Heat Flux Dissipation Research Articles

Enhanced flow boiling heat transfer with three-section sudden expansion microchannels

In this study, a three-section sudden expansion microchannels (TSE-MCs) heat sink was proposed to stabilize the flow boiling and improve the thermal performance of the heat sink exposed to high-heat-flux scenarios. The structural effect of newly designed TSE-MC and operating conditions on the heat transfer coefficient (HTC), pressure drop penalty, and flow instability were experimentally investigated and contrasted with continuous straight microchannels (CS-MCs). The experiments were performed at a saturation temperature of 35.5 °C, the mass flux ranging from 468–1033 kg/m2 s, and the heat flux up to ∼132 W/cm2. A comparative analysis based on the experimental results was conducted. Compared to CS-MCs, the nucleate boiling in TSE-MCs was initiated in advance with 0.2–1.2 °C reduction of wall superheat. The maximum HTCs at four mass fluxes, which was up to 62784 W/m2 K, were enhanced by 18.9–23.6 %. The uniformity of wall temperature was improved and the average wall temperature was reduced. HTCs and visualized results indicated that the dominant mechanism for heat transfer in TSE-MCs was nucleate boiling. Meanwhile, the pressure drop in TSE-MCs was slightly reduced, and pressure drop oscillations were greatly suppressed. The flow reversal in the inlet plenum was completely eradicated, and the performance evaluation criterion (PEC) of TSE-MC outperformed that of CS-MCs and was improved by 79.81 %–86.25 %. Overall, the present work demonstrates the great advantages of the newly proposed TSE-MCs, it offers a reference for the design of microchannel heat sinks for the real high heat flux dissipation applications.

Thermal management for microelectronic chips under non-uniform heat flux with supercritical CO2

With the rapid growth of information technology and the evolution in the use of microelectronic chips, these components are facing major challenges of high heat dissipation and inhomogeneous heat flux. To address the hotspot issues, a combination of microchannel heat sinks (MCHS) with cavity-rib designs and supercritical fluids is a potential solution. This study compares the thermo-hydraulic properties of water and supercritical carbon dioxide (sCO2) under various boundary conditions and hotspot locations during non-uniform heating. The results showed that sCO2 can effectively improve temperature uniformity along the heat sink in the presence of hotspots as compared to water. Considering a mass flow rate of 600 kg/(m2·s), the inhomogeneity index of the basal temperature of sCO2 is found to be 0.24, significantly lower than 4.22 for water. This indicates that sCO2 eliminates hot spots by rapidly increasing specific heat capacity near the pseudo-critical temperature. Furthermore, it is noted that maintaining the operating temperature of sCO2 near the pseudo-critical temperature can increase the specific heat capacity of the fluid in a short time, in addition to reducing the corresponding density and viscosity. Consequently, the entropy generation rate of sCO2 under ideal conditions is 46.6 % of that of water. Therefore, the proposed combination of a microchannel of complex structure and sCO2 in this study is demonstrated to effectively reduce the influence of hot spots and improve the overall thermal performance of heat sinks.

Impact of non-uniform heat flux, Arrhenius activation energy on gyrotactic microorganisms in conducting a nanofluid flow

ABSTRACT The primitive focus of this article is to examine the consequences of unsteady electrically conducting non-Newtonian magnetised tangent hyperbolic hybrid nanofluid flow which slides along the extensible surface with a porous medium along with Darcy–Forchheimer in a flow. Here we have taken into account the thermophoresis and Brownian movement for single- and multi-wall CNT dispersed in water. The temperature profile is accompanied by non-linear heat flux and viscous dissipation. The aftermath of activation energy on the concentration and the flow of gyrotactic microorganisms are taken into consideration. Differential equations after introducing various parameters are converted into ODE with the help of similarity transformations, which are later on, are solved using the bvp4c solver in the MATLAB software. For the range 0 ≤ Sq ≤ 4 there is an upsurge in the picture profiles of concentration and temperature obtained. However, the velocity of the flow gets diminished when the range of MHD and porosity parameter is confined between 0 ≤ M , K p ≤ 6 .

Study of the Effect of Initial Plate Temperature in Jet Impingement Cooling Process

The microstructure characteristics and the properties of rolled steels are significantly affected by the heat transfer and boiling phenomena occurring during the jet impingement cooling on run‐out tables (ROT). In this study, experiments are conducted using a full industrial‐scale ROT facility with rectangular plates made of low‐carbon stainless steel (type 316L). The plate is heated up to a temperature ranging from to , then rapidly impinged using a single circular water jet, and the temperature drop is captured using an infrared thermal camera (FLIR A615 25°–50 Hz type). The dissipated heat flux, estimated experimentally using a 2D inverse heat conduction analysis, ranges from 6.1 to 3.4 MW m−2 across different zones along the plate surface. The impact of different initial plate temperature on the boiling behavior is studied by developing a 2D‐computational fluid dynamics (CFD) model, and the results are closely aligned with the experimental findings. The results reveal that when estimating the heat flux from CFD simulations, the best accuracy is obtained when considering fluid temperature at a point close to the plate surface (about 1 μm above the surface). Furthermore, the maximum extracted heat flux (MHF) is significantly influenced by the initial temperature of the plate. Increasing the initial plate temperature from 500 to 900 °C led to an increase of 82% in the MHF in stagnation zone, and 137% increase in the parallel‐flow region. The CFD model presented in this study and the full calculation of the boiling curves numerically will pave the road for investigating various practical parameters in jet impingement cooling.

Design and performance assessment of a triply-periodic-minimal-surface structures-enhanced gallium heat sink for high heat flux dissipation: A numerical study

This study numerically investigates a phase-change material heat sink using gallium and Primitive Triply Periodic Minimal Surface (TPMS) cells structure as in-fill for applications requiring high heat-flux dissipation, e.g., electronics. Initially, we used only gallium without thermal conductivity enhancers, relying solely on buoyancy-driven circulations of melted gallium for the convective cooling of a hot sink base. However, this study aims to surpass gallium’s innate heat-dissipation capability. Therefore, the sink is enhanced with a high conductivity Primitive TPMS cells structure. Hybridization of conduction and convection heat dissipation enhancements is accomplished by using only one layer of the TPMS cells installed at the hot sink base. Comparison with the full TPMS structure filling option is made. In the full TPMS structure filling option, the sink relies mainly on conduction through the TPMS structure’s body and less on natural convection. However, equipping the sink with TPMS structures reduces the overall latent heat storage capacity. Therefore, additional gallium is added to the sink to match the overall gallium content in the baseline case without TPMS structures. Furthermore, the effect of the boundary conditions applied at the wall is explored. The results show considerable improvements in heat dissipation and peak temperatures with the TPMS cells, where by the time 100 s (about 20 s post complete melting) peak temperatures are about 13 percent lower than in the case without TPMS structures. Furthermore, the full structure filling option demonstrates superior performance over the partially filled ones, highlighting the importance of conduction through TPMS cells over convection in the free gallium space. Unlike the partial filling option, conduction in the full filling option has a continuous favorable impact on heat dissipation from the onset of the heating process.

Thermal Conductivity of AlSi12/Al2O3-Graded Composites Consolidated by Hot Pressing and Spark Plasma Sintering: Experimental Evaluation and Numerical Modeling

Functionally graded metal matrix composites have attracted the attention of various industries as materials with tailorable properties due to spatially varying composition of constituents. This research work was inspired by an application, such as automotive brake disks, which requires advanced materials with improved wear resistance on the outer surface as combined with effective heat flux dissipation of the graded system. To this end, graded AlSi12/Al2O3 composites (FGMs) with a stepwise gradient in the volume fraction of alumina reinforcement were produced by hot pressing and spark plasma sintering techniques. The thermal conductivities of the individual composite layers and the FGMs were evaluated experimentally and simulated numerically using 3D finite element (FE) models based on micro-computed X-ray tomography (micro-XCT) images of actual AlSi12/Al2O3 microstructures. The numerical models incorporated the effects of porosity of the fabricated AlSi12/Al2O3 composites, thermal resistance, and imperfect interfaces between the AlSi12 matrix and the alumina particles. The obtained experimental data and the results of the numerical models are in good agreement, the relative error being in the range of 4 to 6 pct for different compositions and FGM structure. The predictive capability of the proposed micro-XCT-based FE model suggests that this model can be applied to similar types of composites and different composition gradients.

Chemically reactive non-Newtonian fluid flow through a vertical microchannel with activation energy impacts: A numerical investigation

This work examines the second law analysis of an electrically conducting reactive third-grade fluid flow embedded with the porous medium in a microchannel with the influence of variable thermal conductivity, activation energy, viscous dissipation, joule heating, and radiative heat flux. A suitable non-dimensional variable is included into the governing equations to transform them into an ensemble of equations that are devoid of dimensions. The acquired equations are then tackled using the Runge Kutta Felhberg 4th and 5th order (RKF-45) approach in conjunction with the shooting methodology. Through comparison with the current results, the numerical results are verified, which provides a good agreement. From the present outcomes, it is established that the entropy generation is supreme for the viscous heating constraint, variable thermal conductivity, Frank Kameneski, heat source ratio parameter and third-grade fluid material constraint. The Bejan number boosts up with larger values of activation energy, and Frank Kameneski constraint and the decreasing nature is noticed for increasing third-grade material parameter, viscous heating parameter. With magnetism, the fluid’s velocity slows down because of a resistive force. A similar impact in the channel on velocity is noticed for larger third-grade fluid, activation energy parameter, and Frank-Kameniski parameters and increasing behavior is noticed for variable thermal conductivity, and permeability parameter. Further, it is cleared that the variable thermal conductivity assumption in the channel plate leads to a significant under prediction of the irreversibility rate.

Comprehensive comparative study of experimental and simulated critical heat flux in special high-flux cooling devices: The Short Helical Minichannel-Evaporators

Short Helical Minichannel Evaporators are compact heat exchangers characterized by small, helical channels that allow high heat flux dissipation by means of direct cooling. It is a promising cooling solution in applications requiring high heat transfer rates in a limited space, such as power electronics, machining processes, injection molding among others. Optimal and safe operation of these devices is critically dependent on accurate determination of the critical heat flux (CHF) when nucleate boiling changes to filmwise regime. Misestimation of the CHF could lead to system burnout or suboptimal performance, highlighting the need for reliable theoretical models. In this study, the performance of a theoretical model was compared with a series of experiments carried out on a custom-built test rig. The results show a strong correlation between the experimental data and the adapted Groeneveld model, with a Mean Absolute Error (MAE) of 8.51kWm−2, a Mean Error (ME) of −4.71kWm−2, and a Deviation (Dev) of 8.77kWm−2. Notably, 96.8% of the simulated values were within a 15% error band. The validated model is also applied to increase knowledge about design parameters beyond the experimental data. The study emphasizes the practicality of the Groeneveld model in accurately calculating the CHF for these specific heat exchangers, encouraging improvements for performance and operational safety.

3-D numerical simulation of forced convection heat transfer in microscale rectangular channels for low GWP refrigerants

This study presents a numerical evaluation of the performance of low Global Warning Potential (GWP) refrigerants R600a, R290, R1270, and R134a in heat dissipation by forced convection in a microchannel heat sink. The heat sink comprises 50 parallel microchannels with a cross-sectional area equal to 123 × 494 [µm2]. The differential equations describing the physical behavior interaction between the refrigerant and the copper matrix are solved using the finite volume method and the SIMPLEC coupling algorithm. The numerical model is used to predict fluid mechanics and heat transfer for single-phase laminar conditions including the friction factor, the Nusselt number and the average wall temperatures, as well as the whole performance of the microchannel heat sink. The accuracy of the numerical model is validated by comparing the performance of R600a with experimental data, resulting in deviations within the range of the uncertainty of each parameter. The evaluation of the performance of different refrigerants reveals that the friction factor and Nusselt number are significantly influenced by the microchannel geometry and thermal conditions, exhibiting unique yet similar trends for different refrigerants. Furthermore, the analysis of the average wall temperature in the microchannels demonstrates that the hydrocarbon-based refrigerants effectively reduce the temperature of the copper matrix compared to R134a, suggesting a superior performance in the dissipation of heat flux under single-phase laminar conditions.

Non-similar analysis of radially magnetized flow and heat transfer of Reiner–Philippoff based nanofluid over a curved stretching surface with viscous dissipation

The aim of this study is to conduct a non-similar analysis of flow and heat transfer rheology of non-Newtonian fluid over a radially magnetized curved stretching surface in the presence of multiple type of nanoparticles. Reiner–Philippoff viscosity and homogenous models are incorporated in the governing equation to study the effects of non-Newtonian fluid and nanoparticles respectively. Reiner–Philippoff viscosity model is a complicated non-Newtonian fluid model presenting an implicit stress-strain relationship. This fluid model has ability to present viscosity behavior in response to varying viscoelastic conditions of shear-thinning, shear-thickening as well as Newtonian fluid. The nanoparticles of nickel, molybdenum disulfide, and tantalum are used to study the enhancement of the thermal conductivity of the fluid with influences of radiative heat flux and viscous dissipation. To attain a more precise and generalized analysis of the heat transfer and flow, the governing boundary layer equations are converted to non-similar form. The local non-similarity method up to second level of truncation is employed to numerically solve the resulting non-similar PDEs via bvp4c in MATLAB tools. To examine the impact of physical factors on flow and heat transfer, numerical data are visually and tabulated displayed. It is worth mentioning that the thermal radiation, curvature parameter, and magnetic number play important role in controlling wall drag and heat flux.

Non-Fourier heat flux and Joule dissipation in hybrid nanoparticles suspension with Williamson fluid

Non-Fourier heat flux and Joule dissipation in hybrid nanoparticles suspension with Williamson fluid

Characterizing Subglacial Hydrology Within the Amery Ice Shelf Catchment Using Numerical Modeling and Satellite Altimetry

AbstractMeltwater forms at the base of the Antarctic Ice Sheet due to geothermal heat flux (GHF) and basal frictional dissipation. Despite the relatively small volume, this water has a profound effect on ice‐sheet dynamics. However, subglacial melting and hydrology in Antarctica remain highly uncertain, limiting our ability to assess their impact on ice‐sheet dynamics. Here we examine subglacial hydrology within the Amery Ice Shelf catchment, East Antarctica, using the subglacial hydrology model GlaDS. We calculate subglacial melt rates using a higher‐order ice‐flow model and two GHF estimates. We find a catchment‐wide melt rate of 7.03 Gt year−1 (standard deviation = 1.94 Gt year−1), which is ≥50% greater than previous estimates. The contribution from basal dissipation is approximately 40% of that from GHF. However, beneath fast‐flowing ice streams, basal dissipation is an order of magnitude larger than GHF, leading to a significant increase in channelized subglacial flux upstream of the grounding line. We validate GlaDS using high‐resolution interferometric‐swath radar altimetry, with which we detect active subglacial lakes and fine‐scale ice‐shelf basal melting. We find a network of subglacial channels that connects areas of deep subglacial water coincident with active subglacial lakes, and channelized discharge at the grounding line coinciding with enhanced ice‐shelf basal melting. The concentrated discharge of meltwater provides 36% of the freshwater released into the ice‐shelf cavity, in addition to ice‐shelf basal melting. This suggests that ice‐shelf basal melting is strongly influenced by subglacial hydrology and could be affected by future changes in subglacial discharge, such as lake drainage or channel rerouting.

Effect of flow pulsation on heat transfer performance of biomimetic bark microchannel heat sink

Pumping coolant or using pulse flow through microchannels with novel structures on microelectronic devices is suitable for high heat flux dissipation and sensor development. This study proposes a novel microchannel designed as a series of biomimetic bark channel networks. Simulation and experimental testing of temperature distribution and heat transfer performance are conducted under different working conditions, including various fluid parameters. The results show that combining biomimetic bar microchannel and pulsation flow can improve heat transfer performance. The effect of pulsating flow frequency on the temperature is only evident outside the range of 10 mm from the inlet. Compared with non-slip boundaries, the boundary slip of pulsating flow slightly enhances heat transfer. Pulsating flow has an optimal frequency, minimizing thermal resistance for different inlet temperatures.

Cooling optimization of asphalt pavement by topology optimization and cooling mechanism analysis

The higher temperature in the hot summer area will seriously damage the safety and comprehensive performance of the asphalt pavement, thus it must be cooled down quickly and orderly. At present, the cooling pavements are designed mainly based on engineering experience, and the quantitative relationship between design objective and variable is not constructed during the design process. In addition, it is difficult to determine whether the material distribution of cooling pavement is optimal. These limit the further improvement of the pavement cooling effect. In this study, the relationship between the design objective (minimum average temperature of upper layer) and design variable (thermal conductivity of pavement) of cooling pavement was built by numerical simulation, and the cooling pavement with the best cooling effect was obtained by topological optimization technology. The influence of the initial value and distribution of the thermal conductivity on the average temperature were explored during the design process. The thermal effect analysis and thermal resistance were used to determine cooling mechanism of optimized cooling pavement. The topology optimization results demonstrated that the minimum average temperature could be obtained when the initial value of the thermal conductivity gradually increased with the increase in pavement depth. The optimized cooling pavement showed good cooling effect at night. The thermal effect analysis results showed that the design of optimized cooling pavement reduced the net heat absorption and the heat transfer efficiency of the pavement, and increased the thermal resistance inside the pavement, thus achieving the pavement cooling. Compared with the ordinary asphalt pavement, the pavement surface temperature and interior temperature could be reduced by up to 9.18 °C and 13.29 °C, respectively. The maximum heat absorption, dissipation and net heat flux absorption of the optimized cooling pavement were decreased by 65.59 %, 63.87 % and 59.40 %, respectively. The reduction of the net heat flux absorption and heat release in the optimized cooling pavement are conducive to mitigating the high temperature rutting and the heat island effect at night, respectively. Finally, the indoor irradiation test was carried out to evaluate the cooling effect of optimized model. The temperatures of optimized group at 7 cm and surface were 5.29 °C and 2.5 °C lower than those of control group, respectively. The effectiveness of the topology optimization design for cooling pavement were verified.

Experimental investigation on thermal-hydraulic performance of manifold microchannel with pin-fins for ultra-high heat flux cooling

The manifold microchannel (MMC) with pin-fins is fabricated and its thermal-hydraulic performance is experimentally investigated. The MMC with pin-fins is an embedded cooling device made of a manifold wafer and a microchannel wafer, anodically bonded to form a total thickness of 1 mm. A microchannel wafer has the etched micro pin-fins with a porosity of 0.75, fin diameter of ▪, and fin height of ▪. For comparison, MMC with plate-fins is also fabricated, in which the plate-fins have the same porosity, fin thickness, and fin height as the pin-fins. Experiments are performed using single-phase deionized water as the working fluid with flow rates ranging from 50 to 300 ml/min, corresponding to pumping powers ranging from 0.28 to 33 mW, which enables the dissipation of an effective heat flux up to 1.2 kW/cm2. The experimental results demonstrate that employing pin-fins improves the thermal-hydraulic performance of the MMC heat sinks compared to using the plate-fins: an average 40% reduction in the effective thermal resistance (the total thermal resistance subtracting the conduction resistance) at a fixed pumping power condition. This is attributed to the fact that the MMC with pin-fins exhibits 20% higher heat transfer coefficient and 40% greater effective heat transfer area, even with 25% lower pressure drop on average compared to the MMC with plate-fins. At the highest tested flow rate of 300 ml/min, the MMC with pin-fins successfully dissipates the heat flux of about 1.2 kW/cm2 without phase-change heat transfer while maintaining the heater temperature below ▪. This is achieved with only 7 mW of pumping power, corresponding to the COP of 41,300 – a 5.3-fold increase in the COP compared to the MMC with plate-fins under the identical heater temperature and the flow rate conditions. Therefore, this study suggests that the MMC with pin-fins is an energy-efficient cooling device for the thermal management of ultra-high heat flux electronics.

Experimental research and energy effectiveness analysis on chip-level two-stage loop thermosyphon system for data centre free cooling

The development of 5G technology has put forward new requirements for computing the abilities of chips, and chip power has also significantly increased. Consequently, the heat load of the rack will increase rapidly in the future. Traditional computer room air conditioning (CRAC) systems cannot satisfy the rack’s high heat flux dissipation requirements, and new cooling forms such as chip-level cooling should be adopted. In this study, a two-stage chip-level cooling system, which is pumpless and waterless, offers flexible and detachable installation based on practical requirements, was proposed. The cooling system removes heat from the chips to the outdoors via two thermosiphon loops, where the heat is first transferred to cold plates tightly attached to the chip surfaces, then transferred through heat exchangers attached to the rack side, and finally dissipated outdoors through air cooling. In this study, a two-stage chip-cooling system was constructed and tested in an enthalpy-difference laboratory. The effects of the liquid filling ratio on the thermal resistance, total temperature difference, and fluid flow pattern under different heat loads were investigated. Second, a heat transfer model for analysing thermal resistance networks was constructed, and the proportions of different types of thermal resistance were determined. Third, an energy-saving analysis of the system is established. The experimental results showed that at single chip heat load 200 W and total heat load 2 kW, the heat transfer temperature difference between chips and outdoors is less than 20 °C at extremely high energy efficiency (cooling load factor reaches 0.05 at outdoor temperature 40 °C), which makes it feasible for free cooling throughout the year in most Chinese areas. The annual PUE in Beijing using the proposed system is 1.15, which indicates a 30 % reduction of the total energy consumption of data centres.

Experimental investigation of post and vented vapor chamber designs for high heat flux dissipation

To enhance the dryout heat flux of vapor chambers over a 1 cm × 1 cm area, this study describes the testing of four different vapor chamber design architectures (each having an overall size of 50 mm × 50 mm × 5.5 mm). The designs leverage a combination of internal liquid feeding posts and evaporator vapor venting features to improve the capillary-fed boiling performance. The study provides systematic insight into increasing the dryout limit of a vapor chamber and lowering the thermal resistance by assessing the effect of each geometric feature independently. A jet impingement air cooling test facility is used to measure the total thermal resistance of the package in a representative application, while a liquid cooling test facility is used to measure the thermal resistance of the vapor chamber itself. The results show that a vapor chamber with a combination of machined posts coated with sintered wick and vapor vent features has superior performance over vapor chambers with independent features. It dissipated the highest heat flux of 589 W/cm2 and provided the lowest total package thermal resistance of 0.28 K/W for a 1 cm2 heat input area. The performance improvements are attributed to an improved liquid supply utilizing the porous-wick-coated machined posts and a reduction vapor egress pressure utilizing the vent features above the heater area.

Enhanced boiling heat transfer via microporous copper surface integration in a manifold microgap

Heat flux dissipation from electronic devices has increased with their miniaturization owing to the increasing performance demands and development of microfabrication technologies. Improving the heat transfer performance is crucial for enhancing heat dissipation. However, this often leads to an increase in pressure drop, which reduces energy efficiency. Microgap heat sink is a promising approach in this regard owing to its geometrical simplicity and facile fabrication while providing heat transfer performance comparable to that of microchannel heat sinks with substantially lower pressure drops. In this study, we develop a manifold microgap heat sink integrated with a porous copper surface that effectively enhances heat transfer while using significantly low pumping power. A three-dimensional liquid routing manifold is used to achieve better flow distribution and alleviate temperature non-uniformity while providing improved heat transfer by enabling jet impingement and mixing of the thermal boundary layer on the microgap surface with minimal additional pressure drop. Moreover, a microscale inverse opal structure is used to facilitate nucleate boiling on the microgap surface, which improves heat transfer while maintaining a relatively low flow resistance. A maximum heat flux of 322.8 W/cm2 was achieved at the mass flux of 472 kg/m2 s, and the corresponding pressure drop and maximum heater temperature were 0.6 kPa and 140 ℃, respectively. The coefficient of performance (COP) achieved herein was significantly higher than those reported in previous relevant studies, indicating that the proposed cooling technique can potentially be used for energy-efficient thermal management in electronics devices.

Turbulent heat flux and wall heat transfer in hypersonic turbulent boundary layers with wall disturbances

Hypersonic turbulence over disturbed walls can be encountered when the fuselage of the vehicles is ablated or installed with transpiration-cooling porous media, resulting in the variation of the wall heat transfer that complicates its accurate predictions. In this paper, we study the turbulent heat flux and wall heat transfer in hypersonic turbulent boundary layers at the free-stream Mach number of 6.0 subject to wall disturbances with different wall temperatures, with our focus on the compressibility effects. We found that the temperature fluctuation intensity and the turbulent heat flux are enhanced in the outer region, which is attributed to the higher mean temperature gradient induced by the wall disturbances. The solenoidal and dilatational components of the turbulent heat flux, obtained by the Helmholtz decomposition that splits the velocity fluctuations into the solenoidal and dilatational components, are of opposite signs, with the latter smaller in magnitude but showing the tendency of mitigating the former. The integration formula that decomposes the wall heat transfer into various physical processes reveals that the viscous dissipation generates the wall heat transfer, while the turbulent heat flux, work of pressure on dilatation and the mean flow convection transport it towards the free stream. The contribution of the dilatational motions to the viscous dissipation and turbulent heat flux is negligible compared with that of the solenoidal components.

Effects of Viscous Dissipation and Periodic Heat Flux on MHD Free Convection Channel Flow with Heat Generation

Effects of Viscous Dissipation and Periodic Heat Flux on MHD Free Convection Channel Flow with Heat Generation