Narrow Results

This work focuses on the heat transfer analysis of the magnetohydrodynamic peristaltic flow of blood through the gap between two coaxial flexible tubes of different wavelengths. In this model, the non-Newtonian biviscosity fluid is assumed to be blood, which is flowing through the annulus region between the inclined tubes. The governing equations for the considered problem are simplified under the assumptions of a zero Reynolds number and long wavelength approximations. An analytical expression for the temperature is obtained in its closed form, while a semi-analytical solution for the axial velocity of the moving fluid is determined using the homotopy perturbation method. Expressions for various flow variables such as shear stress, volumetric flow rate, pressure rise, and frictional force at the surface of inner and outer tubes are also obtained. In this work, we discussed the impact of various flow parameters like the Hartmann number, Grashof number, heat source, upper limit apparent viscosity coefficient, amplitude ratios of inner and outer tubes, radius ratio, and wavelength ratio on the above flow variables. The streamline contour plots are also drawn for the realization of the flow pattern of the blood inside the endoscope. The comparison of shear stresses for the peristaltic and rigid endoscopes and the validation of the present result with the previously established results are also discussed. A noteworthy observation drawn from the present model is that the pressure gradient enhances for increasing values of wavelength ratio when the wavelength of the inner tube is less than the wavelength of the outer tube, whereas the pressure gradient gets suppressed for increasing values of wavelength ratio when the wavelength of the inner tube is greater than the wavelength of the outer tube. From the present analysis, it is also found that the shear stress ${\tau }_{rz}$ of blood is the least for a peristaltic endoscope as compared to the rigid one. Therefore, this study may be applicable to medical practitioners for laparoscopic purposes, as a peristaltic endoscope may be a more appropriate device due to its flexibility than a rigid endoscope.

This study incorporates the impact of shape factor and slip conditions on a radiative hybrid magnetic nanofluid over slanted sheet being convectively heated within a porous medium, providing valuable insights for enhancing thermal management systems in manufacturing techniques such as the extrusion of plastic films, cooling of metallic plates, and the drawing of polymer fibers. The effect of viscous dissipation, thermal radiation, aligned magnetic field, velocity slip, heat generation, buoyancy force, porosity, and thermal slip on the dynamics of fluid movement are comprehensively discussed. The governing equations were simplified into nonlinear ordinary differential equations through similarity variables and Bvp4c solver in MATLAB was utilized to observe the effects of pertinent parameters on temperature and velocity profiles, alongside the local Nusselt number and skin friction coefficient. It was determined that the hybrid nanofluid’s effective thermal conductivity was most significantly enhanced by blade-shaped nanoparticles. The local Nusselt number enhanced with upsurge of thermal radiation parameter and Biot number whereas opposite trend was observed with incrementation in other parameters. The augmentation in thermal slip and velocity slip resulted in lowering local skin friction coefficient. This research highlights the complex interplay between various physical factors and their influence on the dynamics of hybrid nanofluids, offering potential strategies for optimizing performance of thermal systems comprising hybrid nanofluids.

Research Problem: The importance of improving the temperature properties of commonly used fluids in industrial processes is being addressed in this research. Nanofluids, which are composed of extremely small particles dispersed in common liquids such as water or petrol, are the main subject of this area of study. Using a vertically stretchable surface subjected to thermal radiation, the study examines the heat transfer behavior and efficiency of nanofluids.

Methodology: Nanofluids that convey heat are studied by applying the fundamental rules of fluid physics to the variables that control their motion. To measure the amount of energy transferred, a nanofluid model is used. Similarity transformations are used to convert the system’s differential equations into ordinary differential equations (ODEs). The subsequent set of nonlinear ODEs is solved using numerical methods. Utilizing graphical analysis, patterns of velocity and temperature may be seen, and their responses to changes in other parameters can be investigated.

Implications: This research has important implications for our knowledge of how nanofluids act in heat transfer applications, especially when exposed to thermal radiation and working with vertically stretchy surfaces. The effects of flow direction and thermal conductivity on distributions of velocity and temperature were elucidated, among other important results. More effective heating and cooling systems may be possible as a result of these findings, which have consequences for improving heat transfer processes in industrial environments.

Future Work: To better understand how nanofluids behave in heat transfer applications, future studies might investigate more complicated situations and boundary circumstances. It may be possible to optimize nanofluid formulations by studying the impact of various nanoparticle kinds and concentrations on heat transfer efficiency. Research could be more applicable to real-world industrial processes if the numerical results were experimentally validated.

This study investigates the impact of variable permeability as well as chemical reactions on the oscillatory free convective flow that passes parallel porous flat plates with fluctuating temperature and concentration in the presence of a magnetic field. A vertical channel is assumed to be rotating at an angular velocity $\mathrm{\Omega }$. Periodic free stream velocity causes oscillations in one plate, while periodic suction velocity causes oscillations in the other plate. Complex variable notations are used to solve the governing equations. The perturbation technique is used to derive analytical expressions for the temperature, concentration, and velocity fields. In this study, various parameters were investigated in relation to mean velocity, mean temperature, mean concentration, amplitude, and phase difference. The study also examines the impact on secondary velocity, primary velocity, temperature, concentration, and heat transfer rate during transients. The outcomes are presented graphically for the physical parameters of the problem. The findings contribute to optimizing systems and improving efficiency in heat transfer, fluid dynamics, and environmental remediation.

In this research, a novel design stochastic numerical technique is presented to investigate the unsteady form magnetohydrodynamic (MHD) slip flow along the boundary layer to analyze the transportation and heat transfer in a solar collector through nano liquids which is a revolution in the field of neurocomputing. Thermal conductivity in variable form is dependent on temperature and wall slips are assumed over the boundary. For mathematical modeling, the solar collector is assumed in the form of a nonlinear stretching sheet and a quite new artificial neural networks (ANNs) based approach is used to solve the current problem in which inverse multiquadric radial basis (IMRB) kernel is sandwiched between a global search solver named genetic algorithms (GAs) and a highly effective local solver named sequential quadratic programming (SQP) i.e. IMRB-GASQP solver. The governing boundary value problem is altered in the form of a system of nonlinear ordinary differential equations (ODEs) through the utilization of similarity transformation and then the obtained system of ODEs is solved using IMRB-GASQP solver by altering the values of distinguished parameters involved in it to observe the fluctuation in the velocity and temperature profiles of nanofluid. The obtained results are effectively compared with the reference solutions using the Adams numerical technique in graphical and tabulated form. An exhaustive error analysis using performance operators is presented while the efficacy of the designed solver using various statistical operators is also part of this research.

Thermal conductivity of nanoparticles is a vibrant parameter in the heat transfer applications applied in thermal, mechanical and chemical engineering. The use of nanoparticles in the conventional fluids augments the thermal conductance which directly affects the heat transfer mechanism. It greatly depends on the nature of nanoparticles. Hence, the excellent conductivity of hybrid Fe₃O₄/MnZnFe₂O₄ allows to select for catalytic agent with EG as primary solvent for heat transfer applications. Besides nanoparticles, the physical phenomena like heating species, Cattaneo Christov thermal flux and variable temperature of the surface potentially alter the performance of single phase nanofluids. Therefore, the current effort aims to formulate a single phase problem through slanted elongating surface having acute angle with the ground level and influenced parametric ranges. The final problem was examined numerically (shooting scheme coupled with RK scheme) and then analyzed and predicted the ranges for better performance. The parallel results reveal that the nanofluid movement is slower than common fluid over the domain because of dominant denser effects. The heat generative parameter ($Q=1.0,2.0,3.0,4.0)$ and radiation number ($\mathrm{\text{Rd}}=1.0,3.0,5.0,7.0)$ are observed to be excellent catalytic parameters to boost the model efficiency. However, thermally radiative nanofluids are more efficient which augment the performance remarkably. The shear drag improved from $1.76343$ to $1.81136$ (for ${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4∕\mathrm{\text{EG}})$, $1.75772$ to $1.79190$ (for ${\mathrm{\text{MnZnFe}}}_2{\mathrm{\text{O}}}_4∕\mathrm{\text{EG}})$ against $\varphi =0.02$ to $\varphi =0.08$. Further, the heating source Q enhances the heat transport rate at the slanted surface from $10.9348$ to $11.3078$ (for ${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4∕\mathrm{\text{EG}})$, and $10.8495$ to $11.2196$ (for ${\mathrm{\text{MnZnFe}}}_2{\mathrm{\text{O}}}_4∕\mathrm{\text{EG}})$. However, it is prevailing for ${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4∕\mathrm{\text{EG}}$ for specified values of Q.

Motivation: Vortex flow, which refers to the movement of fluid around an axis called a vortex line, finds applications in designing aircraft wings, mixing processes in chemical, and pharmaceutical processes, and understanding flows around tornadoes and cyclones. Background: Previous research on variable properties has demonstrated they are crucial in scenarios with significant temperature gradients. Methodology: This paper looks at the boundary layer developments under a generalized vortex flow considering temperature-dependent fluid properties. The generalized vortex represents the far-field tangential velocity in a power-law format and can be simplified to two specific cases: (i) rigid-body rotation and (ii) potential vortex. For mathematical analysis, two distinct variable viscosity models are employed, where a correlation between viscosity and temperature is inversely linear, while the other one is on the exponential temperature dependency model. Numerical Method: A highly robust and convenient built-in tool of MATLAB known as bvp5c is implemented to present exact similarity analyses of the models. Main Findings: The study concludes that velocity profiles obtained under variable physical properties are lower than those calculated with constant properties. Moreover, when liquid properties are considered, the solution curves from the two variable viscosity models show a close resemblance. Thicker thermal diffusion layers and reduced boundary heat flux are associated with increased values of the power law parameter.

This study highlights the thermal radiation’s impacts on heat transmission in the presence of reduced effects of gravity using the numerical method. For smooth algorithm and integration, the similarity form of stream functions is employed to transform the system of nonlinear partial differential equations into the system of ordinary differential equations. The shooting approach (BVP4C) is employed to acquire the numerical solution of the current model. The numerical findings are acquired using the MATLAB program and are then displayed in tabular and graph forms. The energy equation in the mathematical model includes the thermal radiation impacts along with the expressions for reduced gravity effects. The physical characteristics of the flow profile and thermal distribution for varying values of reduced gravity parameters ($R_g)$, radiation parameter $(F)$, positive number ($m)$ and Prandtl numbers $(\mathrm{\text{Pr}})$ are shown graphically along with the results for skin friction and thermal transmission influenced by various emerging parameters are displayed in tables. The aspect of reduced gravity provides new insight into thermal management in diverse applications such as aerospace, microgravity, environments and high-altitude operations. Further, the incorporation of both heat source and sink into the prescribed mathematical model gives a more comprehensive understanding of heat transfer dynamics. Moreover, this study focuses on a moving surface introducing a dynamic component to the analysis. By combining principles from fluid dynamics, thermodynamics and applied physics, this paper promotes an interdisciplinary approach, which could pave the way for further research in related fields.

The objective of this study is to determine the irreversible losses and associated entropy generation within a fluid system, considering the combined effects of magnetic field, convective boundaries, and porous media. It accomplishes this objective by a thorough investigation into the second law analysis and entropy generation of a magnetohydrodynamic (MHD) Eyring–Powell fluid flowing through a symmetric porous medium. To achieve this, the governing equations for the Eyring–Powell fluid are formulated using the conservation laws of mass, momentum, and energy, while incorporating the magnetic field’s effects. In order to account for the porous character of the medium, the equations are coupled with the Darcy model. Using appropriate computational techniques, the resulting system of partial differential equations is numerically solved. The local irreversibility ratio calculates the system’s entropy generation number, revealing its distribution. The Hartmann number and Eyring–Powell fluid parameters are also studied. The primary findings indicate that $A^{\ast }$ enhances velocity and diminishes temperature and entropy, while $B^{\ast }$ has the opposite effect. Entropy is also increased by Hartmann and Brinkman numbers, which are a result of the enhanced heat transfer and stronger magnetic fields. The findings emphasize the need and importance of studying irreversible losses and improving fluid system energy efficiency.

In this paper, we propose a class of high-order time integration schemes combined with high-order IsoGeometric Analysis (IGA) in three space dimensions. The combined methods offer robust solutions of nonlinear heat diffusion in three-dimensional composites that pose numerical challenges. This tailored strategy significantly enhances computational efficiency, especially crucial when addressing nonlinear heat transfer in three-dimensional enclosures. Leveraging precise geometry representation and seamless high-order element continuity of the IGA, this method effectively exploits these advantages. It emphasizes the vital synergy between high-order spatial discretization and an equivalent high-order time integration scheme. This study also highlights the risks of overlooking this pairing, which can lead to a degradation of the overall high-order accuracy and increased computational demands due to the complexity of high-order nonuniform rational B-splines. Numerical examples, such as applications involving a furnace wall segment and a rail wheel heat transfer, are used to validate the efficiency and accuracy of the combined approach. Consistently surpassing the conventional methods in both aspects, the proposed method notably excels in providing precise solutions for steep heat gradients even on coarse meshes. Consequently, this approach constitutes a substantial advancement in the field of transient heat transfer analysis within composite domains.

In this research, the influences of quadratic Boussinesq approximation and quadratic thermal radiation on the heat transfer analysis of magnetized Sisko nanofluid flow with Cattaneo–Christov heat flux through stretching surfaces are studied. The formulated mathematical model is solved by the finite difference technique, and heat transfer rate and skin friction coefficients are computed for acting parameters, i.e., magnetic field, Eckert number, Forchheimer parameter, thermal relaxation parameter, radiation parameter, porosity parameter and Biot number. For sensitivity analysis, the response surface method (RSM) with a face-centered central composite design is utilized. The RSM is elucidated by applying nonlinear regression, analysis of variance and goodness of fit. The results indicate that the friction coefficient and Nusselt number have positive sensitivities for the Forchheimer parameter. The heat transfer rate decreases with an increase in magnetic field, Biot number and thermal relaxation parameter values for shear thickening $(n>1)$ and shear thinning $(n<1)$. Further for $n<1$, a one unit increase in $A_1$ leads to a 33% drop in SFC and 48% in LNN; and an increase of 8 units in $F_r$ leads to a 67.18% rise in LNN.

Bioheat transfer analysis in tissue has attracted the attention of numerous researchers due to its widespread potential applications in the medical field, mainly in thermotherapy and the human thermoregulation system. Also, temperature regulation of the human body primarily occurs through bioheat transfer. Due to the widespread biomedical applications of bio-heat transfer, we aim to investigate the movement of biofluid and bioheat in human organs with the influences of thermal radiation and ciliary waves. The mathematical model for Ellis fluid flow through a tube includes the metachronal wave of cilia motion and convective conditions. The governing equations are created based on mass, momentum conservation, and energy. The current problem is displayed and exact solutions are managed under long wavelength $(\delta \ll 1)$ and low Reynolds number $(R_e\ll 1)$ approximations. An analytical approach is employed to derive expressions for longitudinal velocity, temperature, pressure gradient, and stream function as a function of the parameters of the problem. The physical behavior of the peristaltic motion of the Ellis fluid is explained in detail and illustrated graphically for various parameter values. The results of the current study provide potential information for advancement in the biomedical industry, particularly in the development of biomedical devices and processes.

In the present paper, a comparative study of numerical solutions for steady flows with heat transfer based on the finite volume method (FVM) and the relatively new lattice Boltzmann method (LBM) is presented. In the last years, the LB methods have challenged the classical FV methods to solve the Navier–Stokes equations and have proven to be superior in accuracy and efficiency for certain applications. Most of these studies were related to the transport of mass and momentum. In the meantime, significant effort has been invested in the application of the LBM to simulate flows including heat transfer. The studies in the present paper are the analysis of performance and accuracy aspects of LBM applied to the prediction of these flows. For a fully developed laminar flow between parallel plates, analytical solutions for the heat transfer in fully developed thermal boundary layers are available and may be compared with the respective numerical results. Finally, a hybrid approach is proposed to circumvent numerical problems of the thermal LB methods.

The natural convection problem in a square cavity filled with heterogeneously porous medium is solved by lattice Boltzmann method. The temperature distribution is fully coupled with the fluid velocity through relaxation time. The present calculated results are in good agreement with available published data. It is found that the porosity of porous media near the walls has significant influence on the heat transfer, and the porosity of middle porous medium has little influence on the natural convection. It is of particular interest for thermal management in electronic packages, since it can reduce the space of air.

The problem of a steady boundary layer MHD slip flow over a stretching sheet in a water-based nanofluid containing different type of nanoparticles: Cu, Al₂O₃ and Ag has been investigated. An external strong magnetic field is applied perpendicular to the plate and the Hall effect is taken into consideration. The surface of the stretching sheet is assumed to move with a linear velocity and subject to power-law variation of the surface temperature. The governing partial differential equations are transformed into nonlinear ordinary differential equations using a similarity transformation, before being solved numerically by a Runge–Kutta–Fehlberg method with shooting technique. Effects of the physical parameters on the primary velocity, the secondary velocity and the temperature as well as on the wall shear stress and the rate of heat transfer have been presented graphically and discussed in detail. Investigated results indicate that the nanoparticle volume fraction and the slip parameter produce opposite effects on the skin friction coefficients of the primary and secondary flow. Also, the nanoparticle volume fraction and the types of nanoparticles demonstrate a more pronounced influence on the secondary flow than that on the primary flow and temperature distribution.

In this paper, a bilinear interpolation finite-difference scheme is proposed to handle the Neumann boundary condition with nonequilibrium extrapolation method in the thermal lattice Boltzmann model. The temperature value at the boundary point is obtained by the finite-difference approximation, and then used to determine the wall temperature via an extrapolation. Our method can deal with the boundaries with complex geometries, motions and gradient boundary conditions. Several simulations are performed to examine the capacity of this proposed boundary method. The numerical results agree well with the analytical solutions. When compared with a representative boundary method, an improved performance is observed. The results also show that the proposed scheme together with nonequilibrium extrapolation method has second-order accuracy.

The aim of this work is to conduct numerical study of fluid flow and natural convection heat transfer by utilizing the nanofluid in a two-dimensional horizontal channel consisting of a sinusoidal obstacle by lattice Boltzmann method (LBM). The fluid in the channel is a water-based nanofluid containing Cuo nanoparticles. Thermal conductivity and nanofluid’s viscosity are calculated by Patel and Brinkman models, respectively. A wide range of parameters such as the Reynolds number ($\mathrm{\text{Re}}=100$–400) and the solid volume fraction ranging ($\mathrm{\Phi }=0$–0.05) at different non-dimensional amplitude of the wavy wall of the sinusoidal obstacle ($A=0$–20) on the streamlines and temperature contours are investigated in the present study. In addition, the local and average Nusselt numbers are illustrated on lower wall of the channel. The sensitivity to the resolution and representation of the sinusoidal obstacle’s shape on flow field and heat transfer by LBM simulations are the main interest and innovation of this study. The results showed that increasing the solid volume fraction $\mathrm{\Phi }$ and Reynolds number Re leads to increase the average Nusselt numbers. The maximum average Nusselt number occurs when the Reynolds number and solid volume fraction are maximum and amplitude of the wavy wall is minimum. Also, by decreasing the $A$, the vortex shedding forms up at higher Reynolds number in the wake region downstream of the obstacle.

In this study, lattice Boltzmann method (LBM) simulation is performed to investigate laminar forced convection of nanofluids in a horizontal parallel-plate channel with three rectangular cavities. Two cavities are considered as located on the top wall of the channel and one on the bottom wall. The effects of the Reynolds number (100–400), the cavity aspect ratio (AR = 0.25, 0.5), the various distances of the cavities from each other ($X_c^{\prime }$) at different solid volume fractions of nanofluids ($\varphi =0-0.05$) on the velocity and the temperature profiles of the nanofluids are studied. In addition, the flow patterns, i.e. the deflection and re-circulation zone inside the cavities, and the local and averaged Nusselt numbers on the channel walls are calculated. The results obtained are used to ascertain the validity of the written numerical code, which points to the excellent agreement across the results. The results show that, as the solid volume fraction of nanofluids is enhanced, the transfer of heat to working fluids increases significantly. Further, the results show that the maximum value of the averaged Nusselt number in the channel is obtained at $X_c^{\prime }=0.1204$ for AR = 0.5 and $X_c^{\prime }=0.1024$ for AR = 0.25. The interval [0.1224, 0.1304] is the best position for the second cavity. It is concluded that the results of this paper are very useful for designing optimized heat exchangers.

This paper performs a numerical analysis of the natural convection within two-dimensional enclosures (square enclosure and enclosures with curved walls) full of a H₂O-Cu nanofluid. While their vertical walls are isothermal with a cold temperature $T_c$, the horizontal top wall is adiabatic and the bottom wall is kept at a sinusoidal hot temperature. The working fluid is assumed to be Newtonian and incompressible. Three values of the Rayleigh number were considered, viz., 10³, 10⁴, 10⁵, the Prandtl number is fixed at 6.2, and the volume fraction $\varphi$ is taken equal to 0% (pure water), 10% and 20%. The numerical simulation is achieved using a 2D-in-house CFD code based on the governing equations formulated in bipolar coordinates and translated algebraically via the finite volume method. Numerical results are presented in terms of streamlines, isotherms and local and average Nusselt numbers. These show that the heat transfer rate increases with both the volume fraction and the Rayleigh number, and that the average number of Nusselt characterizing the heat transfer raises with the nanoparticles volume fraction.

Magnetohydrodynamic flow of nanofluids and heat transfer between two horizontal plates in a rotating system have been examined numerically. In order to do this, the group method of data handling (GMDH)-type neural networks is used to calculate Nusselt number formulation. Results indicate that GMDH-type NN in comparison with fourth-order Runge–Kutta integration scheme provides an effective means of efficiently recognizing the patterns in data and accurately predicting a performance. Single-phase model is used in this study. Similar solution is used in order to obtain ordinary differential equation. The effects of nanoparticle volume fraction, magnetic parameter, wall injection/suction parameter and Reynolds number on Nusselt number are studied by sensitivity analyses. The results show that Nusselt number is an increasing function of Reynolds number and volume fraction of nanoparticles but it is a decreasing function of magnetic parameter. Also, it can be found that wall injection/suction parameter has no significant effect on rate of heat transfer.