Narrow Results

The process of convective thermal management in the radiative flow of Oldroyd-B fluid over the stretching cylinder is investigated in this paper. In engineering and applied sciences, the viewpoint of fluid flow due to vertically stretched cylinder covers both theoretical and practical significances. Nonlinear ordinary differential equations are first transformed from their corresponding partial differential equations, then rebuilt using sufficient transformations to produce a system of nondimensional equations, using a proper similarity technique, which is then calculated. The MATLAB built-in technique BVP4C, a standard numerical process, is used to solve the regulating flow equations. A comprehensive graphical depiction was used for characteristics like unsteadiness and curvature, Prandtl number, and thermal diffusivity. The relevant flow characteristics of the governing problem are depicted in graphs.

To govern the complex rheological dynamics of fluid simulations, numerous mathematical approaches are being developed. The examination of such mathematical frameworks employs theoretical, iterative, empirical, and analytical methodologies. This work analyzes and evaluates the Laplace transforms to estimate the time-dependent mixed convective flow of hybrid nanofluid in a porous material. A hybrid nanofluid is produced through dispersing molybdenum disulfide (${\mathrm{\text{MoS}}}_2$) and silicone dioxide (${\mathrm{\text{SiO}}}_2$) nanoparticles in carboxymethyl cellulose ($\mathrm{\text{CMC }}-\mathrm{\text{water}}$). The objective of this study is to examine the heat transfer properties of a hybrid nanofluid (${\mathrm{\text{MoS}}}_2-{\mathrm{\text{SiO}}}_2)$/$(\mathrm{\text{CMC }}-\mathrm{\text{water}}$) flowing over a vertical sheet while being subjected to a thermal radiation and heat source and sink. The Laplace transform approach has been used in closed form to solve the resulting partial differential equations governing the flow. This study examines how hybrid nanofluids influence time-dependent flow and heat transmission in the presence of porous medium, heat radiation, and rate of heat generation. The computer program MATHEMATICA is used to emphasize the impact of each flow parameter. Graphs are used to analyze the results of radiation, heat source, magnetic, and nanoparticle volume fraction obtained using the Laplace transform technique for engineering variables like fraction and rate of heat, as well as velocity and thermal distribution. The velocity distribution is an increasing function of mixed convective parameter. Larger values of porosity variable and mixed convection variable result in accelerating the velocity of the fluid. Additionally, we conducted research with various ratios of nanoparticles and discovered several intriguing outcomes that can be used to solve various technical issues, particularly in the cooling process.

Here the Cattaneo–Christov double diffusion model explores the mixed convective flow of third-grade nanoliquid on a stretchable surface with Riga device diverging from the traditional Fourier and Fick’s law. The model incorporates entropy optimization and Soret–Dufour effects, offering a unique perspective on heat and mass transfer phenomena. By employing relevant transformations, the complex partial differential equations are converted into more manageable ordinary differential systems. An optimal analysis method is then applied to solve the resulting nonlinear differential system, shedding light on the intricate interplay of various physical variable. Through the utilization of plots, the study delves into the impact of these physical variable, providing insights into the behavior of the system under different conditions. This comprehensive approach not only enhances our understanding of the underlying mechanisms governing the convective flow of nano-liquids, but also highlights the significance of considering nonclassical models in thermal and mass transport studies. The key finding of this study is that fluid velocity enhances for material parameters due to low viscosity. Temperature and nanoparticle concentration enhance for higher values of Dufour and Soret numbers, respectively. For higher estimations of Reynold number, entropy of the system decreases.

Entropy measures the disorderness and randomness in the thermal systems. It has significant influence over efficiency and performances of the thermal systems. The motive of the research paper is to present a comparative analysis of entropy generation of a heat dissipative Darcy–Forchheimer flow of copper (Cu/H₂O)-based mono and (CuAl₂O₃/H₂O)-based hybrid nanofluid under the influence of thermal dispersion. The mathematical model of the conceptualized flow problem is formulated using single phase nanofluid model along with Darcy–Forchheimer equation for non-Darcy porous medium flow. The system of dimensional Partial Differential Equation (PDE) depicting the flow problem is converted in the system of dimensionless Ordinary Differential Equation (ODE) using the suitable similarity variables and has been solved by MATLAB’s bvp4c package. The flow variables, engineering parameters like skin friction and Nusselt number along with entropy generation, have been analyzed for the active parameters inherited in the problem. The findings suggest that heat transfer rate on the surface enhances with the increment in thermal dispersion parameter. Further, it is reported that the hybrid nanofluid generates lesser entropy as compared to the mono-nanofluid. This research has potential to serve the real-life applications based on electronics and geothermal systems.

This study investigates the mixed convection on a vertically oriented exponentially stretching surface, considering the exponential distributions of velocity, concentration and temperature. The governing highly nonlinear partial differential equations (PDEs) are transmuted into highly nonlinear ordinary differential equations (ODEs) by considering appropriate similarity variables. The highly nonlinear differential equations are solved numerically using the Hermite wavelet method (HWM) in MATHEMATICA 12. The obtained results show excellent agreement with previous studies focusing on different special cases of the problem. A parametric analysis of the physical parameters is shown and illustrative numerical results are presented graphically. The analysis incorporates the radiation, chemical reaction and cross-diffusion effects. The interaction between radiation and chemical reaction is particularly relevant in high-temperature systems, such as combustion, industrial furnaces, photochemistry, polymerization and certain chemical reactions. The results indicate that an increase in radiation enhances the temperature profile in the momentum boundary layer. Higher reaction rate values lead to a decrease in the concentration profile, while an increase in the Dufour value results in increased velocity and temperature and decreased concentration.

The hydrodynamics and thermal characteristics due to mixed convection in a vertical two-sided lid-driven differentially square cavity containing four hot cylinders in a diamond array are investigated by the lattice Boltzmann equation model. The moving walls of the cavity are cold while the others are adiabatic. The flow in the cavity is driven by both the temperature difference and the moving vertical walls. The influence of different flow governing parameters, including the direction of the moving walls (the left wall moves up and the right wall moves down (Case I), both the left and right walls are moving upward (Case II), both the left and right walls are moving downwards (Case III)), the distance between neighboring cylinders $\delta$ ($0.3L\le \delta \le 0.5L$), and the Richardson number $\text{Ri}$ ($0.1\le \mathrm{\text{Ri}}\le 10$) on the fluid flow and heat transfer are investigated with the Reynolds number in the range of $375\le \mathrm{\text{Re}}\le 3752$, the Grashof number of $1.4\times 10^6$ and the Prandtl number of $\mathrm{\text{Pr}}=0.71$. Flow and thermal performances in the cavity are analyzed in detail by considering the streamlines and isotherms profiles, the average Nusselt number, as well as the total Nusselt number. It is found that the heat transfer efficiency is highest when $\mathrm{\text{Ri}}=1.0$ for the cases of the walls moving in the opposite direction. When the walls move in the same directions, the heat transfer efficiency obtained by $\mathrm{\text{Ri}}=0.1$ is maximum among the considered values of $\text{Ri}$. On the other hand, compared with the cases of $\mathrm{\text{Ri}}=1.0$ and $\mathrm{\text{Ri}}=10$, the cylinder positions corresponding to the largest and the smallest Nusselt numbers are very sensitive to the moving direction of the walls for $\mathrm{\text{Ri}}=0.1$. Moreover, the results also show that in terms of the value of Nusselt number and the stability the case of both walls moving downwards works well. Besides, the effect of the distance between neighboring cylinders is also discussed, it is found that increasing or decreasing the spacing between cylinders could enhance heat transfer to different degrees for the range of $\text{Ri}$ number considered. Finally, the empirical relationships among ${\mathrm{\text{Nu}}}_{\mathrm{\text{ave}}}$, $\text{Ri}$, and the spacing between the cylinders ($\delta$) are given, and predictive results match with the computed values very well.

The impact of various sizes and positions of the heater in a nanofluid-saturated porous lid-driven chamber with a uniform Lorentz force is studied numerically. In this investigation, three different lengths of heater with higher temperature at six different locations along the left sidewall of the cavity are considered. Lower temperature is maintained at the right sidewall. Further, lower and moving upper horizontal walls and the rest of left wall are supposed to be thermally insulated. Based on the finite volume method, the system of nondimensional governing equations is solved by SIMPLE algorithm. The results conclude that the average Nusselt number is reduced with the enhancement of Richardson and Hartmann numbers. When the heater length is reduced from bottom to top, the heat transfer rate is increased for all the considered Richardson, Darcy and Hartmann numbers. In the lower permeability of the porous medium, the effect of solid volume fraction of nanofluid is more vulnerable. In the case of nanofluid, the steady state is reached quickly than the pure fluid.

Researchers in heat transfer field always attempt to find new solutions to optimize the performance of energy devices through heat transfer enhancement. Among various methods which are implemented to reinforce the thermal performance of energy systems, one is utilizing porous media in heat exchangers. In this study, characteristics of laminar mixed convection in a porous two-sided lid-driven square cavity induced by an internal heat generation at the bottom wall have been carried out by using a numerical methodology based on the finite volume method and the full multigrid acceleration. The two-sided and top walls of the enclosure are assumed to have cold temperature while the remaining walls of the bottom wall are insulated. The working fluid is air so that the Prandtl number equates 0.71. The behavior of different physical parameters is shown graphically so that computations have been conducted over a wide range of pertinent parameters; (10${}^{-2}\le$ Ri $\le 10$), Darcy number ($10^{-4}\le$ Da $\le 10^{-1}$), internal Rayleigh number ($0\le$ Ra${}_I\le 10^4$), the porosity ($0.2\le \epsilon \le 0.8$) and the Grashof number (10${}^3\le$ Gr $\le 10^6$). Results revealed that heat transfer mechanism and the flow characteristics inside the enclosure are strongly dependent on the Grashof number. For instance, the best heat transfer rates at the considered values of internal Rayleigh numbers are obtained for a high Grashof number. Furthermore, an increase of internal heat generation (Ra_I) leads to a higher flow and temperature intensities for Grashof numbers ranging from $10^4$ to $10^6$ and a specific Richardson number value. Besides, an increase in porosity values ($\epsilon$) leads to an obvious decrease in the average Nusselt number. Maximum temperature ${\theta }_{\mathrm{\text{max}}}$ is optimal for high ($\epsilon$) value. A correlation expression for the average Nusselt number relative to the internal heat source was established in function of two control parameters such as Darcy and Richardson numbers.

The aim of this paper is to examine the influence of heat source/sink on boundary layer flow of a fourth-grade liquid over a stretchable Riga plate on taking account of induced magnetic field and mixed convection. Analysis of mass and heat transport is studied through modified Fourier heat flux model. The governing flow issue is demonstrated with the help of momentum, energy, temperature and concentration equation. The modeled equations are reduced into nondimensional ODEs by opting suitable similarity transformations. The analytic solutions are discussed by means of the optimal technique of homotopy analysis. The influence of several nondimensional parameters on velocity, thermal and concentration gradients are deliberated by using suitable graphs. Also, the skin friction is discussed with the help of graphs. The result outcomes reveal that, velocity of fluid diminishes for advanced values of viscoelastic parameter and fourth-grade liquid parameter but contrary movement is seen for third grade fluid parameters. Fluid temperature boosts up for thermal relaxation parameter and concentration is abridged for rising values of solutal concentration parameter and Schmidt number.

The objective of this paper is to study the mixed convective nonsimilar flow above an exponentially stretching sheet saturated by nanofluid. The leading partial differential equations (PDEs) of the problem have been modified towards dimensionless nonlinear PDEs utilizing newly proposed nonsimilarity transformations. Furthermore, local nonsimilarity procedure up to-second truncation has been operated to change the dimensionless PDEs into ordinary differential equations (ODEs). MATLAB-based algorithm bvp4c is used to observe the consequences of the distinct parameters namely Prandlt number $(\mathrm{\text{Pr}})$, magnetic field $(M)$, Lewis number $(\mathrm{\text{Le}})$, Brownian motion $(N_b)$, Eckert number $(\mathrm{\text{Ec}})$, thermophoresis $(N_t)$ on velocity, concentration and temperature distribution are shown in graphical portray. Additional outcomes presume the heat penetration into the fluid enhances with increase in Biot number and Brownian motion. Increasing values of $M$ and $\xi$ cause decrease of temperature profile.

This paper aims to investigate the time-dependent stagnation point flow of an Oldroyd-B fluid subjected to the modified Fourier law. The flow into a vertically stretched cylinder at the stagnation point is discussed. The heat flux model of a non-Fourier is intended for the transfer of thermal energy in fluid flow. The study is carried out on the surface heating source, namely the surface temperature. The developed nonlinear partial differential equation for regulating fluid flow and heat transport is transformed via appropriate similarity variables into a nonlinear ordinary differential equation. The development and analysis of convergent series solutions were considered for velocity and temperature. Prandtl number numerical values are computed and investigated. This study’s findings are compared to the previous findings. By making use of the bvp4c Matlab method, numerical solutions are obtained. Besides, high buoyancy parameter values are found to increase the fluid velocity for the stimulating approach. By improving the thermal relaxation time parameter values, heat transfer in the fluid flow decreases. The temperature field effects are displayed graphically.

Nowadays, the heat transfer potential of the base fluids can also be improved by adding nanoparticles to them. These nanotechnology-based fluids, called nanofluid, have superior properties such as high thermal conductivity, large critical heat flux (CHF) and improved heat transfer coefficient. The purpose of this paper is to study the thermal effectiveness of nanoparticles in transient flow of Maxwell fluid together the properties of mixed convection and magnetic field. Thermal field is controlled with the novel aspects of variable conductivity and nonuniform heat sink/source. Additionally, the impact of Brownian and thermophoretic diffusions is considered caused by nanoparticles dispersion in the fluid. The appropriate conversions yield the governing nonlinear ordinary differential system. Homotopic approach has been utilized to attain the solution of differential system and results are envisioned graphically. This study explores that the buoyancy ratio and mixed convection parameters enhance the velocity field. Further, the heat transfer rate rises significantly as the thermophoretic and Brownian diffusion parameters increase. Moreover, the effect of nonuniform heat source/sink on temperature field is noticed to be an increasing trend of temperature profile.

Hybrid nanofluid is a novel nanotechnology fluid created by distributing two distinct nanoparticles into conventional energy transfer fluid. The thermal properties of aluminum alloys, namely AA7072 and AA7075 with engine oil (base fluid) of hybrid nanofluid flow induced over a vertical stretchable rotating cylinder are investigated in this study. The focus here is the analysis of energy transportation in the presence of Joule heating, thermal energy source/sink, thermal radiation and activation energy. Moreover, all energy constraints are analyzed through graphical outcomes, which are computed numerically through bvp4c built-in MATLAB. The significant observation made is that as the Reynolds number and the magnetic field parameter enhance, the flow field declines. Additionally, the convective transport of the thermal energy increases for a higher magnitude of resistive heating and buoyant motion of the fluid. It is also noted that the activation energy in the system decreases for mass diffusion.

In this work, heat transfer enrichment using nanofluid in a lid-driven porous cavity having an isothermal solid block has been investigated numerically through three distinct cases based on the moving direction of horizontal wall(s). The modeled governing partial differential equations are numerically solved by SIMPLE algorithm and the resulting outcomes are validated with previous works both in qualitative and quantitative nature. Numerical results of various emerging parameters such as Richardson number ($0.01\le \mathrm{\text{Ri}}\le 100$), Darcy number (10${}^{-5}\le \mathrm{\text{Da}}\le 10^{-1}$), Block length ($0.25\le \mathrm{\text{BL}}\le 0.75$) and volume fraction of suspended nanoparticles ($0.0\le \varphi \le 0.05$) were discussed. The results clearly show that the direction of moving walls plays a crucial role on the flow and heat transfer, in particular, the opposite direction of moving walls yields the highest heat transfer rate. In addition to that, significant influence of isothermal block is found and determined that the block length of 0.75 causes the maximum rate of heat transfer in the entire system.

This research paper shows the insight into the study of magnetohydrodynamics (MHD) reactive nanomaterial flow of Newtonian fluid with Silver (Ag), Ferric Oxide (Fe₃O₄) and Copper (Cu) towards a stretchable surface. The flow is generated subject to stretchable surface with porosity effect. Mixed convection, which is a combination of both free and forced convections, is accounted. The heat source/sink, chemical reaction, Joule heating and activation energy effects are considered in the development of energy and concentration equations. The system of considered problem is solved numerically via shooting method (boundary value problem fourth convergence (bvp4c)) and outcomes are sketched graphically. The engineering impact i.e., skin friction coefficient and Nusselt number is discussed via different parameters and results are displayed in tabular form. The important and main points are listed in the final remarks of the paper. The used nanoparticles have numerous applications in medical industry, applications in sustainability of natural resources and applied mathematics and physics. Also, these nanoparticles can be utilized in engineering sciences, biophysics, high-temperature and cooling process, space technology, biosensors, medicines, cosmetics, paints, medical devices and conductive coatings.

Cancer is a disease that is extremely lethal and dangerous to its patients. This study suggests that blood particles containing gold can control and decimate it because these particles have a large atomic size, which raises the temperature and helps to control cancer cells (malignant tumors). The current exploration is eager to deal with a 2D mixed convection flow through blood heat diffusion, which conveys the blood fluid (Williamson fluid) through the use of gold substances from a moving curved surface. The flow problem is represented by curvilinear coordinates. Magnetic interaction with radiation is also induced. The method of similarity parameters is used to convert the Williamson model’s partial differential equation into nonlinear ordinary differential equations and utilized the bvp4c solver to find dual solutions. Sketches are used to convey numerical results for velocity distribution, the friction factor, and heat transfer with temperature profile. The results indicate that the blood flow interrupts, while the temperature accelerates due to the magnetic field. In addition, the volume fraction enhances the temperature and decelerates the blood velocity.

Recently, in various biological processes such as endoscopic medication, blood pumping from the heart to different parts of the body, food supply, and in maintaining heat transfer phenomenon, slip plays a significant part in all aspects. Therefore, a study is aimed to enlighten the significance of multiple slips with Joule heating in a mixed convective Casson fluid. The flow regime is induced by the thermal radiation, chemical reaction and nonuniform heat source/sink in order to accomplish the heat and mass transportation. The modeled equations generated from the physical problem are transmuted into ordinary differential frameworks. The transformed system of equations was solved by means of numerical technique named Runge–Kutta Fehlberg method. The numerical results for involved engineering parameters like Joule heating, Eckert number, thermal, mass and velocity slip parameters for temperature, velocity and fluid concentration are analyzed by graphs using MATLAB. The numerical values for the drag force and Nusselt number are keenly observed and concluded that slip controls the flow closer to the boundary layer. Furthermore, magnetic factor decreases the velocity field and Eckert number enhances the temperature filed.

This paper deals with a study on flow of fluid which exhibits the characteristics of both ideal fluids and elastic solid and shows partial elastic recovery. For these types of fluids, Jeffrey six-constant model will be used that illustrates the most striking feature connected with the deformation of a viscoelastic substance and simultaneously displays the fluid-like and solid-like characteristics. The flow of the proposed fluid model will be generated in an inclined tube by sinusoidal wave trains propagation with constant speed along the walls of the tube. The governing equations of the fluid along with energy equation are modeled and simplified by using low Reynolds number and long wavelength assumptions. These equations will be solved by utilizing the homotopy perturbation technique and results of flow will be displayed in graphical form under the effects of Jeffrey model’s parameters.

The primary purpose of this study is to investigate the buoyancy mixed convection flow of non-Newtonian fluid over a flat plate. The addition of a small amount of polymers into a Newtonian solvent raises the viscosity and generates elastic properties in the resulting solution. To study the behavior of these viscoelastic fluids, finite extensible nonlinear elastic constitutive equations along with Peterlin’s closure (FENE-P model) are used. Along with mass, momentum and energy equations, viscoelastic constitutive equations are also used to examine the rheology of the resulting polymer solution. Similarity transformations are introduced to convert the governing equations into nondimensional forms. The nondimensional equations are solved using the fourth-order boundary value solver in MATLAB. The distribution of the velocity and temperature fields is displayed graphically under the impact of various involved parameters like Eckert number (Ec), Richardson number (Ri), Prandtl number (Pr). The addition of polymers increases the friction among the different fluid layers, leading to viscous dissipation in the fluid. The presented model’s validation is done with the Newtonian fluid to verify the results. The Nusselt number is also computed and analyzed to study the heat transfer rate. The effects of viscoelastic parameters like Weissenberg number (W${}_i$), polymer viscosity ratio (${\beta }_p$) and polymer extensibility parameter ($L^2$) on heat transfer rate are also shown graphically. Buoyancy parameter (Richardson number, $0\le \mathrm{\text{Ri}}\le 2$) represents the dominance of natural convection relative to that of forced convection. The temperature of the resulting fluid falls with the increase in the value of Ri. The Nusselt number tends to decrease with increasing Richardson number when viscous dissipation effects are active.

The consideration of thermo-capillary or Marangoni convection developed through surface tension continuously remains a focus of immense importance for engineers and scientists. This is due to their ample utilizations that is, thin films spreading, welding, nuclear reactors, materials science, semiconductor processing, crystal growth melts, etc. Having such usefulness of Marangoni convection in view, our objective here is to formulate the non-Newtonian rheological Williamson liquid capturing mixed convection and transpiration aspects. Modeling is done considering radiative magnetohydrodynamic flow. Interface temperature of both dust particles and fluid is selected as a nonlinear (quadratic) function of interface arc-length. Resulting systems are rendered to ordinary problems via opposite variables. Computational analysis is performed considering finite difference scheme. Features of embedded factors against nondimensional quantities are elaborated graphically.