High Heat Transfer Rates Research Articles

Thermal performance enhancement of laminar flow using compound twisted square duct and variable pitch twisted tape inserts

This study involves a computational analysis to find the effectiveness of incorporating twisted tape within a twisted square duct for improving heat transfer, focusing on laminar single-phase flow. The primary goal is to study how varying the tape pitch (y) influences the hydrothermal performance of this system. The twisted square duct pitch (S) and twist ratio (H) were kept constant. The numerical analysis is performed under conditions of uniform wall temperature, and varying the pitch ratio (y/S) across values of 0.25, 0.5,0.75, 1, 1.25, 1.5 and 1.75. The obtained findings suggest that the addition of twisted tape within the twisted square duct results in a greater rate of heat exchange and pressure drop relative to the simple twisted square duct. Research reveals that despite a higher rate of heat transfer for a pitch ratio of 0.25 the increased friction factor results in less effective thermal performance compared to the cases with pitch ratios of 0.75 and 0.5. The thermal performance factor reaches its peak at 1.32, corresponding to the Reynolds number 1000 for a pitch ratio of 0.75 case. Conversely, the lowest thermal performance factor value of 0.89 is observed at the Reynolds number 500 for pitch ratio 1.25 case.

Thermal Frictional Analysis of a Novel Vibrating Cylindrical Turbulator in Double Tube Heat Exchangers for Engine Cooling

This study focuses on enhancing the thermal efficiency of a double-tube heat exchanger used in cooling systems for large-scale internal combustion engines by incorporating a novel vibrating cylindrical turbulator. The experimental investigation examined inlet Reynolds numbers ranging from 1052 to 8430 and evaluated various turbulator configurations, including fixed close-ended, fixed open-ended, vibrating close-ended, and vibrating open-ended cylindrical turbulators. Additionally, the impact of turbulator length, varying from 10 to 30 cm, on thermal-frictional characteristics was analyzed. The optimal configuration was determined using the thermal enhancement factor (TEF). Results showed that close-ended cylindrical turbulators significantly outperformed the open-ended configurations in terms of heat transfer and TEF. Although the vibrating turbulator produced a higher pressure drop compared to the fixed turbulator, it achieved a much higher heat transfer rate and TEF, making it a viable option for heat exchangers. The study also found that increasing the turbulator length leads to increased heat transfer, TEF, and pressure drop. The maximum TEF was recorded with the vibrating close-ended cylindrical turbulator, where heat transfer and pressure drop were up to 385% and 95% greater than those of a plain tube heat exchanger, respectively, resulting in a perfect TEF value of 3.45.

Experimental Study on Heat Transfer Characteristics on Intersecting Spiral Finned Tube Type on Heat Exchanger

Compact heat exchangers play an important role in the industrial world, one of their applications being in thermal machines to dissipate heat generated during mechanical processes. To improve the performance of heat exchangers, many studies have been conducted, including the addition of spiral fins, and the spacing of these fins on the outer surface. This study examines the heat transfer characteristics of the outer surface. The heat exchanger is made of galvanized pipe with an inner diameter of 20 mm and an outer diameter of 22 mm. It has a passage length of 300 mm with a sharp turn of 81 mm. The spiral fins are made of aluminum, with a thickness of 0.3 mm, a spiral fin height of 10 mm, and a distance of 30 mm between the spiral fins. The cross-section of the spiral fins varies, including options without spiral fins, without spiral fins, without intersecting spiral fins, with intersecting 2 mm spiral fins, intersecting 5mm spiral fins, and intersecting 7mm spiral fins. Heat exchangers are supplied with hot at a constant inlet temperature of 80C and a flow rate of 0.57 kg/s. The fan operates at speeds of 3.59 m/s, 4.45 m/s and 5.07 m/s. The results show that the highest heat transfer rate and heat transfer coefficient are produced by the heat exchanger with a cross-section of 5 mm intersecting spiral fins, specifically 11,682.7 W and 604 W/m2.K.

Fire resistance of 3D printed ultra-high performance concrete panels

Ultra-high performance fiber-reinforced concrete (UHPFRC) is highly suitable for 3D concrete printing (3DCP) due to its high flexural strength, thereby reducing the need for reinforcements. However, UHPFRC is susceptible to spalling under exposure to fire, limiting its application as structural members. In this paper, the effect of 3D printing process on the fire behavior of UHPFRC is studied, benchmarking against mold-cast panels. The insulation, integrity, and structural adequacy of the panels are investigated using the heat transfer mechanisms, failure modes, and the post-fire compressive strength of the panels, respectively. The presence of interlayers reduced the spalling of UHPFRC under fire and improved the structural integrity of 3D printed specimens compared to mold-cast specimens. Further, the addition of 0.5 % polypropylene (PP) fibers eliminated the interlayer delamination and spalling in 3D printed UHPFRC panels. Similarly, 3D printed panels showed improved structural adequacy than mold-cast specimens. The residual compressive strength of 3D printed UHPFRC panels after being exposed to fire was observed to be above 50 % of the initial mean compressive strength. However, the insulation property of 3D printed panels was reduced compared to that of the mold-cast counterparts due to the high rate of heat transfer via the porous interlayers. The addition of PP fibers improved the insulation resistance of the interlayer region and surface of the 3D printed panels. The strength anisotropy of the 3D printed UHPFRC reduced significantly following the fire exposure. Further, the thermal bowing of 3D printed panels was higher with an increased dosage of PP fibers due to the increase in the thermal strain of UHPFRC. Therefore, adequate care must be given in the design of 3D printed structures for potential fire resistant wall, slab, and façade elements.

The Impact of Circular Holes in Twisted Tape Inserts on Forced Convection Heat Transfer

This study investigated heat transfer and friction characteristics in a forced convection system using wavy twisted tape inserts with circular holes. The inserts, with twist ratios (TR) of 8.5, 7.5, and 6.5, were placed inside a test pipe to create turbulent flow. The tapes measured 700 mm in length and 18 mm in width, while the test pipe had an outer diameter of 35 mm and an inner diameter of 30 mm, with a test section length of 700 mm. Airflow rates were adjusted to achieve different bulk mean temperatures. Experimental data were used to develop new correlations for the Nusselt number and friction factor. The Reynolds number (Re) ranged from 4,000 to 14,000. Comparisons between the wavy twisted tape inserts with varying twist ratios and pitches and a smooth tube showed that the highest heat transfer rate was achieved with a twist ratio of 6.5.

Experimental study on an improved direct-contact thermal energy storage container

Direct-contact thermal energy storage (TES) systems characterized by high heat density and rapid heat transfer rates have been exploited for the collection of industrial waste or surplus heat for subsequent utilization. In order to address blockage issue at the initial stage of charging process, an improved direct-contact TES container was developed by incorporating a double-pipe structure at both the inlet and outlet. Within the container, a U-shaped tube serving as the inner tube was concentrically positioned from the inlet to the outlet. Erythritol was selected as the phase change material (PCM), while heat transfer oil (HTO) functioned as the heat transfer medium during experimentation. During the charging process, hot HTO initially flowed through the U-shaped tube, establishing an indirect contact with the PCM. The high thermal conductivity of the U-shaped tube wall expedited the formation of a flow channel within the solid PCM. The duration of forming flow channel was 6 to 13 min. In the discharging phase, the liquid PCM was segregated into convection and conduction zones. The indirect-contact TES experiments were also conducted in the same container. Comparison between indirect-contact and direct-contact TES were analysed from the aspects of phase change behavior, charging and discharging time with the identical container structure and theoretical heat capacity. Results indicated that the direct-contact TES container exhibited superior heat storage and release rates, with the direct-contact discharging time being approximately a quarter of the indirect-contact duration. The phase change behavior of the PCM was notably influenced by the movement of HTO within the direct-contact storage container.

Impact of cold block shapes on heat transfer and mixed convection in a ventilated square cavity with Ag/water nanofluid

This study investigates mixed convection in a ventilated square cavity filled with an Ag/water nanofluid, containing central cold blocks of various shapes (square, circle, triangle, and ellipse). The goal is to understand the impact of nanoparticle concentration and the geometric shapes of the blocks on heat transfer. In the cavity, the inlet is located in the upper left corner, while the outlet is positioned in the lower right corner. Mixed convection is induced by cooling at the inlet of the ventilated cavity and uniform heating of its lower wall. The equations governing the flow of an incompressible Newtonian nanofluid are assumed to be two-dimensional, stable, and laminar. The finite volume method is used for numerical simulations. The effect of four different geometric shapes of the cold obstacle (circular, square, triangular, and elliptical) on fluid flow and heat transfer rate is also explored. The results show that increasing the nanoparticle concentration enhances heat transfer within the cavity. This improvement is particularly notable when the central cold obstacle takes on a circular shape, leading to better mixed convection and a higher heat transfer rate. The square and triangular shapes yield similar, albeit slightly lower, results, while the elliptical shape is the least effective for heat transfer.

Heat Transfer Through a Heated Rod Placed in Different Arrangements

Abstract The present work experimentally analyses the surface heat transfer from a thermally active copper rod of circular cross-section placed in different arrangement of dummy rods. All the rods are arranged in cross-flow. Wind-tunnel experiments for nine different arrangements of heated rod at a Reynold’s number of 12600 were investigated. Temperature variation, heat transfer and vertical velocity distribution downstream of the cylinder were studied. Higher heat transfer rate was obtained when the heated rod was placed in downstream position due to the rubbing action of vortex shedding phenomena of upstream rod. Maximum heat transfer rate was reported in tandem arrangement of rod with the thermally active cylinder placed in the downstream row. The wall effect becomes dominant near the wall region and affects the flow and heat transfer in the vicinity of wall. Pressure and logarithmic value of temperature has been reported at suitable positions to explain the thermofluid physics.

Thermal Stress Analysis of Compact Heat Exchanger Produced by Additive Manufacturing

Abstract Compact heat exchangers are renowned for their high heat transfer rates and efficiency, achieved by incorporating mini and micro-channels in their core design. However, operating under conditions of high-pressure fluctuations and significant temperature differences between hot and cold streams can potentially induce fatigue failure. To the best of our knowledge, this study represents the first investigation into the thermal stresses experienced by heat exchanger samples manufactured by selective laser melting technology, focusing on circular channels. Experiments were conducted using hot water in the inner channel, while the remaining channels and the sample surface were subjected to natural convection in ambient air. Strain gauges, thermocouples, and RTDs were employed to measure strain and temperature variations over time. These data were utilized as inputs for a numerical model based on finite element method. The strain measurements were compared with those obtained from the numerical model, revealing an average difference of approximately 20%. Lastly, a thermal fatigue analysis based on the maximum equivalent stresses predicted by the numerical model is presented. The evaluation considered both S-N curves: outlined in the ASME standard and the one obtained with specimens produced through selective laser melting. In the case of circular channels manufactured through additive manufacturing evaluated in this work, thermal stresses alone are insufficient to cause component failure due to fatigue. However, significant pressure cycles superimposed on the model can reverse this situation, making the combined effect of thermal and mechanical stresses influential in determining the component's fatigue behavior.

Thermal performance analysis of sinusoidal corrugated channels: A comparative study of thermo-hydraulic and entropy generation

The physical properties of working fluids—in terms of the Prandtl number—play a crucial role in determining their thermal performance in the internal flow, especially their viscosity. This study first considers the thermo-hydraulic and entropy generation of a sinusoidal corrugated channel in two configurations: symmetrical (raccoon) and asymmetrical (serpentine). Results are presented for different ranges of operating parameters, such as 100≤Re≤700 and 0.72≤Pr≤90, and for geometrical parameters such as the wave amplitude-to-wavelength ratio 0.2≤α≤0.6. In addition, the results of the two channels were compared with each other's and with the straight channel. Control transport equations are solved using finite element methods. It was found that the flow inside the wavy channels generated re-circulatory reigns, and their size was affected by the wave parameters as well as the Reynolds number. Also, employing high values of Pr extremely enhanced the heat transfer rate (HTR) of the wavy channels over the straight for all values of α and for both raccoon and serpentine channels. In addition, the results indicated that raccoon channels have higher HTR and performance factor compared to the serpentine channel. Finally, the thermal entropy generation dominated over the viscous entropy generation and its decrease with both Reynolds number and Prandtl number for raccoon and serpentine channels. This study focused on the heat transfer enhancement of the corrugated channels due to their importance in many industrial applications where the heat dissipation is critical to their work, including heat exchangers and heat sinks. Thus, the current numerical simulation primarily suggests utilizing the raccoon channel over the serpentine one, due to its higher thermal performance and nearly the same total entropy generation.

Theoretical study of the MWCNT particle layer and size impact on sodium alginate heat transfer

This paper theoretically studies the effects of the size of multiwalled carbon nanotube (MWCNT) nanoparticles and layers on the flow of sodium alginate (SA) base fluid in a vertical channel. The nanoparticles are used to improve the thermal characteristics of the base fluid. The nanolayer shows the relationship between the particles and the base fluid, justifying the rise in thermal conductivity, even at a low volume of the nanoparticle in the base fluid. The mechanics of the fluid through the channels are developed using nonlinear models of coupled higher order differentials analyzed using the adomian decomposition method, an analytical scheme. The nanolayer effect of MWCNT particles on pure sodium alginate enhances heat transfer by 31.83% upon a step increase of 0.4 from 0.2 nm. Additionally, the combined effects of the rheological parameters of particle size, radiation and shear stress lead to a high heat transfer rate. The results obtained from the analysis were verified with results obtained from the literature for simple conditions, which validated the analysis. The results of this study may provide meaningful insight into the physical application of the sodium alginate.

Correlations of mixed convection in a double lid‐driven shallow rectangular cavity: The case of non‐Newtonian power‐law fluids

AbstractThis work provides an analytical and numerical assessment, complete with correlations, of mixed convection in a double lid‐driven shallow rectangular enclosure, which confines non‐Newtonian fluids of the Ostwald–de Waele type and which a uniform thermal flux heats. The finite volume method with the SIMPLER algorithm is the numerical method used to solve the governing partial differential equations along with the boundary conditions, where the parallel flow concept is the analytical approach. In the limits of the explored values of the governing parameters of this study, which are the Rayleigh number, the Peclet number, and the behavior index, the results obtained by these approaches appear to be in good harmony. On the basis of the results obtained by these approaches, we established helpful correlating relations between the governing parameters to realize the contribution of mixed convection to heat transfer. This leads to the finding that the ratio Ra/Pe2+n is the mixed convection parameter, which is the key to distinguishing the three convective flow modes. On the basis of this parameter, which allows the transition from one regime to another, it is possible to identify the zones that designate the predominance of natural, forced, and mixed convection. The limits of these latter depend on the behavior index, n, which is diversified from 0.6 to 1.4 to account for shear thinning (0 < n < 1, low apparent viscosity, high fluid flow, and high heat transfer rate), Newtonian (n = 1), and shear thickening (n > 1, high apparent viscosity, slow fluid flow, and low heat transfer rate) fluids. On the other hand, the study presents and interprets the influences of the steering factors on heat transfer and fluid flow.

Experimental and computational investigation of FGM coated cylinder liners prepared using HVOF technique

In the present work, to improve the wear resistance of the cylinder liner, without affecting the heat dissipation, cast steel cylinder liners are coated with five-layer Functionally Graded Material (FGM) coatings prepared using High-velocity oxy-fuel (HVOF) technique. The powders were designated as C1 (WC-10Co-4Cr) which is Tungsten Carbide with 10% Cobalt and 4% Chromium, C2 (WC-12Co) which is Tungsten Carbide with 12% Cobalt and C3 (Ni-25Cr) which is Nickel with 25% Chromium. The results revealed that the FGM coating designated as Functionally Graded Coated Sample-1 (FGCS-1) wears less compared to Functionally Graded Coated Sample-2 (FGCS-2) and Functionally Graded Coated Sample-3 (FGCS-3), due to the presence of wear resistive elements in the composition and uniform material homogeneity. Numerical analysis of FGCS-2, conducted using Ansys Fluent software, revealed a negligible temperature gradient across the coating thickness. This is due to the highly conductive coating material and the extremely thin coating layers, making it suitable for engine cylinder liner applications where less wear and high heat transfer rate is desirable.

Study on effects of anti-freeze protein and polyvinyl alcohol on the production and flow behavior of ice slurry

Ice slurry is a promising functional fluid with high thermal energy density and high heat transfer rate. However, the agglomeration of the ice particles in flowing ice slurry can cause blocking of tubes. In this study, anti-freeze protein (AFP) and polyvinyl alcohol (PVA) were selected as additives to prevent the agglomeration of ice particles in ice slurry. Ice slurry was generated using the release of the supercooled state of 3 mass% NaCl solution containing the additives. The size of the ice particles in the ice slurry was observed, and the average area of the ice particles was evaluated to reveal the effects of the additives on the ice particle size. Furthermore, the flow behavior of the ice slurry in a tube was observed, and the effects of the additives on the flow behavior and prevention of the agglomeration of the ice particles were evaluated experimentally. It was found that the average area decreased with increasing concentration of the additives, and the effect of AFP on the average area was particularly significant. In the case of without the additives, the ice particles flowed in the tube while the ice particles agglomerated. On the other hand, the ice particles in the ice slurry with the additives flowed without agglomeration in the tube, especially in the case of AFP addition. It was found that AFP prevented the agglomeration of the ice particles in the ice slurry flow. Moreover, the ice slurries with AFP show the significant tendency for pseudo-plastic fluid.

Thermo-fluidic and entropy generation analysis of MPCMS in straight, segmental, and rib-groove microchannel heat sinks: A numerical investigation

The efficient management of thermal systems is crucial for various technological applications, necessitating innovative cooling strategies to enhance performance and reduce entropy generation. Microchannels have emerged as a promising solution due to their high heat transfer rates and compact size. This study investigates the thermofluidic characteristics and entropy generation in straight, segmental, and rib-groove microchannels utilizing de-ionized water and microencapsulated phase change slurry (MPCMS) as working fluids. Employing numerical analysis, the investigation integrates a mixture model for the base fluid and micro-encapsulated phase change material (MPCM) using an equivalent heat capacity approach to incorporate the phase transition of the MPCM (composed of paraffin with a Ti shell). Operational parameters include an inlet fluid velocity ranging from 0.575 to 3.45 m/s, heat flux varying between 15 and 30 W/cm2, and MPCM volume fractions of 5% to 20%. The ANSYS Fluent Solver, a finite volume method using a multigrid solver, was used to control the simulation by species transport. Notably, segmental channels exhibit a notable decrease in wall temperature of 29.7% and 26.3% compared to straight and rib-groove channels, respectively, under constant heat flux and flow rate. However, the effectiveness of MPCM in enhancing thermal performance was greater in straight and rib-groove channels, surpassing segmental channels by 2.5% and 3.28%, respectively, under constant heat flux. On analyzing the irreversibility, segmental channels exhibit higher frictional entropy but lower thermal entropy generation due to the fin structure, resulting in an overall reduction in total entropy generation. Moreover, segmental microchannels, when utilizing MPCMS, demonstrate superior performance in reducing irreversibility by 60.66% and 49.6% compared to straight and rib-groove channels, respectively. Total entropy generation increases with higher velocity and heat flux, while it diminishes with higher MPCM concentration across all configurations.

An empirical analysis of hybrid MHD ferrofluid unsteady flow of two-dimensional heat transfer across a porous channel

This research investigates the heat transfer dynamics of a two-dimensional, incompressible, laminar, magnetohydrodynamics, time-dependent flow of a hybrid ferromagnetic fluid with radiation and irregular heat source/sink conditions through two porous channels. The study investigates the unique capability of ferromagnetic solid nanoparticles to improve the thermal efficiency of the host fluid, with potential applications in medicine such as drug targeting, cell separation, and magnetic resonance imaging. A mathematical model is developed as a nonlinear partial differential equation (PDE), which is subsequently converted into a nonlinear ordinary differential equation (ODE) using similarity transformations. The numerical solution is obtained using the 4th-order Runge-Kutta method implemented in Mathematica software. We analyze the impact of various nondimensional factors on the numerical results, including skin friction coefficient and Nusselt number, as well as graphical results depicting the velocity and temperature profiles of the hybrid ferrofluid. Boosting the film thickness parameter (λ) improves the heat transfer rate at the bottom of the porous channel. Raising the irregular heat source/sink parameters ( A * and B * ) and causing opposite impacts on the heat transfer rate at the bottom porous channel. Higher the radiation (R) values, the temperature profile behaves oppositely in both porous channels. The analysis reveals that the hybrid ferrofluid exhibits a higher rate of heat transfer compared to the ferrofluid.

Numerical simulation of an impinging jet array in a square channel covered by a porous layer

AbstractIn many heat transfer applications, the design of the flow field should warrant high heat transfer rates and, meanwhile, reduce the thermal stresses so that hot spots along the heat transfer surface be avoided. A combination of multiple jets impinging on a channel bed together with the surface covered by a porous layer is proposed to satisfy both objectives in the current study. A three‐dimensional numerical simulation using a finite volume method with the second‐order discretization has been applied to visualize the multiple‐impinging jet flow behavior. The impacts of the porous medium parameters, including the thickness, permeability, and porosity, on the magnitude and distribution of the heat transfer along the channel bed have been evaluated. It is shown that the overall heat transfer performance of the proposed flow is significantly improved in comparison with the conventional case of the fluid flowing parallel to the channel bed. The presence of the porous layer leads to a more even spread of the fluid on the target surface, which reduces the thermal stresses and prevents the large differences between the highest and lowest values of heat transfer coefficients. They also found that both the porosity and particularly the permeability of the porous layer enhance the effect of the crossflow along the flow associated with the multiple‐impinging jet setup. For a certain thickness of the porous layer, it is possible to reduce the amplitude of the Nusselt number oscillations effectively, while keeping the overall Nusselt number desirably high.

Effect of Synthetic Jet on Flow Field over Different Shaped Ribs and Its Impact on Heat Transfer

The present work reports the manipulation of the flow field over different shapes of surface-mounted obstacles using a synthetic jet. A round synthetic jet is placed upstream and downstream of surface-mounted ribs on a flat surface. Particle image velocimetry and hotwire anemometry are used to study the flow field characteristics and features. Heat transfer rate was obtained using transient liquid crystal thermography technique. Experiments are carried out at Reynolds number of 32,000 in a low-speed wind tunnel. Flow field features behind ribs are analyzed using time-averaged velocity, streamline, vorticity Reynolds stress and turbulent intensity. The spanwise average Nusselt number distribution for the downstream rib location is compared for two optimum locations of the synthetic jet relative to the rib. The recirculation bubble length formed downstream of a rib varies with the frequency of the synthetic jet, its location, and the shape of the rib. A drastic reduction in reattachment length is observed at 50 and 80 Hz frequencies for square rib. The highest heat transfer rate is obtained for the square rib at 50 Hz and 4 voltage peak-to-peak excitation amplitude for the upstream location of the synthetic jet relative to the rib.

Machine learning enhanced control co-design optimization of an immersion cooled battery thermal management system

The development of lithium-ion battery technology has ensured that battery thermal management systems are an essential component of the battery pack for next-generation energy storage systems. Using dielectric immersion cooling, researchers have demonstrated the ability to attain high heat transfer rates due to the direct contact between cells and the coolant. However, feedback control has not been widely applied to immersion cooling schemes. Furthermore, current research has not considered battery pack plant design when optimizing feedback control. Uncertainties are inherent in the cooling equipment, resulting in temperature and flow rate fluctuations. Hence, it is crucial to systematically consider these uncertainties during cooling system design to improve the performance and reliability of the battery pack. To fill this gap, we established a reliability-based control co-design optimization framework using machine learning for immersion cooled battery packs. We first developed an experimental setup for 21700 battery immersion cooling, and the experiment data were used to build a high-fidelity multiphysics finite element model. The model can precisely represent the electrical and thermal profile of the battery. We then developed surrogate models based on the finite element simulations in order to reduce computational cost. The reliability-based control co-design optimization was employed to find the best plant and control design for the cooling system, in which an outer optimization loop minimized the cooling system cost while an inner loop ensured battery pack reliability. Finally, an optimal cooling system design was obtained and validated, which showed a 90% saving in cooling system energy consumption.

A developed transition simulation model for turbulent plane jet impingement heat transfer

Jet impingement has been widely used due to its high heat transfer rate, but numerical simulation of this flow is highly challenging because of complex flow phenomena. In this paper, a turbulence model based on the physics of jet impingement is developed using the shear stress transport (SST) four-equation transition model and the SST with cross-diffusion correction (SSTCD) model. The proposed method is evaluated for plane jet impingement under various nozzle-plate spacings (2.6, 4 and 6) and different Reynolds numbers ranging from 10,200 to 20,000 in terms of heat transfer and flow fields. The results show that the developed model has the ability to capture the second peak of heat transfer and skin friction at low nozzle-plate spacing. Even at high nozzle-plate spacing, this approach also gives accurate trends for the above two features. However, without the cross-diffusion correction, the transition model provides too high energy and low velocity peaks. With the developed model in hand, the effects of pressure gradient on heat transfer and skin friction coefficient are further investigated. It is found that when the adverse pressure gradient becomes strong, the position of the secondary peak of skin friction occurs earlier than that of the secondary peak of heat transfer rate. Conversely, if the adverse pressure gradient disappears, the positions of these features coincide.