Energy Conservation Equations Research Articles

Comparative Numerical Study of Melting Behavior of a Phase Change Material in Shell and Tube Latent Heat Energy Storage Unit With Longitudinal, Spiral, and Annular Fins in Horizontal and Vertical Orientations

Abstract Owing to the high storage capacity of the latent heat energy storage unit (LHSU), it is preferred among other types of thermal energy storage to overcome the mismatch between energy supply and demand. The orientation of the LHSU affects the melting process of the phase change material (PCM), and this effect could vary according to the fin shape of the LHSU. Thus, the present study aims to numerically examine the impact of vertical and horizontal orientations on the longitudinal, spiral, and annular finned shell and tube LHSUs. The computational fluid dynamics simulation solved the time-dependent conservation equations of mass, momentum, and energy in the three-dimensional domain. The enthalpy-porosity and the Boussinesq approximation were used respectively to simulate the PCM phase change and the change in density. The results show that the LHSUs have completely different behavior in the vertical orientation than in the horizontal orientation due to the various obstructions to the natural convection flow induced by the fins, depending on the fin shape, and the direction of natural convection flow. In the vertical orientation, the annular finned LHSU has a faster melting rate than the longitudinal finned LHSU by 25.6%. In contrast, in the horizontal orientation, the longitudinal finned LHSU melted more rapidly than the annular finned LHSU by 52.5%. The spiral finned LHSU performance was moderate between the two other finned LHSUs in both orientations due to its spiral shape that lies between the shape of the annular and longitudinal fins.

In-situ sensor calibration for building HVAC systems with limited information using general regression improved Bayesian inference

Sensors in building heating, ventilation and air-conditioning systems (HVACs) play important roles in maintaining indoor environmental quality and energy consumption. Owing to the repeatedly varied outdoor working environment and indoor users’ demand, sensor faults could be inevitable in the lifespan. To allow HVACs worked at fault-tolerant way, previous studies developed the in-situ sensor calibration method via energy conservation equations and Bayesian inference (EC-BI). However, the practical application may encounter challenges like limited-variable information, low-quality data and increasing risks of calibration uncertainty by indirect information supplement. These cause increasing in-situ calibration complexity and modeling costs. To address these challenges, this study proposed a general regression improved Bayesian inference (BI) in-situ sensor calibration strategy. The multiple linear regression (MLR) was utilized as a typical example of general regression method to improve the BI method. The proposed MLR-BI method was validated using both simulated and practical data of two building HVAC systems in two case studies. The principle component analysis (PCA)-based sensor fault reconstruction method was used for comparison under five fault conditions covering both single and simultaneous faults. Five variable scenarios were considered to validate the effectiveness of MLR-BI on HVACs with the limited variable information. Results indicated that the calibration accuracy of MLR-BI is over 99% under four conditions of the simulated case 1, which is about 6% and 8% higher than PCA and EC-BI respectively. For all the three variable scenarios of the simulated case 1, the calibration accuracy of MLR-BI is 99.65% on average. Especially in the four-variable scenario with limited variable information, MLR-BI shows the average calibration accuracy of 99.75% while PCA obtains 79.46% and EC-BI fails to work because of variable limitation. For the fault condition of the limitted-variable practical case 2, MLR-BI still outperforms the other two and obtains 97.1% calibration accuracy in two practical scenarios.

Homotopy analysis of mixed convection flow of a magnetized viscoelastic nanofluid from a stretching surface in non-Darcy porous media with revised Fourier and Fickian approaches

This article addresses theoretically the mixed convection hydromagnetic flow of electrically conducting viscoelastic nanofluid from a vertical permeable stretching sheet in a non-Darcy porous medium with Cattaneo–Christov double-diffusion model to evaluate the heat transfer phenomena in steady boundary layer flow on a stretchable surface. In this regard, thermal and solutal hyperbolic wave relaxation effects are included for non-Fourier and non-Fickian models. Heat absorption is also included in the analysis. The Buongiorno two-component nanoscale model is adopted for simulating Brownian motion and thermophoretic body force effects. A non-Darcy drag force model is employed for the porous medium and the Reiner–Rivlin second-grade model for non-Newtonian characteristics. Via appropriate dimensionless similarity variables, the nonlinear dimensional partial differential conservation equations for momentum, energy and concentration with associated boundary conditions are rendered into a nonlinear dimensionless ordinary differential boundary value problem. The homotopy analysis method (HAM) is utilized to solve the boundary value problem and the impact of emerging parameters including thermal relaxation parameters, non-Newtonian material parameter, Darcy permeability parameter, porous inertial parameter and Hartmann magnetic number on the momentum, heat and mass transfer characteristics are visualized graphically and in tables. A 30th-order approximation for HAM is shown to produce sufficient accuracy for the velocity and temperature fields and a 40th-order estimates is adequate for the concentration field. It is observed that increasing the magnitude of thermal and solutal relaxation parameters has the opposite effect on the thermal and concentration distributions. The novelty of the work is the simultaneous inclusion of multiple effects (non-Fourier and non-Fickian thermal relaxation hyperbolic wave models, non-Darcy drag effects and heat generation/absorption) which are relevant to rheological nanomaterials processing and also the deployment of homotopy analysis as an alternative to conventional numerical methods such as finite differences, finite elements and MATLAB solvers. The study is relevant to the manufacture of electro-conductive polymers (ECPs) and smart (functional) magnetic nano-liquids.

GTasb3D: A Novel 3D Framework for Modeling Thermal Evolution and Rarefied Flows in Porous Active Small Bodies with Various Shapes

Volatiles in small bodies provide important clues to solar system evolution and are of in-situ-resource-utilization interest. Explicit modeling of small bodies’ global thermophysical process is essential to assess volatiles’ evolution and abundance. Previous numerical studies commonly use a finite difference/volume method, which has limited capability in simulating the interior thermal dynamics of small bodies with realistic shapes. Here we developed a novel 3D framework using the generalized finite difference method for modeling thermal evolution of active small bodies (GTasb3D). By fully solving the energy and mass conservation equations using a mesh-free, Cartesian-coordinate-based method, this framework can evaluate the heat and mass transport in a porous cometary body of various shapes. Several tests and comparisons with previous studies have been carried out to verify this framework's accuracy and efficiency. We show that the timescale to achieve thermal equilibrium and the global temperature distribution are in good agreement with previous theoretical and numerical estimates. The GTasb3D simulations show that ice sublimation mainly occurs near the ice front, and parts of the resulting vapor recondense beneath the ice front. The surface gas density dramatically decreases as the ice retreats. For a 1 km radius object located at 3 au with initially homogeneous dust-ice distribution, the depth to ice at the equator is >∼2 cm after ∼10 yr, assuming that a dust mantle is left behind after ice depletion. At this stage, the global gas production rate is below the gas emission detection capability but is capable of lifting submillimeter-sized dust from the nucleus’s near-subsurface.

Numerical study on coupled modelling of artificial freezing marine soil

A theoretical model is proposed to investigate the coupling of the hydro-ice-salt-crystalline-thermal-mechanical of the artificial frozen marine soil in coastal areas. The influence of non-convective and thermal permeability in the fields of salt, pressure, thermal, and water, the compressibility of solid particles, as well as solute potential and ice resistance coefficients in convective flux are comprehensively considered based on the mass, energy, and momentum conservation equations. The proposed coupling model is solved using the COMSOL Multiphysics software. The accuracy of the proposed theoretical model is verified by the model test results in the literature. The parametric studies are conducted to investigate the effects of the key parameters on the freezing process. It is found that the salt desorption of the frozen marine soil cannot be ignored. The effect of salt desorption in the frozen area is strong which makes the adsorbed salt content in the unfrozen area greater than that in the frozen area. The change in salt mass fraction has a great influence on the overall frost heave, salt heave and water freezing. With the increase of overburden, the soil is compressed and the desorption effect is enhanced in the frozen area.

Resonance, Rayleigh flows, and thermal choking: Compressible coolant states in porous electromagnetic heat exchangers

Electromagnetic (EM) heat exchangers (HX) are systems that convert EM energy into heat or mechanical work. One potential design consists of a porous lossy ceramic material heated by EM waves with a compressible gas coolant. EM heating of ceramics is nonlinear, since the loss factor is temperature dependent. Designing such EM HXs requires an understanding of coupling between temperature, the electric field, and gas dynamics at the pore scale. To mimic this microscale phenomenon, a single channel with a high-speed gas coolant in perfect thermal contact with a thin solid ceramic layer is considered, with an applied plane-wave electric field propagating normal to the channel walls. From a thin-domain asymptotic analysis, the conservation laws reduce to a Rayleigh flow in the gas coupled with averaged thermal energy conservation equations at leading order. The model predicts that the kinetic energy of the gas increases up to 12.5 times the inlet value when thermal runaway occurs in the ceramic region for the cases considered, and thermal choking is possible when the coolant reaches the sonic state. Local maxima of efficiency occur on a discrete set of ceramic thicknesses that correspond to Fabry–Bragg resonances of the electric field.

Generalized MGT Heat Transfer Model for an Electro-Thermal Microbeam Lying on a Viscous-Pasternak Foundation with a Laser Excitation Heat Source

In this study, the effects of laser light on the heat transfer of a thin beam heated by an applied current and voltage are investigated. Laser heating pulses are simulated as endogenous heat sources with discrete temporal properties. The heat conduction equation is developed using the energy conservation equation and the modified Moore–Gibson–Thompson (MGT) heat flow vector. Thermal and structural analysis of Euler–Bernoulli microbeams is provided with the support of visco-Pasternak’s base with three parameters. Using the Laplace transform method, an approximation of an analytical solution is found for the field variables being examined. A comparison was made of the impacts of laser pulse length, the three foundation coefficients, and the thermal parameters on the responses to changes in measured thermophysical fields, such as deflection and temperature.

Onto Quantifying Unsteady Propulsion Characteristics Using Momentum and Energy Control Volume Assessments

AbstractThis effort presents a novel approach to interrogate efficiency for unsteady, undulating propulsion using variable momentum and energy conservation (VMEC) assessments. These integral approaches utilize large amounts of data from computational fluid dynamics (CFD) to address present difficulties associated with separating thrust from drag associated with propelling bodies as well as potentially resolve issues associated with defining a nonzero efficiency for a body in self-propulsion. Such a fundamental issue is addressed through strategic control volume assessments of the momentum and energy conservation equations. In this work, the Method of Manufactured Solutions (MMS) is used to verify the integral-based evaluation approach and better quantify output. The MMS results indicate the method is valid and that one can separate work associated with lift and drag from the energy budget. This separation procedure provides a means to separate propulsive and drag forces. The effort then studies previously validated CFD simulations of heaving and pitching foils to provide insight associated with separating axial forces into their thrust and drag components for highly complex systems. The effort then presents a new efficiency metric that can obtain nonzero efficiencies in self-propulsion. Overall, the results indicate that energy-based assessments provide insight that is a step forward toward isolating loss from propulsive mechanisms and developing proper metrics of efficiency.

Non-isothermal thin-film flow of a viscoplastic material over topography: critical Bingham number for a partial slump

This paper considers the non-isothermal flow of a viscoplastic fluid on a horizontal or an inclined surface with a flat, a step-up and a step-down topography. A particular application of interest is the spread of a fixed mass—a block—of material under its own weight. The rheology of the fluid is described by the Bingham model which includes the effect of yield stress, i.e. a threshold stress which must be exceeded before flow can occur. Both the plastic viscosity and the yield stress are modelled with temperature-dependent parameters. The flow is described by a reduced model with a thin-film equation for the height of the block and a depth-averaged energy conservation equation for the heat transfer. Results show that for large values of the yield stress, only the outer fraction of the fluid spreads outward, the inner fraction remaining unyielded, hence the block only partially slumps. Conversely, for small values of the yield stress, the entire block of fluid becomes yielded and therefore slumps. We present an analysis which predicts the critical value of the yield stress for which partial slump occurs and how it depends on temperature.Graphical abstract

Simulation of decay heat removal by active means following emergency shutdown in SFRs

Decay heat removal (DHR) is an important safety function in sodium-cooled fast reactors (SFRs). Dedicated systems are provided in the plant for performing DHR functionalities. Transients following reactor shutdown need to be studied to understand the dynamics of DHR systems, design the systems, and establish reactor safety. DHR systems can operate by active as well as passive means, thanks to the phenomenon of natural circulation. In the present work, a DHR system riding on the Balance of Plant (BoP) of a typical medium-sized SFR has been modeled and incorporated into the in-house developed plant dynamics code DYANA-P. DYANA-P already has models of primary and secondary circuits of SFR. With this code enhancement, the simulation of DHR in an integrated manner became possible. In particular, thermal models of the Moisture Separator Tank (MST), Decay Heat Removal Condenser (DHRC), and hydraulic model of the DHRC flow circuit were developed. Two-phase one-dimensional mass, momentum, and energy conservation equations with homogeneous flow assumptions were used to create the models. Simulation of SCRAM in a typical SFR has been carried out to demonstrate the applications of the modified code. Two different DHR deployment schemes were studied and compared – 1. Using DHR systems designed for high pressure of ∼170 bar, 2. Using DHR systems designed for low pressure of ∼15 bar. In the first scheme, reactor cooling was achieved at the desired rate of ∼20 K/h. In the second scheme, the reactor cooling rate will be higher at ∼60 K/h.

Traction-Associated Peridynamic Motion Equation and Its Verification in the Plane Stress and Fracture Problems

How to prescribe traction on boundary surface is still an open question in peridynamics. This problem is investigated in this paper. Through introducing the induced body force defined by boundary traction, the Silling's peridynamic motion equation is extended to a new formulation called the traction-associated peridynamic motion equation, which is verified to be compatible with the conservation laws of linear momentum and angular momentum. The energy conservation equation derived from the traction-associated peridynamic motion equation has the same form as that in the original peridynamics advanced by Silling. Therefore, the constitutive models of the original peridynamics can be directly applied to the traction-associated peridynamic motion equation. Some benchmark examples in the plane stress problems are calculated. The numerical solutions agree well with the classical elasticity solutions, and the volume correction and the surface correction are no longer needed in the numerical algorithm. These results show that the traction-associated peridynamic motion equation not only retains all advantages of the original peridynamics, but also can conveniently deal with the complex traction boundary conditions.

A numerical investigation of methane pyrolysis in a molten catalyst Bath–A single bubble approach

A dynamic one-dimensional numerical model of methane pyrolysis within a rising and pyrolysing bubble in a column of molten Ni0.27Bi0.73, as a molten catalyst, is presented. The model predicts both the behavior of the rising bubble in the column and the chemical reactions within it, accounting for any variations in bubble diameter and rising velocity, which have previously been assumed to be constant. The conservation equations of energy, mass and momentum are solved simultaneously using the implicit Gauss–Seidel numerical method. The model accounts for the main parameters contributing to the methane pyrolysis reaction. The reliability of the model was assessed by comparison with the available experimental data from the literature and a reasonable agreement was found. Considering the model assumptions, the results show that, for the assessed conditions, more than 97% of the overall conversion occurs at the interface of the bubble and the molten bath, while the reaction within the bubble contributes only <3% of the overall conversion. A sensitivity analysis was also undertaken to the variations in the bubble size, column height, molten bath temperature, pressure, gas composition and temperature. Calculations show that methane conversion is more sensitive to the molten bath temperature than the initial gas temperature. Furthermore, it decreases significantly with any increase in pressure. Also, at pressures of > 2 MPa, the equilibrium condition is achieved within the bottom one-third of the column for the assessed conditions.

Modeling the Shape and Velocity of Magmatic Intrusions, a New Numerical Approach

AbstractDykes are magma‐filled fractures propagating through the brittle crust. Understanding the physics of dyking process is essential to mitigate the volcanic hazard associated with the opening of new eruptive fissures at the surface. Often, physics‐based models view either fracturing of the host rock or viscous flow of the magma as the dominating energy sink during dyke propagation. Here, we provide a numerical model that captures the coupling of fracturing at the crack tip and the transport of a viscous fluid. Built with the boundary element technique, our model allows for computation of the shape and velocity of a growing fluid‐filled crack accounting for the viscosity of the fluid: the fluid flow induces a viscous pressure drop acting at the crack walls, and modifies the shape of the crack. The energy conservation equation provides the constraints to solve for the crack growth velocity, assuming that brittle fracturing and viscous flow are the main processes that dissipate energy. Using a parameter range that represents typical magmatic intrusions, we obtain crack shapes displaying some typical characteristics, including a tear‐drop head and an open tail that depend on rock rigidity, magma viscosity, and buoyancy. We show that viscous forces significantly contribute to the energy dissipated during the propagation of magmatic dykes. Applied to the 1998 intrusion at Piton de la Fournaise (La Réunion Island), we provide ranges of dyke lengths and openings by adjusting the numerical velocity to the one deduced from the migration of volcano‐tectonic events.

Induced Navier’s Slip with CNTS on a Stretching/Shrinking Sheet under the Combined Effect of Inclined MHD and Radiation

The present article investigates viscous fluid flow’s heat and mass transfers over a stretching/shrinking sheet using the single and multi-wall carbon nanotube models. The analysis considers the effects of thermal radiation, induced slip, mass transpiration, and inclined magnetic force. The effect of the carbon nanotube model on fluid flow has not been considered in previous studies. By exploiting the similarity variable, the governing nonlinear partial differential equations are converted into nonlinear ordinary differential equation. The derived equations are solved analytically, and we obtained an exact solution for the velocity and energy conservation equation. The physical parameters of interest such as induced slip parameter, suction/injection, magnetic field, thermal radiation, and shear stress are analyzed and presented graphically. In particular, we show that the fluid flow in a single wall carbon nanotube transfers more energy than the multivalued nanotubes.

Turbulent Flame Propagation in Hydrogen-Air and Methane-Air Mixtures in the Field of Synthetic Turbulence: Direct Numerical Simulation

A technique alternative to the direct numerical simulation of turbulent combustion of gas mixtures is proposed. It is based on the solution of the three-dimensional transport equations for species concentrations and the energy conservation equation in the “synthetic” field of constant-pressure homogeneous, isotropic and statistically stationary (forced) turbulence using the detailed reaction mechanism. The synthetic turbulence with given spatial and temporal correlation functions is generated using the Monte Carlo method, assuming that the components of the vector of fluctuation velocity obey the normal Gaussian distribution. The technique is applied to the problem of turbulent combustion of fuel-lean and stoichiometric mixtures of hydrogen and methane with air at a turbulence intensity up to 10 m/s. The calculated turbulent flame propagation velocities agree satisfactorily with the values measured in the fan-stirred bomb. The predicted volume fractions of active reaction centers H, O, and OH in a turbulent flame are shown to be less than in a laminar flame up to an order of magnitude, which also agrees with the experiment. In general, calculations indicate that the “wrinkled flame” model is applicable to fuel-lean and stoichiometric mixtures of hydrogen and methane with air at turbulence intensities up to 10 m/s

Numerical Investigation of the Effects of Chemical Species and Chemical Kinetic Mechanisms on Laminar Premixed Flame-Acoustic Wave Interactions

Numerical simulation of interactions between acoustic waves and flames is of utmost importance in thermo-acoustic instability research. In this study, interactions between a one-dimensional Methane-Air laminar premixed flame and acoustic waves with a frequency of 50 to 50000 Hz are simulated by simultaneously solving the equations for energy conservation, chemical species transport, state and continuity in one-dimensional space. By assuming that the flame thickness is smaller than the acoustic wavelength, the spatial pressure fluctuations can be neglected and the flame experiences only a time-varying acoustic pressure. The GRI mechanisms, as well as their reduced mechanisms, are considered to obtain results for steady flames without acoustic waves, and the interaction of unsteady flames with acoustic waves. Results show that the total heat-release-rate fluctuations for the flame is affected by increasing the frequency of the acoustic wave. An increase in frequency first increases the total heat released, and then decreases it. The obtained results are in good agreement with those of other researchers. Furthermore, at the presence of acoustic waves, various chemical species can affect the total heat-release-rate fluctuations. With Rayleigh's instability criterion, it can be shown that H2O, CO2 and O2 are the main species to the fluctuations of the total heat release rate and lead to flame instability. Results show that heat-release-rate of H2O specie is the most important on the total heat-release-rate. Therefore, for the flame-acoustic waves interaction problem, the best mechanism is the one that could predict the concentration of H2O more precisely.

Microfluidic Transport in Ternary Liquid Layers Due to Sinusoidal Thermocapillary Actuation

Abstract The large-scale applicability of the micro- and nanofluidic devices demands continuous technological advancements in the transport mechanisms, especially to promptly mix the analytes and reagents at such a small scale. To this end, thermocapillarity-induced Marangoni hydrodynamics of three-layered, immiscible fluid streams in a microchannel is analytically explored. The system is exposed to periodic and sinusoidal thermal stimuli, and a theoretical framework is presented. The diffusion of the periodic thermal stimuli across and along the fluidic interfaces creates axial surface tension gradients, which induce vortical motion of the participating fluids within the microconduit. We show that depending on the physical parameters of the three participating fluids, such vortex patterns may be fine-tuned and controlled to obtain desired transport behavior. An analytical solution for the thermal and the hydrodynamic transport phenomena is obtained by solving the momentum and energy conservation equations under the umbrella of creeping flow characteristics (very low Reynolds and thermal Marangoni numbers), and nearly undeformed fluid interfaces (negligibly small Capillary number). The approximate profiles of the deformed interfaces are also quantified theoretically to justify the assumption of flat and undeformed interfaces. The independent influence of crucial thermophysical properties, the microchannel system parameters, and features of the applied thermal stimuli are shown in detail for a fixed combination of other parameters.

Adaptive Finite Element Simulation of Double-Diffusive Convection

Double-diffusive convection plays an important role in many physical phenomena of practical importance. However, the numerical simulation of these phenomena is challenging since fine meshes are often required to capture the flow physics. Hence, several different numerical methods have been employed in the past. This work reports the development and application of an adaptive finite element method for the simulation of these phenomena, thereby avoiding the need for the use of very fine meshes over the whole domain. The weak formulation of the conservation equations for mass, momentum, energy and species concentration is used. The Boussinesq approximation relates the density of the fluid to the temperature and/or the species concentration. A second-order backward difference method is used for time discretization and the Galerkin method is employed for spatial discretization. Both adaptive time step and grid refinement techniques are employed, and the code is parallelized using MPI. Three different stabilization methods of the convective-diffusion equations are compared; namely, the streamline upwind Petrov–Galerkin (SUPG) method, and two modified methods aimed at diminishing spurious oscillations that include an artificial diffusion term. This diffusion term may be either isotropic or orthogonal to the streamlines. The addition of artificial isotropic diffusion to the SUPG method provides enhanced stability. The method is applied to double-diffusive finger convection in a sucrose-salt aqueous mixture and a stratified salt solution heated from below. The method accurately reproduces the experimentally observed temporal evolution of the salt fingers in the former case and the location of the interfaces between convective and non-convective zones in the latter.

A new study of multi-phase mass and heat transfer in natural gas hydrate reservoir with an embedded discrete fracture model

Studies of the hydrate cores have shown that natural fractures can be frequently observed in hydrate reservoirs, resulting in a fracture-filled hydrate. Therefore, it is highly necessary for industries to predict the gas well productivity of fracture-filled hydrate reservoirs. In this work, an embedded discrete fracture model is applied to characterize the natural fractures of fracture-filled gas-hydrate reservoirs. The non-linear mass and energy conservation equations which are discretized with the finite-difference method are solved by the fully implicit approach, and the proposed model is justified by a commercial simulator. On the basis of the proposed model, we investigate the influences of natural fractures, fracture conductivity, and hydrate dissociation rate on the gas well productivity and the distributions of pressure, temperature, and hydrate saturation. The simulation results show that hydraulic and natural fractures exert significant impacts on the gas well productivity of the fracture-filled hydrate reservoirs, and the cumulative gas production is increased by 45.6% due to the existence of the connected natural fractures. The connected natural fractures can impose a more important influence on the gas well productivity than the unconnected natural fractures. The cumulative gas production is increased by 6.48% as Nnf is increased from 2 to 50, whereas the increase is 43.38% as Nf_con is increased from 0 to 4. In addition, A higher hydraulic fracture conductivity can be more favorable than a higher natural fracture conductivity for improving the gas well productivity, and a higher hydrate dissociation rate can lead to a lower temperature along fractures due to a more noticeable reduction of solid hydrate. This study provides a theoretical basis for developing fracture-filled hydrate reservoirs efficiently in the future.

Transient Coupled Flow Model for Matrix-Fracture in High-Pressure Gas Reservoirs Opened by Gas Drilling

Gas drilling technology is an effective method to protect low permeability tight sandstone reservoirs from damage. However, using this technology to drill high-pressure fractured reservoirs, the fluid flow characteristics are extremely complex, leading to drilling safety challenges. Therefore, based on the conservation equations of mass, momentum, and energy, a new transient coupled flow model in matrix-fracture is established for high-pressure gas reservoirs opened by gas drilling, considering convection term and energy equation, to research the pressure and flow velocity transient behaviors. This model is solved by Shaher Momani’s algorithm and CyabJiBe format, and the type curves of the pressure and flow velocity are plotted. The three flow stages are developed, and the impact of parameters and equation terms on the transient flow behavior is analyzed and discussed, such as the energy equation, the matrix permeability ( k ), the fracture aperture ( L f ), and the fracture outlet pressure. It is found that the energy equation term of the model has a great influence on the transient characteristics such as velocity and pressure, which cannot be ignored. In the first flow stage, the flow velocity characteristics are not affected by the matrix parameters being extremely unstable, but in the second and third stages, the influence of the gas supplied to fracture cannot be ignored. The proposed transient coupled flow model provides a new understanding of the transient flow behavior in matrix-fracture for high-pressure reservoirs during gas drilling, which can be used to interpret the characteristics of pressure and velocity more realistically, to provide support for safe drilling of gas drilling.