On the stability of the flow and heat transfer over a moving thin needle with prescribed surface heat flux

The steady flow and heat transfer over a moving thin needle with prescribed surface heat flux is studied. The similarity equations are obtained by using similarity transformation technique. The problem is solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The plots of the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are presented and their behaviors are discussed for different values of the needle size and the velocity ratio parameter. Results show that the decreasing of the needle size enhance the skin friction coefficient and the local Nusselt number on the needle surface. It is found that dual solutions exist (upper and lower branches) for a certain range of the velocity ratio parameter. A stability analysis of the solutions are performed and it shows that the upper branch solution is stable, while the lower branch solution is unstable.     

Thermally stratified flow of hybrid nanofluids with radiative heat transport and slip mechanism: multiple solutions

Research on flow and heat transfer of hybrid nanofluids has gained great significance due to their efficient heat transfer capabilities.In fact,hybrid nanofluids are a novel type of fluid designed to enhance heat transfer rate and have a wide range of engineering and industrial applications.Motivated by this evolution,a theoretical analysis is performed to explore the flow and heat transport characteristics of Cu/Al₂O₃ hybrid nanofluids driven by a stretching/shrinking geometry.Further,this work focuses on the physical impacts of thermal stratification as well as thermal radiation during hybrid nanofluid flow in the presence of a velocity slip mechanism.The mathematical modelling incorporates the basic conservation laws and Boussinesq approximations.This formulation gives a system of governing partial differential equations which are later reduced into ordinary differential equations via dimensionless variables.An efficient numerical solver,known as bvp4c in MATLAB,is utilized to acquire multiple(upper and lower)numerical solutions in the case of shrinking flow.The computed results are presented in the form of flow and temperature fields.The most significant findings acquired from the current study suggest that multiple solutions exist only in the case of a shrinking surface until a critical/turning point.Moreover,solutions are unavailable beyond this turning point,indicating flow separation.It is found that the fluid temperature has been impressively enhanced by a higher nanoparticle volume fraction for both solutions.On the other hand,the outcomes disclose that the wall shear stress is reduced with higher magnetic field in the case of the second solution.The simulation outcomes are in excellent agreement with earlier research,with a relative error of less than 1%.     

Locally-rotationally-symmetric Bianchi type-V cosmology with heat flow

In this paper we present a spatially homogeneous locally-rotationally-symmetric (LRS) Bianchi type-V cosmological model with perfect fluid and heat flow. A general approach is introduced to solve Einstein’s field equations using a law of variation for the mean Hubble parameter, which is related to average scale factor of the model that yields a constant value for the deceleration parameter. Exact solutions that correspond to singular and non-singular models are found with heat flow. The physical constraints on the solution and, in particular, the thermodynamical laws that govern such solutions are discussed in some detail.     

Numerical study of magneto-convective heat and mass transfer from inclined surface with Soret diffusion and heat generation effects: A model for ocean magnetic energy generator fluid dynamics

A mathematical model is developed for steady state magnetohydrodynamic (MHD) heat and mass transfer flow along an inclined surface in an ocean MHD energy generator device with heat generation and thermo-diffusive (Soret) effects. The governing equations are transformed into nonlinear ordinary differential equations with appropriate similarity variables. The emerging two-point boundary value problem is shown to depend on six dimensionless thermophysical parameters - magnetic parameter, Grashof number, Prandtl number, modified Prandtl number, heat source parameter and Soret number in addition to plate inclination. Numerical solutions are obtained for the nonlinear coupled ordinary differential equations for momentum, energy and salinity (species) conservation, numerically, using the Nachtsheim–Swigert shooting iteration technique in conjunction with the Runge–Kutta sixth order iteration scheme. Validation is achieved with Nakamura's implicit finite difference method. Further verification is obtained via the semi-numerical Homotopy analysis method (HAM). With an increase in magnetic parameter, skin friction is depressed whereas it generally increases with heat source parameter. Salinity magnitudes are significantly reduced with increasing heat source parameter. Temperature gradient is decreased with Prandtl number and salinity gradient (mass transfer rate) is also reduced with modified Prandtl number. Furthermore, the flow is decelerated with increasing plate inclinations and temperature also depressed with increasing thermal Grashof number.     

The influence of heat transfer in an MHD second grade fluid film over an unsteady stretching sheet

The flow and heat transfer problem of a second grade fluid film over an unsteady stretching sheet is considered. The fluid is incompressible and electrically conducting in the presence of a uniform applied magnetic field. The series solutions of the governing boundary value problems are obtained by employing homotopy analysis method (HAM). The convergence of the developed solutions is discussed explicitly. The dependence of velocity and temperature profiles on various parameters is shown and discussed through graphs. The values of skin-friction coefficient, Nusselt number and free surface temperature are given in tabular form for various emerging parameters.     

Coupled flow and heat transfer of power-law nanofluids on non-isothermal rough rotary disk subjected to magnetic field

We study the coupled flow and heat transfer of power-law nanofluids on a non-isothermal rough rotating disk subjected to a magnetic field. The problem is formulated in terms of specified curvilinear orthogonal coordinate system. An improved BVP4C algorithm is proposed, and numerical solutions are obtained. The influence of volume fraction, types and shapes of nanoparticles, magnetic field and power-law index on the flow, and heat transfer behavior are discussed. The obtained results show that the power-law exponents (PLE), nanoparticle volume fraction (NVF), and magnetic field inclination angle (MFIA) have almost no effects on velocities in the wave surface direction, but have small or significant effects on the azimuth direction. The NVF has remarkable influences on local Nusselt number (LNN) and friction coefficients (FC) in the radial direction and the azimuth direction (AD). The LNN increases with NVF increasing while FC in AD decreases. The types of nanoparticles, magnetic field strength, and inclination have small effects on LNN, but they have remarkable influences on the friction coefficients with positively correlated heat transfer rate, while the inclination is negatively correlated with heat transfer rate. The size of the nanoparticle shape factor is positively correlated with LNN.     

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.     

MHD Flow Towards a Permeable Surface with Prescribed Wall Heat Flux

The steady magnetohydrodynamic （MHD） mixed convection flow towards a vertical permeable surface with prescribed heat flux is investigated. The governing partial differential equations are transformed into a system of ordinary differential equations, which is then solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analysed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions exist for the assisting flow, besides the solutions usually reported in the literature for the opposing flow.     

Experimental investigation of flow boiling heat transfer enhancement under ultrasound fields in a minichannel heat sink

Ultrasound is considered to be an effective active heat transfer enhancement method, which is widely used in various fields. But there is no clear understanding of flow boiling heat transfer characteristics in micro/mini-channels under ultrasonic field since the studies related are limited up to now. In this paper, a novel minichannel heat exchanger with two ultrasonic transducers inside the inlet and outlet plenum respectively is designed to experimentally investigate the impacts of ultrasound on flow boiling heat transfer enhancement in a minichannel heat sink. Flow visualization analyses reveal that ultrasound can promote rapid bubble motion, bubble detachment from heating wall surface and thereby new bubble generation, and decrease the length of confined bubble. Furthermore, the flow boiling experiments are initiated employing working fluid R141b at different ultrasonic parameters (e.g., frequency, power, angle of radiation) and heat flux under three types of ultrasound excitations: no ultrasound (NU), single inlet ultrasound (IU), inlet and outlet ultrasound (IOU). The results indicate that ultrasound has obvious augmentation effects on flow boiling heat transfer even though the intensification effects will be limited with the heat flux increases. The higher ultrasonic power, the lower ultrasonic frequency and the higher ultrasonic radiation angle, the better intensification efficiency. The maximum enhancement ratio of h_ave in the saturated boiling section reaches 1.88 at 50 W, 23 kHz and 45° under the experimental conditions. This study will be beneficial for future applications of ultrasound on flow boiling heat transfer in micro/mini-channels.     

Similarity solutions for boundary layer flow and heat transfer of a FENE-P fluid with thermal radiation

This Letter presents a numerical study of the flow and heat transfer of an incompressible FENE-P fluid over a non-isothermal surface. The governing partial differential equations are converted into ordinary differential equations by a similarity transformation. The effects of the thermal radiation are considered in the energy equation, and the variations of dimensionless surface temperature and dimensionless surface temperature gradient, as well as the heat transfer characteristics with various physical parameters are graphed and tabulated. Two cases are studied, namely, (i) the sheet with prescribed surface temperature (PST case) and (ii) the sheet with prescribed heat flux (PHF case). Moreover, the mechanical characteristics of the corresponding flow are also presented.     

New shear-free relativistic models with heat flow

We study shear-free spherically symmetric relativistic models with heat flow. Our analysis is based on Lie’s theory of extended groups applied to the governing field equations. In particular, we generate a five-parameter family of transformations which enables us to map existing solutions to new solutions. All known solutions of Einstein equations with heat flow can therefore produce infinite families of new solutions. In addition, we provide two new classes of solutions utilising the Lie infinitesimal generators. These solutions generate an infinite class of solutions given any one of the two unknown metric functions.     

A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities

We introduce a multidimensional peridynamic formulation for transient heat-transfer. The model does not contain spatial derivatives and uses instead an integral over a region around a material point. By construction, the formulation converges to the classical heat transfer equations in the limit of the horizon (the nonlocal region around a point) going to zero. The new model, however, is suitable for modeling, for example, heat flow in bodies with evolving discontinuities such as growing insulated cracks. We introduce the peridynamic heat flux which exists even at sharp corners or when the isotherms are not smooth surfaces. The peridynamic heat flux coincides with the classical one in simple cases and, in general, it converges to it in the limit of the peridynamic horizon going to zero. We solve test problems and compare results with analytical solutions of the classical model or with other numerical solutions. Convergence to the classical solutions is seen in the limit of the horizon going to zero. We then solve the problem of transient heat flow in a plate in which insulated cracks grow and intersect thus changing the heat flow patterns. We also model heat transfer in a fiber-reinforced composite and observe transient but steep thermal gradients at the interfaces between the highly conductive fibers and the low conductivity matrix. Such thermal gradients can lead to delamination cracks in composites from thermal fatigue. The formulation may be used to, for example, evaluate effective thermal conductivities in bodies with an evolving distribution of insulating or permeable, possibly intersecting, cracks of arbitrary shapes.     

Dual solutions and stability analysis of flow and heat transfer of Casson fluid over a stretching sheet

The aim of the current study is to find out the dual solutions of the two-dimensional magnetohydrodynamic (MHD) flow of Casson fluid and heat transfer over the stretching sheet. The focus of the study is to examine the linear thermal radiation effects on dual solutions for both the steady and unsteady flow of Casson fluid over the stretching sheet under the influence of uniform magnetic field. The governing equations are formed as system of partial differential equations (PDEs). Using suitable transformations, the system of PDEs are converted into favorable nonlinear system of ordinary differential equations (ODEs). Simulations are performed in Maple 2015 to form the dual solutions in order to achieve the velocity, temperature, skin friction and heat transfer profiles of the Casson fluid over the stretching sheet. It is concluded that the dual solutions for the corresponding model are numerically stable. Furthermore, the upper branch solutions of the Casson fluid profiles are numerically stable as compared to the lower branch solutions. Results indicate that positive Eigen values of the MHD flow of Casson fluid provide stable profiles as compared to the negative Eigen values. It is believed that the current study would provide a base for the dual solution of the other types of the non-Newtonian fluid flows over various categories of surfaces.     

Higher dimensional spherically symmetric inhomogeneous cosmological model with heat flow

We study spherically symmetric inhomogeneous cosmological model with heat flow in higher dimensional space-time and present a class of solutions in which the velocity field is shear-free. Some of these solutions are analogous to the known solutions in 4-dimension while some are totally new.     

边界净流条件下的超声速热波

 物质中的辐射热波的行为一直是人们非常关注的问题。但是由于辐射热传导方程具有很强的非线性，其精确的解析解很难求出。利用微扰论推导出了任意边界净流条件下的边界温度的变化行为和热波传播轨迹的理论公式，并与辐射流体力学程序计算的数值结果进行了对比，结果显示理论计算的热波轨迹与数值模拟的结果符合得非常好。     

Rotating viscous-fluid cosmologies with scalar field and heat flux

Rotating cosmological models under the influence of both shear and bulk viscosity, together with scalar field and heat flow, are studied. Exact solutions of the field equations are obtained. The solutions have nonzero expansion, shear, and rotation. The properties of the solutions are studied and the temperature distribution is also given explicitly.     

Enhancement of gas phase heat transfer by acoustic field application

This study discusses a possibility for enhancement of heat transfer between solids and ambient gas by application of powerful acoustic fields. Experiments are carried out by using preheated Pt wires (length 0.1-0.15 m, diameter 50 and 100 micro m) positioned at the velocity antinode of a standing wave (frequency range 216-1031 Hz) or in the path of a travelling wave (frequency range 6.9-17.2 kHz). A number of experiments were conducted under conditions of gas flowing across the wire surface. Effects of sound frequency, sound strength, gas flow velocity and wire preheating temperature on the Nusselt number are examined with and without sound application. The gas phase heat transfer rate is enhanced with acoustic field strength. Higher temperatures result in a vigorous radiation from the wire surface and attenuate the effect of sound. The larger the gas flow velocity, the smaller is the effect of sound wave on heat transfer enhancement.     

Stagnation point transient heat flux measurement analysis from coaxial thermocouples

The transient heat flux measurement at stagnation point is a significant solicitation at highly compressed flow field environment. In aerodynamics surface heating point of view, the estimation of stagnation heat fluxes at the tip of a blunt body is very imperative. When the blunt body is exposed to high-speed flow field environments, at the stagnation point heat transfer would be maximum. The coaxial surface junction thermocouples (CSJTs) are convenient for short duration time scale due to the fast response in the range of millisecond or less (?0.1 ms). These robust CSJTs have the tractability of intensifying them directly on any type of surface and can be used for routine measurement in ground-based impulse amenities as a temperature measuring devices where rapid heat loads are anticipated. In this work, three different types of coaxial thermocouples K-type, E-type, and J-type have been designed and contrived. The microstructural analysis of measuring surface property has been carried out to see the surface morphology using field emission scanning electron microscopy (FESME) and chemical characterization of these CSJTs materials using energy dispersive X-ray analysis (EDXA) technique is used to verify qualitatively appraise the CSJTs materials composition. The thermal coefficient of resistance (TCR) and sensitivity (S) of each coaxial thermocouple have been determined by using oil-bath calibration technique with the linear variation of resistance corresponding to the variation of temperature and found that these coaxial thermocouples are highly sensitive and suitable for highly transient heat transfer measurements. For this purpose, these three types of CSJTs have been tested under highly compressed heated air 310 K temperature for 100 ms at pressure 6.1 bar with Mach number unity (M = 1) using compressor test rig. Numerical simulation has also been carried out with these three RTDs to satisfy the experimental parameters using Ansys Fluent 15.0 and typical transient temperature recorded. Surface heat fluxes recovered from experimental and numerical transient temperatures histories using semi-infinite heat conduction modeling having good agreement with accuracy ±3% or less. This study divulges the expertise of these handmade coaxial thermocouples for transient surface heat flux measurement for short durations at highly compressed air facilities.     

Flow boiling heat transfer enhancement under ultrasound field in minichannel heat sinks

The enhancement of the heat transfer assisted by ultrasound is considered to be an interesting and highly efficient cooling technology, but the investigation and application of ultrasound in minichannel heat sinks to strengthen the flow boiling heat transfer are very limited. Herein, a novel installation of ultrasound transducers in the flow direction of a minichannel heat sink is designed to experimentally study the characteristics of heat transfer in flow boiling and the influence of operation parameters (e.g., heat flux, mass flux rate) and ultrasound parameters (e.g., frequency, power) on the flow boiling heat transfer in a minichannel heat sink with and without ultrasound field. Bubble motion and flow pattern in the minichannel are analyzed by high-speed flow visualization, revealing that the ultrasound field induces more bubbles at the same observation position and a forward shift of the onset of nucleation boiling along the flow direction, as ultrasonic cavitation produces a large number of bubbles. Moreover, bubbles hitting the channel wall on the left and right sides are found, and the motion speed of the bubbles is increased by 31.9% under the ultrasound field. Our results demonstrate that the heat transfer coefficient obtained under the ultrasound field is 53.9% higher than in the absence of the ultrasound field under the same conditions, and the enhancement ratio is decreased in the high heat flux region due to the change of the flow regime with increasing heat flux. This study provides a theoretical basis for the application of an ultrasound field in minichannel heat sinks for the enhancement of flow boiling heat transfer.     

Flow and heat transfer of a hybrid nanofluid past a permeable moving surface

A steady flow and heat transfer of a hybrid nanofluid past a permeable moving surface is investigated. In this study, 0.1 solid volume fraction of alumina (Al₂O₃) is fixed, then consequently, various solid volume fractions of copper (Cu) are added into the mixture with water as the base fluid to form Cu-Al₂O₃/water hybrid nanofluid. The similarity equations are obtained by converting the governing equations of the hybrid nanofluid using the technique of similarity transformation. The bvp4c function available in Matlab software is used to solve the similarity equations numerically. The numerical results are obtained for selected parameters and discussed in detail. It is found that hybrid nanofluid enhances the heat transfer rate compared to the regular nanofluid. The results show that two solutions exist up to a certain value of the moving parameter and suction strengths. The critical value in which the solution is in existence decreases as nanoparticle volume fractions increase. The temporal stability analysis is conducted in determining the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.