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The purpose of this study is to investigate the unstable propagation of parallel hydraulic fractures induced by interferences of adjacent perforation clusters and thermal diffusion. Fracture propagation in the process of multistage fracturing of a rock mass is deflected owing to various factors. Hydrofracturing of rock masses in deep tight reservoirs involves thermal diffusion, fluid flow and deformation of rock between the rock matrix and fluid in pores and fractures.

To study the unstable propagation behaviours of three-dimensional (3D) parallel hydraulic fractures induced by the interferences of adjacent perforation clusters and thermal diffusion, a 3D engineering-scale numerical model is established under different fracturing scenarios (sequential, simultaneous and alternate fracturing) and different perforation cluster spacings while considering the thermal-hydro-mechanical coupling effect. Stress disturbance region caused by fracture propagation in a deep tight rock mass is superimposed and overlaid with multiple fractures, resulting in a stress shadow effect and fracture deflection.

The results show that the size of the stress shadow areas and the interaction between fractures increase with decreasing multiple perforation cluster spacing in horizontal wells. Alternate fracturing can produce more fracture areas and improve the fracturing effect compared with those of sequential and simultaneous fracturing. The larger the temperature gradient between the fracturing fluid and rock matrix, the stronger the thermal diffusion effect, and the effect of thermal diffusion on the fracture propagation is significant.

This study focuses on the behaviours of the unstable dynamic propagation of 3D parallel hydraulic fractures induced by the interferences of adjacent perforation clusters and thermal diffusion. Further, the temperature field affects the fracture deflection requires could be investigated from the mechanisms; this paper is to study the unstable propagation of fractures in single horizontal well, which can provide a basis for fracture propagation and stress field disturbance in multiple horizontal wells.

The purpose of this paper is to conduct a theoretical study on steady fully developed non-linear natural convection and mass transfer flow past an infinite vertical moving porous plate with chemical reaction and thermal diffusion effect. Closed-form expressions for dimensionless velocity, concentration, Sherwood number and skin-friction are obtained by solving the present mathematical model.

The fully developed steady non-linear natural convection and mass transfer flow near a vertical moving porous plate with chemical reaction and thermal diffusion effect is investigated. The non-linear density variation and Soret effect were taken into consideration. The dimensionless velocity, temperature and concentration profiles were obtained in terms of exponential functions, and were used to compute the governing parameters, skin-friction and Sherwood number.

The effect of coefficient of the non-linear density variation with the temperature (NDT) and concentration (NDC) parameter, chemical reaction parameter, thermal diffusion parameter are discussed with the aid of line graphs and tables. The analysis of the result shows that the velocity as well as skin-friction having higher values in the case of non-linear variation of density with temperature and concentration in comparison to linear variation of density with temperature and concentration. It is observed that the velocity and skin-friction increase with an increase in the Soret parameter.

The aim of this paper is to extend the work of Muthucumaraswamy (2002) by incorporating the thermal diffusion (Soret) effect and non-linear density variation with temperature (NDT) and concentration (NDC), on which, to the best knowledge of the authors, no studies have been carried out.

The purpose of this paper is to analyze the thermal-diffusion and diffusion-thermo effects on magnetohydrodynamics (MHD) natural convective flow through porous medium in a rotating system with ramped temperature.

Using the non-dimensional variables, the flow governing equations along with corresponding initial and boundary conditions have been transformed into non-dimensional form. These non-dimensional partial differential equations are solved by using finite element method. This method is powerful and stable. It provides excellent convergence and flexibility in providing solutions.

The effects of Soret number, Dufour number, rotation parameter, magnetic parameter, Hall current parameter, permeability parameter, thermal Grashof number, solutal Grashof number, Prandtl number, thermal radiation parameter, heat absorption parameter, Schmidt number, chemical reaction parameter and time on the fluid velocities, temperature and concentration are represented graphically in a significant way and the influence of pertinent flow governing parameters on the skin frictions and Nusselt number are presented in tabular form. On the other hand, a comparison for validation of the numerical code with previously published work is performed, and an excellent agreement is observed for the limited case existing literature.

A very useful source of information for researchers on the subject of MHD flow through porous medium in a rotating system with ramped temperature.

The problem is moderately original, as it contains many effects like thermal-diffusion (Soret) and diffusion-thermo (Dufour) effects and chemical reaction.

The aim of this work is to analyze the combined effects of melting, thermal-diffusion and diffusion-thermo on the flow of non-Newtonian fluid.

An efficient approach namely homotopy analysis method is applied to compute the solution of the non-linear problem. Moreover, numerical results using MATLAB function bvp4c are also computed.

Main findings are an increase in the melting process corresponding to increase in the velocity and the boundary layer thickness. However, surface heat and mass transfer decrease by increasing the values of melting parameter M.

Combined effects of thermal-diffusion and diffusion-thermo are analyzed and the solutions are computed both numerically and analytically. Some deduced results can be obtained in a limiting sense.

The purpose of this paper is to report the impact of thermophoresis and Brownian moment on MHD two-dimensional forced convection flow of nanofluid past a permeable stretching sheet in the presence of thermal diffusion.

The flow governing PDEs are reduced to ODEs by utilizing pertinent transmutations and then resolved by employing a fourth-order Runge-Kutta-based shooting technique. The energy and diffusion equations are incorporated with Brownian motion, thermophoresis and Soret parameters. The velocity, thermal and concentration attributes along with skin friction factor, local Nusselt and Sherwood number are discussed under the influence of sundry pertinent parameters and presented with the assistance of graphical and tabular values.

The results infer that Sherwood number is accelerated by Soret parameter but it controls the thermal transport rate. And also, Brownian and thermophoresis play a vital role in enhancing heat conduction process.

Considering the industrial applications of flow of magnetic nanofluid over a stretching surface, this paper presents the solution of the flow problem considering thermophoresis, Brownian motion, magnetic field and thermal diffusion effects. In addition, the aim and objectives of this paper fills a gap in the industry.

The authors presented the time-dependent flow of an upper-convected Maxwell (UCM) fluid in the presence of chemical reaction, thermal-diffusion and diffusion-thermo effects. The paper aims to discuss these issues.

Recent technique namely homotopy analysis method (HAM) is utilized to compute the solution of the problem.

Chemical reaction has opposite effects on the concentration field for the destructive and constructive cases. The Deborah number acts as a retarding agent.

Combined effects of thermal-diffusion, diffusion-thermo and chemical reaction are analyzed.

Ultrasonic additive manufacturing (UAM) is a rapid prototyping process through which multiple thin layers of material are sequentially ultrasonically welded together to form a finished part. While previous research into the peak temperatures experienced during UAM have been documented, a thorough examination of the heating and cooling curves has not been conducted to date.

For this study, UAM weldments made from aluminum 3003‐H18 tapes with embedded Type‐K thermocouples were examined. Finite element modeling was used to compare the theoretical thermal diffusion rates during heating to the observed heating patterns. A model was used to calculate the effective thermal diffusivity of the UAM build on cooling based on the observed cooling curves and curve fitting analysis.

Embedded thermocouple data revealed simultaneous temperature increases throughout all interfaces of the UAM build directly beneath the sonotrode. Modeling of the heating curves revealed a delay of at least 0.5 seconds should have existed if heating of lower interfaces was a result of thermal diffusion alone. As this is not the case, it was concluded that ultrasonic energy is absorbed and converted to heat at every interface beneath the sonotrode. The calculated thermal diffusivity of the build on cooling was less than 1 percent of the reported values of bulk aluminum, suggesting that voids and oxides along interfaces throughout the build may be inhibiting thermal diffusion through thermal contact resistance across the interface.

This work systematically analyzed the thermal profiles that develop during the UAM process. The simultaneous heating phenomenon presented here has not been documented by other research programs. The findings presented here will enable future researchers to develop more accurate models of the UAM process, potentially leading to improved UAM bond quality.

This paper aims to study the heat transfer of nanofluid flow driven by the move of channel walls in a microchannel under the effects of the electrical double layer and slippery properties of channel walls. The distributions of velocity, temperature and nanoparticle volumetric concentration are analyzed under different slip-length. Also, the variation rates of flow velocity, temperature, concentration of nanoparticle, the pressure constant, the local volumetric entropy generation rate and the total cross-sectional entropy generation are analyzed.

A recently developed model is chosen which is robust and reasonable from the point of view of physics, as it does not impose nonphysical boundary conditions, for instance, the zero electrical potential in the middle plane of the channel or the artificial pressure constant. The governing equations of flow motion, energy, electrical double layer and stream potential are derived with slip boundary condition presented. The model is non-dimensionalized and solved by using the homotopy analysis method.

Slip-length has significant influences on the velocity, temperature and nanoparticle volumetric concentration of the nanofluid. It also has strong effects on the pressure constant. With the increase of the slip-length, the pressure constant of the nanofluid in the horizontal microchannel decreases. Both the local volumetric entropy generation rate and total cross-sectional entropy generation rate are significantly affected by both the slip-length of the lower wall and the thermal diffusion. The local volumetric entropy generation rate at the upper wall is always higher than that around the lower wall. Also, the larger the slip-length is, the lower the total cross-sectional entropy generation rate is when the thermal diffusion is moderate.

The findings in this work on the heat transfer and flow phenomena of the nanofluid in microchannel are expected to make a contribution to guide the design of micro-electro-mechanical systems.

This investigation has been carried out for thermal-diffusion (Dufour) and diffusion-thermo (Soret) effects on the boundary layer flow of Jeffrey fluid in the region of stagnation-point towards a stretching sheet. Heat transfer occurring during the melting process due to a stretching sheet is considered. The paper aims to discuss these issues.

The authors convert governing partial differential equations into ordinary differential equations by using suitable transformations. Analytic solutions of velocity and temperature are found by using homotopy analysis method (HAM). Further graphs are displayed to study the salient features of embedding parameters. Expressions of skin friction coefficient, local Nusselt number and local Sherwood number have also been derived and examined.

It is found that velocity and the boundary layer thickness are increasing functions of viscoelastic parameter (Deborah number). An increase in the melting process enhances the fluid velocity. An opposite effect of melting heat process is noticed on velocity and skin friction.

The boundary layer flow in non-Newtonian fluids is very important in many applications including polymer and food processing, transpiration cooling, drag reduction, thermal oil recovery and ice and magma flows. Further, the thermal diffusion effect is employed for isotope separation and in mixtures between gases with very light and medium molecular weight.

Very scarce literature is available on thermal-diffusion (Dufour) and diffusion-thermo (Soret) effects on the boundary layer flow of Jeffrey fluid in the region of stagnation-point towards a stretching sheet with melting heat transfer. Series solution is developed using HAM. Further, the authors compare the present results with the existing in literature and found excellent agreement.

The purpose of this study is to investigate the two-dimensional unsteady inclined stagnation point flow and thermal transmission of Maxwell fluid on oscillating stretched/contracted plates. First, based on the momentum equation at infinity, pressure field is modified by solving first-order differential equation. Meanwhile, thermal relaxation characteristic of fluid is described by Cattaneo–Christov thermal diffusion model.

Highly coupled model equations are transformed into simpler partial differential equations (PDE) via appropriate dimensionless variables. The approximate analytical solutions of unsteady inclined stagnation point flow on oscillating stretched and contracted plates are acquired by homotopy analysis method for the first time, to the best of the authors’ knowledge.

Results indicate that because of tensile state of plate, streamline near stagnation point disperses to both sides with stagnation point as center, while in the case of shrinking plate, streamline near stagnation point is concentrated near stagnation point. The enhancement of velocity ratio parameter leads to increasing of pressure variation rate, which promotes flow of fluid. In tensile state, surface friction coefficient on both sides of stagnation point has opposite symbols; when the plate is in shrinkage state, there is reflux near the right side of the stagnation point. In addition, although the addition of unsteady parameters and thermal relaxation parameters reduce heat transfer efficiency of fluid, heat transfer of fluid near the plate can also be enhanced by considering thermal relaxation effect when plate shrinks.

First, approximate analytical solutions of unsteady inclined stagnation point flow on oscillating stretched and contracted plates are researched, respectively. Second, pressure field is further modified. Finally, based on this, thermal relaxation characteristic of fluid is described by Cattaneo–Christov thermal diffusion model.