Constant Wall Heat Flux Research Articles

Numerical Investigation of Heat Transfer, Pressure Drop and Wall Shear Stress Characteristics of Al2O3-Water Nanofluid in a Square Duct

Turbulent heat transfer, pressure drop and wall shear stress behavior of the nanofluid Al2O3-water mixture in a square duct under constant wall heat flux are investigated numerically. Single-phase approach is taken into account during the simulations. All of the nanofluid properties depend on the temperature and the nanoparticle volume concentration. The renormalization group theory RNG \({k-\varepsilon}\) model is employed in order to model turbulence. Validation tests of the numerical results are done by using water as the first working fluid. Similar models and methods are chosen for the simulation of nanofluid (Al2O3-water) flow and heat transfer. A very good agreement is realized with the previous water and nanofluid related theoretical-empirical heat transfer and pressure drop correlations. The rate of heat transfer is increased by the presence of nanofluids when compared to that of water. Increasing Re number and particle’s volumetric concentration increases the convection heat transfer coefficient, pressure drop and wall shear stress along the duct. On the other hand, this study confirmed that single-phase model approach is appropriate for the simulation of Al2O3-water flow and heat transfer.

Heat Transfer Enhancement in Circular Tube using Twisted Tape Inserts of Different Width Ratio under Constant Wall Heat flux Condition

Heat Transfer Enhancement in Circular Tube using Twisted Tape Inserts of Different Width Ratio under Constant Wall Heat flux Condition

Modeling and Simulation of Supercritical-Pressure Turbulent Heat Transfer of Aviation Kerosene with Detailed Pyrolytic Chemical Reactions

Regenerative cooling of the high-temperature components in propulsion and power-generation systems plays a paramount role in maintaining the reliability and durability of the systems. In this paper, a mathematical model is developed for studying fluid dynamics and heat-transfer characteristics of the aviation kerosene RP-3 at supercritical pressures. The model accommodates a detailed pyrolytic chemical reaction mechanism, which consists of 18 species and 24 elementary reactions (Jiang, R.; Liu, G.; Zhang, X. Thermal cracking of hydrocarbon aviation fuels in regenerative cooling microchannels. Energy Fuels 2013, 27, 2563−2577). Accurate calculations of thermophysical properties at supercritical pressures are properly incorporated. After rigorous model validations, numerical studies of turbulent heat transfer of RP-3 in a micro cooling tube at a supercritical pressure of 5 MPa are conducted under operating conditions of both constant wall heat flux and constant surface temperature to obtain a fundamental understanding of the complex physicochemical processes. Results indicate that the endothermic fuel pyrolysis, which prevails once the bulk fluid temperature rises above 750 K, dictates the fluid flow and heat-transfer process in the high fluid temperature region. Significant variations of the fluid thermophysical properties also make strong impacts; two scenarios of heat-transfer enhancement resulting from property variations under the tested conditions are analyzed. This work has fundamental and practical implications for effective thermal management in propulsion and power-generation systems.

Thermo-fluidic characteristics of ice slurry in horizontal circular pipes

Ice slurry is composed of ice particles and aqueous solution, and it can be utilized as cold storage medium and secondary refrigerant in a secondary-loop refrigeration. In the present study, the forced convective flow and heat transfer of ice slurry in horizontal pipes were numerically investigated, in which 3D Euler–Euler multiphase model based on kinetic theory of granular flow was adopted. The model was firstly validated with the experimental results from the literature. Thereafter, it was applied to investigate the flow and heat transfer characteristics of ice slurry under various conditions. The numerical results showed that more ice particles were suspended on the upper side of pipe at higher inlet velocity and solid volume fraction due to larger turbulent dispersion force and collision interaction among ice particles. During the flow melting process of ice slurry in a horizontal circular pipe under constant wall heat flux, the local heat transfer coefficient decreased rapidly in the entrance region, followed by an approximately constant value. However, when the solid volume fraction near the wall decreased to a small value, ice particles in the center region were difficult to be melted. Hence, the contribution of phase change to heat transfer decreased along the flow direction, resulting in decreasing local heat transfer coefficient. When the solid volume fraction near the wall decreased to zero, a solution region formed near the wall and it extended along the flow direction. Thus the heat from the wall caused rapid increase in the mean fluid temperature, resulting in increasing heat transfer coefficient. After ice slurry was fully melted into aqueous solution, the temperature increase of fluid resulted in decreasing viscosity and increasing turbulent intensity along the flow direction. Therefore, the heat transfer coefficient in the solution region continued increasing in the fully-melted region.

On the effects of exothermicity and endothermicity upon the temperature fields in a partially-filled porous channel

Forced convection of heat in a two-dimensional channel, partially filled by a porous insert is considered. This system is assumed under fully developed conditions and constant wall heat flux. Further, the fluid and solid phases can feature internal heat generation (exothermicity) and consumption (endothermicity). Analytical solutions are developed for the solid and fluid temperature fields by applying local thermal non-equilibrium (LTNE) conditions and the Darcy-Brinkman model of momentum transport. Two existing interface models (Models A and B) are employed to describe the thermal boundary conditions at the porous-fluid interface. The developed solutions for the temperature fields are compared to those found by applying the local thermal equilibrium (LTE) assumption and, therefore, the validity of the LTE is examined. This is done for a wide range of pertinent parameters including Biot number, conductivity ratio, Darcy number and thickness of the porous insert. It is found that the thermal behaviour of the investigated partially filled system is influenced by the heat sources in both solid and fluid phase. It is further shown that the LTE approach remains an acceptable assumption only for some specific regions of the parametric space. Furthermore, the occurrence of temperature gradient bifurcation on the surface of the porous-fluid interface is examined. It is demonstrated that this effect is highly sensitive to the intensity of the energy sources.

Numerical Simulation of Natural Convection in Solar Cavity Receivers

Cavity receivers used in solar power towers and dish concentrators may lose considerable energy by natural convection, which reduces the overall system efficiency. A validated numerical receiver model is desired to better understand convection processes and aid in heat loss minimization efforts. The purpose of this investigation was to evaluate heat loss predictions using the commercial computational fluid dynamics (CFD) software packages fluent 13.0 and solidworks flow simulation 2011 against experimentally measured heat losses for a heated cubical cavity receiver model (Kraabel, 1983, “An Experimental Investigation of the Natural Convection From a Side-Facing Cubical Cavity,” Proceedings of the ASME JSME Thermal Engineering Joint Conference, Vol. 1, pp. 299–306) and a cylindrical dish receiver model (Taumoefolau et al., 2004, “Experimental Investigation of Natural Convection Heat Loss From a Model Solar Concentrator Cavity Receiver,” ASME J. Sol. Energy Eng., 126(2), pp. 801–807). Simulated convective heat loss was underpredicted by 45% for the cubical cavity when experimental wall temperatures were implemented as isothermal boundary conditions and 32% when the experimental power was applied as a uniform heat flux from the cavity walls. Agreement between software packages was generally within 10%. Convective heat loss from the cylindrical dish receiver model was accurately predicted within experimental uncertainties by both simulation codes using both isothermal and constant heat flux wall boundary conditions except when the cavity was inclined at angles below 15 deg and above 75 deg, where losses were under- and overpredicted by fluent and solidworks, respectively. Comparison with empirical correlations for convective heat loss from heated cavities showed that correlations by Kraabel (1983, “An Experimental Investigation of the Natural Convection From a Side-Facing Cubical Cavity,” Proceedings of the ASME JSME Thermal Engineering Joint Conference, Vol. 1, pp. 299–306) and for individual heated flat plates oriented to the cavity geometry (Pitts and Sissom, 1998, Schaum's Outline of Heat Transfer, 2nd ed., McGraw Hill, New York, p. 227) predicted heat losses from the cubical cavity to within experimental uncertainties. Correlations by Clausing (1987, “Natural Convection From Isothermal Cubical Cavities With a Variety of Side-Facing Apertures,” ASME J. Heat Transfer, 109(2), pp. 407–412) and Paitoonsurikarn et al. (2011, “Numerical Investigation of Natural Convection Loss From Cavity Receivers in Solar Dish Applications,” ASME J. Sol. Energy Eng. 133(2), p. 021004) were able to do the same for the cylindrical dish receiver. No single correlation was valid for both experimental receivers. The effect of different turbulence and air-property models within fluent were also investigated and compared in this study. However, no model parameter was found to produce a change large enough to account for the deficient convective heat loss simulated for the cubical cavity receiver case.

Transient MHD heat transfer and entropy generation in a microparallel channel combined with pressure and electroosmotic effects

By using the method of Laplace transform, analytical investigations are performed for combined unsteady electroosmotic, pressure driven and magnetohydrodynamic (MHD) flow of an electrically conducting, incompressible and viscous fluid through a slit parallel plate microchannel under the action of a vertical magnetic field. The velocity profiles for different time and their dependence on several non-dimensional parameters are explained graphically. Based upon the velocity field of steady part, the thermally fully developed heat transfer problem are analyzed by taking the viscous dissipation, the volumetric heat generation due to Joule heating effect and electromagnetic couple effect into account. The exact solution of temperature field is derived subjected to constant wall heat flux condition. The dependence of several dimensionless parameters on temperature and the Nusselt number Nu based on channel height is presented graphically. Finally, the entropy generation analysis of MHD heat transfer is performed. The variations of local and global entropy generations with related parameters are interpreted and the results are discussed.

A Numerical Study of the Extended Graetz Problem in a Microchannel with Constant Wall Heat Flux: Shear Work Effects on Heat Transfer

ABSTRACTHeat convection of a microchannel gas flow with constant wall heat flux boundary condition is investigated numerically, considering viscous dissipation and axial conduction. The shear work due to the slipping fluid at the wall is incorporated in the analysis. An analytical solution for fully developed conditions is also derived. The effect of the shear work on heat transfer is quantified through a comparative analysis in both the entrance- and the fully developed- regions. The analysis shows that the shear work effect on heat transfer is considerable, and neglecting this term leads to an overestimation of the Nusselt number in gas heating and an underestimation in gas cooling. The over/under estimation of the Nusselt number is dependent on both the Knudsen number and the Brinkman number. The results presented also demonstrate the significance of the shear work in the developing flow region. It is shown that in the developing flow region the Nusselt number is less sensitive to viscous dissipation when the shear work is neglected. It can be concluded from this study that the shear work effect is significant and neglecting it can lead to considerable errors in microchannel flow heat transfer.

Heat transfer and entropy generation for laminar forced convection flow of graphene nanoplatelets nanofluids in a horizontal tube

The results are reported of an investigation of the heat transfer characteristics and entropy generation for a graphene nanoplatelets (GNP) nanofluid with specific surface area of 750m2/g under laminar forced convection conditions inside a circular stainless steel tube subjected to constant wall heat flux. The analysis considers constant velocity flow and a concentration range from 0.025wt.% to 0.1wt.%. The impact of the dispersed nanoparticles concentration on thermal properties, convective heat transfer coefficient, thermal performance factor and entropy generation is investigated. An enhancement in thermal conductivity for GNP of between 12% and 28% is observed relative to the case without nanoparticles. The convective heat transfer coefficient for the GNP nanofluid is found to be up to 15% higher than for the base fluid. The heat transfer rate and thermal performance for 0.1wt.% of GNP nanofluid is found to increase by a factor of up to 1.15. For constant velocity flow, frictional entropy generation increases and thermal entropy generation decreases with increasing nanoparticle concentration. But, the total entropy generation tends to decrease when nanoparticles are added at constant velocity and to decrease when velocity rises. Finally, it is demonstrated that a GNP nanofluid with a concentration between 0.075wt.% and 0.1wt.% is more energy efficient than for other concentrations. It appears that GNP nanofluids can function as working fluids in heat transfer applications and provide good alternatives to conventional working fluids in the thermal fluid systems.

Statistical Analysis of Laminar Convective Heat Transfer of MWCNT-Deionized Water Nanofluid Using the Response Surface Methodology

According to the response surface methodology (RSM), a statistical analysis of laminar forced convective heat transfer behavior of the multiwalled carbon nanotube (MWCNT)-deionized water nanofluid was carried out using a horizontal circular tube under constant wall heat flux. Sodium dodecyl sulfate, cetyltrimethylammonium bromide, and gum Arabic (GA) were used as surfactants to disperse MWCNT in the deionized water in order to synthesize MWCNT-deionized water nanofluids. MWCNT-deionized water nanofluids in the presence of different surfactants and MWCNT were prepared at various weight ratios (0.5:1, 1:1, and 2:1). The properties of stability, dispersion, and wettability were then studied. According to the results, MWCNT-deionized water nanofluid in the presence of GA at a ratio of 1:1 was selected as the best sample. Nanofluids at concentrations of 0.05 and 0.1% wt% were then prepared. According to the statistical model (RSM), a total of 15 experiments were tested under the laminar flow regime and a flow rate of 171.4–545.4 ml/min, concentration of 0–0.1 wt%, and a magnetic field 0–400 G. The maximum heat transfer coefficient (1,600.1 W/m2K) was obtained at a concentration of 0.09wt%wt, a flow rate of 301.3 ml/min, and a magnetic field of 400 G. The experimental results are in agreement with the results obtained by RSM method, confirming the validity and responsiveness of the method.

A thermal circuit model consistent with integral energy balance for internal forced convection in a circular tube

The equivalent thermal resistance circuit based on integral energy balance of thermally developing forced convection in a circular tube is derived describing the heat flow path between the heated tube wall and inlet fluid. The axial heat conduction of the flow is assumed to be negligibly small. To validate the thermal circuits developed, numerical simulations have been performed for laminar thermally developing forced convection of water in a circular tube with an imposed constant heat flux or constant wall temperature. The overall thermal resistances for the convective circuit separating the heated tube wall and inlet fluid are simply the convection thermal resistances due to the local/average heat transfer coefficients, respectively, defined based on the difference between local/average tube wall temperature and inlet fluid temperature. Applications of the convection thermal circuit derived have been demonstrated for direct or indirect evaluation of the pertinent heat transfer parameters of technical interest characterizing the forced convection heat transfer of thermally developing fluid flow in the iso-flux or iso-thermally heated tube.

Thermal Enhancement in Tubes with Dual Twisted Tapes

Influence of the dual twisted tapes (DTs) on the heat transfer enhancement in a circular tube is reported. The effects of twist ratio (y/w = 2.0, 3.0 and 4.0) on the heat transfer rate, friction factor, and thermal performance factor in a tube under constant wall heat flux were investigated in turbulent regions. Computations, based on a finite volume method, and the SIMPLE algorithm, were carried out by QUICK schemes. From the numerical results, heat transfer rate and pressure loss increased as twist ratio of tape (y/w) decreased. Based on the same pumping power consumption, the optimum thermal performance was achieved by the use of the tapes with twist ratio of 3.0. In addition, the predictions of flow-thermal phenomena (streamline, velocity vector, TKE and local Nusselt number) are also described.

Effect of frequency on heat transfer due to oscillating water flow in open-cell metal foam: An experimental study

Heat transfer due to oscillating water flow in open-cell aluminum-foam pipe subjected to constant wall heat flux was investigated experimentally. The foam had 20 pores per inch and a porosity of 87.6%. Three flow displacements 1.5, 1.9 and 2.2 pipe diameters, at kinetic Reynolds numbers in the range 1873–9366 were applied. Higher flow displacement and higher frequency generally produced higher heat transfer rates and led to lower and more uniform wall temperature. The flow displacement had the most profound influence on heat transfer. A correlation was obtained for the time- and length-average Nusselt number as a function of non-dimensional flow displacement and kinetic Reynolds number. The dependence on kinetic Reynolds number might be universal for oscillating heat transfer in porous media. Steady-state heat transfer experiments were also conducted in the same porous medium and test facility. Oscillating flow was seen to produce lower rates of heat transfer compared to steady flow. This unexpected finding was explained. The current results were compared to other studies from the literature employing oscillating air and water flows in various kinds of porous media. Some agreements and disagreements were stated and discussed.

Laminar flow heat transfer studies in a twisted square duct for constant wall heat flux boundary condition

The problem of fluid flow and heat transfer was studied for flow inside twisted duct of square cross-section. Three-dimensional numerical solutions were obtained for steady fully developed laminar flow and for uniform wall heat flux boundary conditions using commercially available software. Reynolds number range considered was 100–3000. Twist ratio used are 2.5, 5, 10 and 20. Fluids considered are in Prandtl number range of 0.7–20. Product of friction factor and Reynolds number is found to be a function of Reynolds number and maximum values are observed for a twist ratio of 2.5 and Reynolds number of 3000. Maximum Nusselt number is observed for the same values along with Prandtl number of 20. Correlations for friction factor and Nusselt number are developed involving swirl parameter. Local distribution of friction factor ratio and Nusselt number across a cross-section is presented. Based on constant pumping power criteria, enhancement factor is defined to compare twisted ducts with straight ducts. Selection of twisted square duct is presented in terms of enhancement factor. It is found that twisted duct performs well in the laminar region for range of parameters studied. Heat transfer enhancement for Reynolds number of 3000 and Prandtl number of 0.7 for twist ratio of 2.5, 5, 10, and 20 is 20%, 17.8%, 16.1% and 13.7%, respectively. The results are significant because it will contribute to development of energy efficient compact size heat exchangers.

Analysis on the heat transfer characteristics of a micro-channel type porous-sheets Stirling regenerator

To avoid the high flow frictional loss associated with conventional wire mesh Stirling regenerators, a micro-channel type stacked porous-sheets Stirling regenerator is investigated. An analytical solution is derived for the transient heat transfer characteristics of the fully developed reciprocating laminar flow under prescribed wall temperature profiles. The complex Nusselt number (Nu) is expressed as a function of kinetic Reynolds number (Reω) and Prandtl number (Pr). At low Reω of less than 10, the real part of Nu has an almost constant value of 6.0, approximately equal to the known real-valued Nu for the fully developed unidirectional laminar flow under constant wall heat flux, while the imaginary part is negligible, thus “scaling effect” can be utilized to enhance heat transfer. At higher Reω, both the real and imaginary parts of Nu increase with the increase of Reω and Pr, and the phase shift between the temperature difference and the heat flux gradually increases and approaches 45°. Approximate analytical solutions are also deduced for the entrance region from the integral boundary layer equations in both cases of “Thermally developing flow” and “Simultaneously developing flow”. The heat transfer is enhanced in the entrance region and the local Nu in the flow direction approaches the corresponding values of fully developed flow. The analytical results are confirmed by dynamic mesh CFD results, and the obtained Nu∼ Reω data and patterns generally agree with available analytical and experimental data from published literatures. Application of the analytical results to the design and optimization of Stirling regenerator are also shown.

Thermal development in open-cell metal foam: An experiment with constant wall heat flux

Experimental heat transfer results for a commercial open-cell aluminum foam cylinder heated at the wall by a constant heat flux and cooled by water flow, are presented. The results cover thermal-entry and fully-developed regions. Measurements include wall temperature along flow direction as well as average inlet and outlet temperatures of the water. Flow rates are in the Darcy and non-Darcy (transitional and Forchheimer) regimes. The wall temperature along the foam clearly shows two distinct behaviors related to thermally-developing and fully-developed conditions, which is confirmed by the behavior of local Nusselt number. The thermal entry length is determined and discussed in detail; it is also compared to its analytical counterpart for Darcy flow. The thermal entry region in metal foam is found to be significant and much longer than its analytically-predicted value. A method for estimating the bulk fluid temperature is envisioned for calculating the local Nusselt number. Previously undiscussed phenomenon is captured in the behavior of Nusselt number for non-Darcy regimes, which suggests periodic thermal development along the foam. The fully-developed data for the Darcy flow cases is compared to its analytical counterpart, and a correlation for the Nusselt number as a function of Reynolds number is proposed for non-Darcy flows.

Heat transfer enhancement of TiO2/water nanofluid in a heat exchanger tube equipped with overlapped dual twisted-tapes

Titanium dioxide (TiO2) in water as nanofluid was employed for heat transfer enhancement together with overlapped dual twisted tapes (O-DTs). The study encompassed Reynolds numbers from 5400 to 15,200, O-DTs with overlapped twist ratios (yo/y) of 1.5, 2.0 and 2.5 and nanofluids with TiO2 volume concentrations (ϕ) of 0.07%, 0.14% and 0.21%. The experimental and numerical results indicated that O-DTs with smaller overlapped twisted ratio delivered a stronger swirl intensity and higher turbulent kinetic energy (TKE). The use of O-DTs at the smallest overlapped twist ratio of 1.5 enhanced heat transfer rates up to 89%, friction factor by 5.43 times and thermal performance up to 1.13 times as compared to those of plain tube. In addition, heat transfer increased as TiO2 volume concentration of nanofluid increased, owing to the increases of contact surface and thermal conductivity. The simultaneous use of the O-DTs having twist ratios 1.5 with the nanofluid with TiO2 volume concentration of 0.21% resulted in heat transfer enhancement around 9.9–11.2% and thermal performance improvement up to 4.5% as compared to the use of O-DTs alone. The empirical correlations of heat transfer rate (Nu), friction factor (f) and thermal performance (η) in a constant wall heat flux tube equipped O-DTs at different overlapped twist ratios (yo/y) and volume concentrations of TiO2 nanoparticles (ϕ) are also reported for heat transfer applications.

Constant wall heat flux boundary condition in micro-channels filled with a porous medium with internal heat generation under local thermal non-equilibrium condition

Forced convection heat transfer in a micro-channel filled with a porous material saturated with rarefied gas with internal heat generation is studied analytically in this work. The study is performed by analysing the boundary conditions for constant wall heat flux under local thermal non-equilibrium (LTNE) conditions. Invoking the velocity slip and temperature jump, the thermal behaviour of the porous-fluid system is studied by considering thermally and hydrodynamically fully-developed conditions. The flow inside the porous material is modelled by the Darcy–Brinkman equation. Exact solutions are obtained for both the fluid and solid temperature distributions for two primary approaches models A and B using constant wall heat flux boundary conditions. The temperature distributions and Nusselt numbers for models A and B are compared, and the limiting cases resulting in the convergence or divergence of the two models are also discussed. The effects of pertinent parameters such as fluid to solid effective thermal conductivity ratio, Biot number, Darcy number, velocity slip and temperature jump coefficients, and fluid and solid internal heat generations are also discussed. The results indicate that the Nusselt number decreases with the increase of thermal conductivity ratio for both models. This contrasts results from previous studies which for model A reported that the Nusselt number increases with the increase of thermal conductivity ratio. The Biot number and thermal conductivity ratio are found to have substantial effects on the role of temperature jump coefficient in controlling the Nusselt number for models A and B. The Nusselt numbers calculated using model A change drastically with the variation of solid internal heat generation. In contrast, the Nusselt numbers obtained for model B show a weak dependency on the variation of internal heat generation. The velocity slip coefficient has no noticeable effect on the Nusselt numbers for both models. The difference between the Nusselt numbers calculated using the two models decreases with an increase of the temperature jump coefficient.

Mean statistics of a heated turbulent pipe flow at supercritical pressure

Direct numerical simulations (DNS) of a heated turbulent pipe flow with a fluid at supercritical pressure are performed at a Reynolds number of Reτ=360, based on pipe diameter and friction velocity at the inlet. A constant wall heat flux is applied and the temperature range within the flow domain incorporates the thermodynamic region where large variations in thermophysical properties occur. The contribution of these property variations on the mean flow is studied. As compared to ideal gas heat transfer, additional terms appear in the mean flow governing equations. These terms can significantly affect the energy balance, because they modify the averaged wall heat flux and the enthalpy diffusion close to the pipe wall. Furthermore, the averaged thermophysical properties, especially the isobaric heat capacity cp, deviate significantly from those evaluated using the mean temperature or enthalpy. This is due to an averaging artifact called the Jensen inequality, caused by the enthalpy fluctuations and the non-linear dependence of thermophysical properties with respect to enthalpy. Turbulent statistics for one forced convection and two mixed convection cases in an upward flow are discussed. A decrease in turbulent kinetic energy is observed for the forced convection and the low buoyancy case, which cause heat transfer deterioration indicated by high wall temperatures. For the high buoyancy case the turbulence activity first reduces (heat transfer deterioration) and then increases due to turbulence recovery.

Effects of Reynolds number, baffle angle, and baffle distance on three-dimensional turbulent flow and heat transfer in a circular pipe

In this study, steady-state three-dimensional turbulent forced convection flow and heat transfer characteristics in a circular pipe with baffles attached inside pipe have been numerically investigated under constant wall heat flux boundary condition. Numerical study has been carried out for Reynolds number Re of 3000-50,000, Prandtl number Pr of 0.71, baffle distances s/D of 1, 2, and 3, and baffle angle a of 30o-150o. Ansys Fluent 12.0.1 software has been used to solve the flow field. It is observed that circular pipe having baffles has a higher Nusselt number and friction factor compared to the smooth circular pipe without baffles. Maximum Nusselt number and friction factor are obtained for the baffle angle of 90o. Nusselt number increases while baffle distance increases in the range of studied; however, friction factor decreases. Periodically fully developed conditions are obtained after a certain module. Thermal performance factor increases with increasing baffle distance in the rage of studied but decreases with increasing Reynolds number; maximum thermal performance factor is obtained for the baffle angle of 150?. Results show that baffle distance, baffle angle, and Reynolds number play important role on both flow and heat transfer characteristics. The accuracy of the results obtained in this study is verified by comparing the results with those available in the literature for smooth circular pipes. All the numerical results are correlated within accuracy of ?10 and ?15% for average Nusselt number and Darcy friction factor, respectively.