uniform wall fluxes

The effects of recycle at the ends on the heat transfer through a concentric circular tube with uniform wall fluxes are studied analytically by an orthogonal expansion technique with eigenfunction power series expansion. The heat transfer problem is solved for fully developed laminar velocity profiles in a double-pass circular heat exchanger with ignoring axial conduction and fluid properties of temperature independence. Analytical results show the external recycle can enhance the heat transfer efficiency compared with that in an open tube (without an impermeable circular tube inserted and without recycle). The compensation between the forced-convection increment and heat-transfer driving force decrement are used to study the heat transfer behavior. The effects of the impermeable-tube location on heat transfer efficiency enhancement as well as the power consumption increment have been also discussed.     

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.     

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.     

Recycle effect on heat transfer enhancement in double-pass heat exchangers under asymmetric isotherm conditions

The mathematical formulation of a heat transfer flow problem in the recycling parallel-plate heat exchanger under asymmetric wall temperatures was developed theoretically with ignoring axial conduction, and the analytical solution was obtained using a superposition principle and an orthogonal expansion technique in extended power series. The influences of the design parameters of the impermeable-sheet position (∆), and the operating parameters of the Graetz number (Gz), wall temperature ratio (σ) and recycle ratio (R) are examined. Significant heat transfer improvement is obtainable by employing double-pass devices instead of using single-pass ones for a larger Graetz number system. 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 wall temperature ratios.     

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.     

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.     

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.     

Double-pass flow heat transfer in a parallel-plate channel for improved device performance under uniform heat fluxes

A design of inserting in parallel an impermeable sheet to divide an open conduit into two subchannels for conducting double-pass laminar countercurrent operations under uniform heat fluxes, resulting in substantially improved the heat-transfer rate, has been designed and investigated theoretically by using an eigenfunction expansion in terms of power series for the homogeneous part and an asymptotic solution for the non-homogeneous part. The theoretical results of heat-transfer efficiency enhancement in double-pass parallel-plate heat exchangers are represented graphically and compared with those in the single-pass operations without an impermeable sheet inserted. 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.     

Conjugated heat transfer in double-pass laminar counterflow concentric-tube heat exchangers with sinusoidal wall fluxes

An analytical method is proposed to predict the temperature distribution and local Nusselt number for laminar flow in a double-pass countercurrent heat exchanger with sinusoidal heat flux distribution. A design of inserting in parallel an impermeable barrier to divide an open conduit into two subchannels for conducting double-pass operations, resulting in substantially improved the heat transfer rate, has been evaluated theoretically in the fully developed region. Comparison with the theoretical results shows that the heat-transfer efficiency improvement for double-pass concentric circular heat exchangers is generally higher than those in the single-pass operations without an impermeable barrier inserted. The influences of the impermeable-barrier location on the heat-transfer efficiency improvement and power consumption increment, as indicated from theoretical predictions, can be used to determine the economical feasibility in operating double-pass devices.     

The influences of recycle on a double-pass laminar counterflow concentric-tube heat exchangers with sinusoidal wall fluxes

The effects of external recycle at the ends on double-pass laminar countercurrent heat exchangers with sinusoidal heat flux distribution are investigated analytically by setting a general solution to separate the original boundary value problem into a partial differential equation, which is solved by Frobenius method, and an ordinary differential equation. Analytical results show that recycle effects enhance the heat-transfer efficiency due to that the desirable effect of forced-convection increment has more influence than the undesirable effect of the heat-transfer driving-force decrement, and hence the forced-convection increment by increasing the recycle ratio leads to improved device performance in heat-transfer rate as compared with that in the single-pass operation (without an impermeable sheet inserted).     

A THEORETICAL STUDY OF THE RECYCLE EFFECT ON HEAT TRANSFER EFFICIENCY IN COOL-THERMAL DISCHARGE SYSTEMS FROM ICE MELTING WITH PRODUCING CHILLED AIR

The influence of the recycle effect on cool-thermal discharge systems in a parallel-plate channel with one side cooled by melting ice and the other side insulated is studied theoretically. The mathematical formulations are developed with moving boundary and the theoretical predictions are calculated using the integral boundary layer to estimate the required air mass flow and outlet chilled air temperature. Theoretical results show that the recycle operation can effectively enhance the heat transfer efficiency compared with that in the device without external refluxes. Numerical examples of inlet ambient air temperatures varied with time are illustrated to simulate practical systems from sunrise to sunset. The power consumption increment is also discussed.     

Evaluation of thermal efficiency of double-pass solar collector with porous–nonporous media

The double-pass solar collector with porous media in the lower channel provides a higher outlet temperature compared to the conventional single-pass collector. Therefore, the thermal efficiency of the solar collector is higher. A theoretical model has been developed for the double-pass solar collector. An experimental setup has been designed and constructed. The porous media has been arranged in different porosities to increase heat transfer, area density and the total heat transfer rate. Comparisons of the theoretical and the experimental results have been conducted. Such comparisons include the outlet temperatures and thermal efficiencies of the solar collector for various design and operating conditions. The relationships include the effect of changes in upper and lower channel depth on the thermal efficiency with and without porous media. Moreover, the effects of mass flow rate, solar radiation, and temperature rises on the thermal efficiency of the double-pass solar collector have been studied. In addition, heat transfer and pressure drop relationships have been developed for airflow through the porous media. Close agreement has been obtained between the theoretical and experimental results. The study concluded that the presence of porous media in the second channel increases the outlet temperature, therefore increases the thermal efficiency of the systems.     

Improvement in performance on laminar counterflow concentric circular heat exchangers with external refluxes

Considerable improvement of heat transfer in laminar counterflow concentric heat exchangers is obtainable by inserting in parallel an impermeable, resistless sheet to divide an open duct into two subchannels for double-pass operations with external refluxes. Efficiency improvement in heat transfer has been investigated analytically by using an orthogonal expansion technique. The results of improvement in heat transfer efficiency are represented graphically and compared with those in a single-pass operation. The influences of improvement-sheet location and reflux ratio on the enhancement of transfer efficiency as well as on the increment of power consumption have been discussed.     

Heat transfer enhancement in cool-thermal discharge systems from ice melting with time–velocity variations

A mathematical model for the cool-thermal discharge systems which produce chilled air by melting ice to supply on-peak daytime air-conditioning needs under time-velocity variations and external recycle was developed. The model resolves the moving liquid–solid interface problem with the integral boundary-layer analysis method. For specified target of the outlet air temperature, time variation of the air velocity can be theoretically predicted for the given ambient air inlet temperature functions. The heat transfer efficiency can be improved by employing the external recycle design under the expense of power consumption. The analysis indicates that the recycle effect is more significant for the case with higher outlet air temperature target. Besides, optimal reflux ratio exists for the analyzed system.     

Improvement in device performance of multi-pass flat-plate solar air heaters with external recycle

A study on improvement in device performance of multi-pass solar air heaters with external recycle has been carried out under countercurrent-flow operations. An absorbing plate and insulation sheet were inserted horizontally and vertically, respectively, into a parallel-plate channel to divide the open duct into four subchannels. The coupled nonlinear ordinary differential equations were derived and solved numerically. The theoretical results show that the new device of four-pass flat-plate solar air heater with external recycle can enhance the heat transfer rate compared with that in an open conduit (without the vertical insulation sheet inserted and the absorbing plate glued on the bottom insulation plate, the so-called a downward-type single-pass solar air heater) under the same flow rate and working dimensions. The effects of inserting the absorbing plate and insulation sheet on the transfer efficiency enhancement as well as on the hydraulic dissipated power increment have been also discussed.     

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.