Theoretical Calculation Model of Heat Transfer for Deep-derived Supercritical Fluids with a Case Study

Based on a set of equations established by Duan et al. (1992, 1996) for a geofluid system H2O-CO2-CH4(-N2), a formula is obtained to calculate the heat changes. Combining the geological T-P conditions (geothermal gradients and lithostatic and hydrostatic pressures), the enthalpy of some typical geofluids is figured out. Then the principles of heat transfer of deep-derived supercritical fluids are discussed. The result shows that deep-derived geofluids can bring a large amount of thermal heat and release most heat to the shallow surroundings as they move up, because the molar enthalpies vary very greatly from the deep to shallow, increasing with the increases of T and P. Generally, more than tens of kilojoules heat per molar can be released. Furthermore, the molar enthalpy is affected by the compositions of the geofluids, and the molar enthalpy of CO2, CH4, or N2 is greater than that of H2O, being twice, more than twice, and about 140% of H2O, respectively. Finally, a case study is conducted by investigating a source rock sequence affected hydrothermally by magmatic fluids in the Huimin depression of Shengli Oilfield. The thermal heat calculated theoretically of the fluids related to a diabase intrusion is quite large, which can increase the temperature near the diabase to about 300℃, and that can, to some extent, account for the abnormal rise of the vitrinite reflectance, with the highest of about 3.8% (Ro).

Effect of different heat transfer fluids on discharging performance of phase change material included cylindrical container during forced convection

In the present work,effects of various heat transfer fluids on the discharging performance of a phase change material(PCM) included cylindrical container are numerically assessed during forced convection.The heat transfer fluid air,hydrogen,water and nanofluid with alumina particles are used and the the geometric variation of the PCM embedded region is also considered.The finite element method is used as the solver.Dynamic features of heat exchange with various phases are explored for different heat transfer fluid types,Reynolds number(between 100 and 300) and PCM embedded region geometric variation(h_(x)between 0.01 d_(1) and 0.65 d_(1),hybetween 0.1 h_(1) and 0.4 h_(1)).It is observed that discharging time is significantly influenced by the heat transfer fluid type while full phase transition time for air is obtained as more than 10 times when hydrogen is utilized as heat transfer fluid.The best performance is achieved with nanofluid.When the PCM integrated region size is reduced,discharging time is generally reduced while due to the form of the geometry,vortex formation is established in the PCM region.This results in performance degeneration at the highest radius and height of the inner cylinder.Discharging time increases by about 12% when radius of the inner cylinder is increased from h_(x)=0.35 d_(1) to h_(x)=0.45 d_(1).Dynamic features of PCM temperature and liquid fraction are affected with Reynolds number while discharging time is reduced by about 48% when configurations with the lowest and highest Reynolds number are compared.

Air-Side Heat Transfer Performance Prediction for Microchannel Heat Exchangers Using Data-Driven Models with Dimensionless Numbers

This study explores the effectiveness of machine learning models in predicting the air-side performance of microchannel heat exchangers.The data were generated by experimentally validated Computational Fluid Dynam-ics(CFD)simulations of air-to-water microchannel heat exchangers.A distinctive aspect of this research is the comparative analysis of four diverse machine learning algorithms:Artificial Neural Networks(ANN),Support Vector Machines(SVM),Random Forest(RF),and Gaussian Process Regression(GPR).These models are adeptly applied to predict air-side heat transfer performance with high precision,with ANN and GPR exhibiting notably superior accuracy.Additionally,this research further delves into the influence of both geometric and operational parameters—including louvered angle,fin height,fin spacing,air inlet temperature,velocity,and tube temperature—on model performance.Moreover,it innovatively incorporates dimensionless numbers such as aspect ratio,fin height-to-spacing ratio,Reynolds number,Nusselt number,normalized air inlet temperature,temperature difference,and louvered angle into the input variables.This strategic inclusion significantly refines the predictive capabilities of the models by establishing a robust analytical framework supported by the CFD-generated database.The results show the enhanced prediction accuracy achieved by integrating dimensionless numbers,highlighting the effectiveness of data-driven approaches in precisely forecasting heat exchanger performance.This advancement is pivotal for the geometric optimization of heat exchangers,illustrating the considerable potential of integrating sophisticated modeling techniques with traditional engineering metrics.

Magnetic Field Effect and Heat Transfer of Nanofluids within Waveform Microchannel

In this research,a numerical study of mixed convection of non-Newtonian fluid and magnetic field effect along a vertical wavy surface was investigated.A simple coordinate transformation to transform wavy surface to a flat surface is employed.A cubic spline collocation numerical method is employed to analyze transformed equations.The effect of various parameters such as Reynolds number,volume fraction 0-,Hartmann number,and amplitude of wave length was evaluated in improving the performance of a wavy microchannel.According to the presented results,the sinusoidal shape of the microchannel has a direct impact on heat transfer.By increasing the microchannel wave amplitude,the Nusselt number has risen.On the other hand,increasing the heat transfer in the higher wavelength ratio corrugated channel is seen as an effective method of increasing the heat transfer,especially at higher Reynolds numbers.The results showed that with increasing Hartmann numbers,the flow line near thewall becomesmore regular and,according to the temperature gradient created,theNusselt number growth.

Casson fluid flow and heat transfer over a nonlinearly stretching surface

A boundary layer analysis is presented for non-Newtonian fluid flow and heat transfer over a nonlinearly stretching surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. By using suitable transformations, the governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained with the shooting method. The effect of increasing Casson parameter is to suppress the velocity field. However the temperature is enhanced with the increasing Casson parameter.

NUMERICAL ANALYSIS OF THREE-DIMENSIONAL FLUID FLOW AND HEAT TRANSFER IN TIG WELD POOL WITH FULL PENETRATION

A model is established to analyze three-dimensional fluid flow and heat transfer in TICweld pools with full penetration.It considers the deformation of the molten pool surfaceat the condition of full penetrated workpieees,takes the are pressure as the drivingforce of the pool surface deformation,and determines the surface configuration of weldpool based on the dynamic balance of arc pressure,pool gravity and surface tension atdeformed weld pool surface. The SIMPLER algorithm is used to calculate the fluid flowfield and temperature distribution in TIG weld pools of stainless steel workpieces.TIGwelding experiments are made to verify the validity of the model.It shows the calculatedresults by the model are in good agreement with experimental measurements. professor,Dept of Welding Engineering,Harbin Institute of Technology,Harbin 150006,China

Heat transfer analysis in peristaltic flow of MHD Jeffrey fluid with variable thermal conductivity

The effect of an inclined magnetic field in the peristaltic flow of a Jeffrey fluid with variable thermal conductivity is discussed. The temperature dependent thermal conductivity of fluid in an asymmetric channel is taken into account. A dimensionless nonlinear system subject to a long wavelength and a low Reynolds number is solved. The explicit expressions of the stream function, the axial velocity, the pressure gradient, and the temperature are obtained. The effects of all physical parameters on peristaltic transport and heat transfer characteristics are observed from graphical illustrations. The behaviors of θ∈ [0, π/2] and θ∈ [π/2, π] on fluid flow and heat transfer are found to be opposite. Further, the size of trapped bolus is greater for the case of the inclined magnetic field （θ≠ π/2） than that for the case of the transverse magnetic field （θ = π/2）. The heat transfer coefficient decreases when the constant thermal conductivity （Newtonian） fluid is changed to the variable thermal conductivity （Jeffrey） fluid.

Stagnation-point flow of couple stress fluid with melting heat transfer

Melting heat transfer in the boundary layer flow of a couple stress fluid over a stretching surface is investigated. The developed differential equations are solved for homotopic solutions. It is observed that the velocity and the boundary layer thickness are decreasing functions of the couple stress fluid parameter. However, the temperature and surface heat transfer increase when the values of the couple stress fluid parameter increase. The velocity and temperature fields increase with an increase in the melting process of the stretching sheet.

Experimental and CFD Heat Transfer Studies of Al2Oa-Water Nanofluid in a Coiled Agitated Vessel Equipped with Propeller

This paper presents the heat transfer characteristics of A1203-water nanofluid in a coiled agitated vessel with propeller agitator. The experimental study was conducted using 0.10%, 0.20% and 0.30% volume concentra tion of A1203-water nanofluids. The results showed considerable enhancement of convective heat transfer using the nanofluids. The empirical correlations developed for Nusselt number in terms of Reynolds number, Prandtl number, viscosity ratio and volume concentration fit with the experimental data within ±10%. The heat transfer characteris tics were also simulated using computational fluid dynamics using FLUENT software with the standard ke model and multiple reference frame were adopted. The computational fluid dynamics （CFD） predicted Nusselt number agrees well with the experimental value and the discrepancy is found to be less than ＋8%.

Effect of viscous dissipation and heat source on flow and heat transfer of dusty fluid over unsteady stretching sheet

This paper investigates the problem of hydrodynamic boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface. The study considers the effects of frictional heating （viscous dissipation） and internal heat generation or ab- sorption. The basic equations governing the flow and heat transfer are reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations. The transformed equations are numerically solved by the Runge-Kutta-Fehlberg-45 order method. An analysis is carried out for two different cases of heating processes, namely, variable wall temperature （VWT） and variable heat flux （VHF）. The effects of various physical parameters such as the magnetic parameter, the fluid-particle interaction pa- rameter, the unsteady parameter, the Prandtl number, the Eckert number, the number density of dust particles, and the heat source/sink parameter on velocity and temperature profiles are shown in several plots. The effects of the wall temperature gradient function and the wall temperature function are tabulated and discussed.

MHD flow and heat transfer of micropolar fluid between two porous disks

A numerical study is carried out for the axisymmetric steady laminar incompressible flow of an electrically conducting micropolar fluid between two infinite parallel porous disks with the constant uniform injection through the surface of the disks. The fluid is subjected to an external transverse magnetic field. The governing nonlinear equations of motion are transformed into a dimensionless form through yon Karman＇s similarity transformation. An algorithm based on a finite difference scheme is used to solve the reduced coupled ordinary differential equations under associated boundary conditions. The effects of the Reynolds number, the magnetic parameter, the micropolar parameter, and the Prandtl number on the flow velocity and temperature distributions are discussed. The results agree well with those of the previously published work for special cases. The investigation predicts that the heat transfer rate at the surfaces of the disks increases with the increases in the Reynolds number, the magnetic parameter, and the Prandtl number. The shear stresses decrease with the increase in the injection while increase with the increase in the applied magnetic field. The shear stress factor is lower for micropolar fluids than for Newtonian fluids, which may be beneficial in the flow and thermal control in the polymeric processing.

Heat transfer on peristaltic flow of fourth grade fluid in inclined asymmetric channel with partial slip

In this paper, the effects of slip and heat transfer are studied on the peristaltic transport of a magnetohydrodynamic （MHD） fourth grade fluid. The governing equations are modeled and solved under the long wavelength approximation by using a regular perturbation method. Explicit expressions of solutions for the stream function, the velocity, the pressure gradient, the temperature, and the heat transfer coefficient are presented. Pumping and trapping phenomena are analyzed for increasing the slip parameter. Further, the temperature profiles and the heat transfer coefficient are observed for various increasing parameters. It is found that these parameters considerably affect the considered flow characteristics. Comparisons with published results for the no-slip case are found in close agreement.

Effects of slip, viscous dissipation and Joule heating on the MHD flow and heat transfer of a second grade fluid past a radially stretching sheet

The flow and heat transfer of an electrically conducting non-Newtonian second grade fluid due to a radially stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero （total adhesion） and infinity （full slip）. Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective numerical scheme is adopted to solve the obtained differential equations even without augmenting any extra boundary conditions. The important findings in this communication are the combined effects of the partial slip, magnetic interaction parameter and the second grade fluid parameter on the velocity and temperature fields. It is interesting to find that the slip increases the momentum and thermal boundary layer thickness. As the slip increases in magnitude, permitting more fluid to slip past the sheet, the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter, i.e., the fluid behaves as though it were inviscid. The presence of a magnetic field has also substantial effects on velocity and temperature fields.

Convective heat transfer of water flow in intersected rock fractures for enhanced geothermal extraction

Numerous intersected rock fractures constitute the fracture network in enhanced geothermal systems.The complicated convective heat transfer behavior in intersected fractures is critical to the heat recovery in fractured geothermal reservoirs.A series of three-dimensional intersected fracture models is constructed to perform the flow-through heat transfer simulations.The geometry effects of dead-end fractures(DEFs)on the heat transfer are evaluated in terms of intersected angles,apertures,lengths,and the connectivity.The results indicate that annular streamlines appear in the rough DEF and cause an ellipse distribution of the cold front.Compared to plate DEFs,the fluid flow in the rough DEF enhances the heat transfer.Both the increment of outlet water temperatureΔToutand the ratio of heat production Qrpresent the largest at the intersected angle of 90°while decline with the decrease of the intersected angle between the main flow fracture(MFF)and the DEFs.The extension of the length of intersected DEFs is beneficial to heat production while enhancing its aperture is not needed.Solely increasing the number of intersected DEFs induces a little increase of heat extraction,and more significant heat production can be obtained through connecting these DEFs with the MFF forming the flow network.

Numerical Simulation of Fluid Flow and Heat Transfer in Funnel Shaped Mold of Thin Slab Continuous Caster

Thin slab casting is used widely in the world. The control of molten steel flow and solidification in the mold is difficult due to the high casting speed and complicated configuration of the mold. Numerical simulation was carried out to study the fluid flow and heat transfer in the funnel shaped mold. The influence of nozzle design, casting speed and nozzle submersion depth on the flow and temperature fields in the mold was investigated, and guidance for selecting configurations of submerged nozzle was obtained.

Heat transfer analysis of Williamson fluid over exponentially stretching surface

This study explores the effects of heat transfer on the Williamson fluid over a porous exponentially stretching surface. The boundary layer equations of the Williamson fluid model for two dimensional flow with heat transfer are presented. Two cases of heat transfer are considered, i.e., the prescribed exponential order surface temperature （PEST） case and the prescribed exponential order heat flux （PEHF） case. The highly nonlinear partial differential equations are simplified with suitable similar and non-similar variables, and finally are solved analytically with the help of the optimal homotopy analysis method （OHAM）. The optimal convergence control parameters are obtained, and the physical fea- tures of the flow parameters are analyzed through graphs and tables. The skin friction and wall temperature gradient are calculated.

Experimental investigation on boiling heat transfer and pressure drop of R245fa in a horizontal micro-fin tube

An experimental investigation on the boiling heat transfer and frictional pressure drop of R245fa in a 7 mm horizontal micro-fin tube was performed.The results show that in terms of flow boiling heat transfer characteristics,boiling heat transfer coefficient(HTC)increases with mass velocity of R245fa,while it decreases with the increment of saturation temperature and heat flux.With the increase of vapor quality,HTC has a maximum and the corresponding vapor quality is about 0.4,which varies with the operating conditions.When vapor quality is larger than the transition point,HTC can be promoted more remarkably at higher mass velocity or lower saturation temperature.Among the four selected correlations,KANDLIKAR correlation matches with 91.6%of experimental data within the deviation range of±25%,and the absolute mean deviation is 11.2%.Also,in terms of frictional pressure drop characteristics of flow boiling,the results of this study show that frictional pressure drop increases with mass velocity and heat flux of R245fa,while it decreases with the increment of saturation temperature.MULLER-STEINHAGEN-HECK correlation shows the best prediction accuracy for frictional pressure drop among the four widely used correlations.It covers 84.1%of experimental data within the deviation range of±20%,and the absolute mean deviation is 10.1%.

Existence and uniqueness theorem for flow and heat transfer of a non-Newtonian fluid over a stretching sheet

Analysis is carried out to study the existence, uniqueness and behavior of exact solutions of the fourth order nonlinear coupled ordinary differential equations arising in the flow and heat transfer of a viscoelastic, electrically conducting fluid past a continuously stretching sheet. The ranges of the parametric values are obtained for which the system has a unique pair of solutions, a double pair of solutions and infinitely many solutions.

Controlling Roll Temperature by Fluid-Solid Coupled Heat Transfer

Currently, when magnesium alloy sheet is rolled, the method of controlling roll temperature is simple and inaccurate. Furthermore, roll temperature has a large influence on the quality of magnesium alloy sheet; therefore, a new model using circular fluid flow control roll temperature has been designed. A fluid heat transfer structure was designed, the heat transfer process model of the fluid heating roll was simplified, and the finite di erence method was used to cal?culate the heat transfer process. Fluent software was used to simulate the fluid?solid coupling heat transfer, and both the trend and regularity of the temperature field in the heat transfer process were identified. The results show that the heating e ciency was much higher than traditional heating methods(when the fluid heat of the roll and tempera?ture distribution of the roll surface was more uniform). Moreover, there was a bigger temperature di erence between the input and the output, and after using reverse flow the temperature di erence decreased. The axial and circum?ferential temperature distributions along the sheet were uniform. Both theoretical calculation results and numerical simulation results of the heat transfer between fluid and roll were compared. The error was 1.8%–12.3%, showing that the theoretical model can both forecast and regulate the temperature of the roll(for magnesium alloy sheets) in the rolling process.

Magnetohydrodynamic peristaltic flow of a hyperbolic tangent fluid in a vertical asymmetric channel with heat transfer

In the present paper we discuss the magnetohydrodynamic （MHD） peristaltic flow of a hyperbolic tangent fluid model in a vertical asymmetric channel under a zero Reynolds number and long wavelength approximation. Exact solution of the temperature equation in the absence of dissipation term has been computed and the analytical ex- pression for stream function and axial pressure gradient are established. The flow is analyzed in a wave frame of reference moving with the velocity of wave. The expression for pressure rise has been computed numerically. The physical features of pertinent parameters are analyzed by plotting graphs and discussed in detail.