Heat Source Parameter Research Articles

Temperature response and chemical reactions of energetic materials under thermal radiation and heat conduction

Thermal radiation from a high-temperature source is the primary cause of energetic material explosions. However, current research cannot meet the need to prevent thermal radiation-caused explosions. This paper proposes a novel numerical calculation model for temperature response and the chemical reaction of energetic materials under thermal radiation based on the physical mechanisms and evolution of the thermal effect during the chain explosion accident. This model is essential for rapidly evaluating the effect of thermal radiation in chain explosion accidents. The numerical model in this study efficiently obtained the thermal response of energetic materials under thermal radiation, as well as the critical conditions for energetic material explosion under thermal radiation. The results reveal that heat conduction is difficult to cause the explosion of ammonium nitrate, but thermal radiation can. The critical temperature of explosion for ammonium nitrate is 1668 K, the critical duration is 15.93 s, and the critical distance is 7.85 m. The temperature, duration, and radiation distance of the heat source are crucial factors that induce the ammonium nitrate explosion. Firefighters must cover and protect ammonium nitrate within 7200 s and 15.93 s, respectively, when the external heat flow absorbed by the material is 2.688 kW/m2 and 28 kW/m2. The model proposed in this paper can predict the effect of thermal radiation once the heat source parameters are known. Besides, combined with machine learning, the model can also predict the heat source parameters once the parameters of the thermal radiation effect are known. Compared with the current numerical models to evaluate the effect of thermal radiation, the numerical model presented in this paper can evaluate the effect of thermal radiation in engineering more efficiently and has broad application prospects.

Optimal design on fin-metal foam hybrid structure for melting and solidification phase change storage: An experimental and numerical study

A fin-metal foam composite structure is employed in the phase change energy storage coupled Organic Rankine Cycle system to enhance thermal performance. The 3-D numerical model is validated through an experimental system to analyze the impact of metal foam parameters and fluctuating heat source parameters (amplitude and half-period) on the system's storage-release process during heat source fluctuation. According to the Taguchi method, metal foam porosity significantly influences the total storage-release time. An increase in porosity leads to a continuous increase in the total storage-release time, while an increase in PPI and a decrease in heat source amplitude initially increase and then decrease the total storage-release time. Under constant metal foam PPI (10) and porosity (0.97), Case T (half period = 60 and amplitude = 1.0) demonstrates a 2.04 % increase in average heat transfer rate and a 1.78 % reduction in total storage-release time compared to Case 0 (constant heat source). The average heat release rate sees a 4.23 % increase, while total heat storage and heat release rise by 0.96 % and 1.87 %. The research has specific technical significance for the photothermal application of phase change energy storage technology to the variability and unpredictability of solar energy.

Application of design of experiments for single-attribute optimization using response surface methodology for flow over non-linear curved stretching sheet

Optimizing the heat transmission rate of the flow through the statistically designed chain of experiments has major applications in product designing and improvising. Here, statistic design is framed by implementing response surface optimization methodology to contemplate the flow of dual non-Newtonian fluids allowed to flow over non-linear stretched geometry. The fluid flow model is designed under Cattaneo-Christov diffusion theory over a magnetized-radiative surface. The boundary condition is enriched with the slip regime and Newtonian heating. Numerical computations are acquired by employing the shooting technique approach in association with Runge-Kutta Fehlberg numerical scheme. Statistical and numerical consequences disclose that non-linear stretching index causes a depletion in velocity and temperature. When the Eckert number and the heat generating parameter are both large, the heat transfer rate is also large. Mass transport rate is lowest for higher ratios of diffusion coefficients. The 0.265365 is the maximum possible heat transport rate attained for the 8th experimental run with the key elements: Eckert number, heat source and radiation parameter. The critical point claimed by the Pareto chart shows that the slightest manipulation of the radiation parameter is critical for the heat transport rate, whereas the heat source parameter and Eckert number have almost similar influences on the response.

Numerical simulation of heat transfer and nanoparticle transport in a nanofluid within a tumour surrounding a blood vessel

A Newtonian nanofluid containing suspended nanoparticles can substantially improve heat transfer due to enhanced energy transport mechanisms. This theoretical study investigates heat and mass transfer in biological tissues using such a nanofluid under a magnetic field. These properties have promising medical and engineering applications. The nonlinear governing equations were transformed into ordinary differential equations using similarity variables and numerically solved with MATLAB boundary value problem solver bvp4c, subject to appropriate boundary conditions. Results demonstrated increasing the heat source parameter dramatically raised tumor interstitial temperature. This heating, along with improved nanoparticle accumulation within the tumor due to the thermal effects, are together essential for effective hyperthermia treatment. The model provides new insights into tuning heat and mass transport mechanisms in biological tissues via nanofluids for therapeutic applications. Therefore, the findings of this study may improve the efficacy of thermal therapy in treating cancer.

Effect of slip boundary conditions on unsteady pulsatile nanofluid flow through a sinusoidal channel: an analytical study

A novel analysis of the pulsatile nano-blood flow through a sinusoidal wavy channel, emphasizing the significance of diverse influences in the modelling, is investigated in this paper. This study examines the collective effects of slip boundary conditions, magnetic field, porosity, channel waviness, nanoparticle concentration, and heat source on nano-blood flow in a two-dimensional wavy channel. In contrast to prior research that assumed a constant pulsatile pressure gradient during channel waviness, this innovative study introduces a variable pressure gradient that significantly influences several associated parameters. The mathematical model characterising nano-blood flow in a horizontally wavy channel is solved using the perturbation technique. Analytical solutions for fundamental variables such as stream function, velocity, wall shear stress, pressure gradient, and temperature are visually depicted across different physical parameter values. The findings obtained for various parameter values in the given problem demonstrate a significant influence of the amplitude ratio parameter of channel waviness, Hartmann number of the magnetic field, permeability parameter of the porous medium, Knudsen number due to the slip boundary, volume fraction of nanoparticles, radiation parameter, Prandtl number, and heat source parameters on the flow dynamics. The simulations provide valuable insights into the decrease in velocity with increasing magnetic field and its increase with increasing permeability and slip parameters. Additionally, the temperature increases with increasing nanoparticle volume fraction and radiation parameter, while it decreases with increasing Prandtl number.

Impact of Shape Factor on a Couple Stress Flow of a Ternary Hybrid Nanofluid over an Inclined Flat Plate when Non-Uniform Heat Source and Thermal Radiation are Significant: A Darcy-Forchheimer Model

Abstract The study of fluid flow over an inclined flat plate finds applications in a diverse range of engineering fields including aerodynamics, energy production and automotive design. This study theoretically investigates the steady and radiative flow of a ternary hybrid nanofluid (Water + TiO2 + CoFe2O4 + MgO) with couple stress, using the Darcy-Forchheimer model. The flow occurs through a tilted flat plate and is subjected to irregular heat source parameter and entropy generation. The problem’s equations have been transformed into a collection of ordinary differential equations (ODEs), which has been skillfully resolved using the bvp4c solver. Graphs are utilized to elucidate outcomes for two instances of shape components, namely platelet and spherical. An escalation in the couple stress parameter (S) is demonstrated to be inversely related to the fluid velocity, resulting in a drop. Specifically, when 0.5 ≤ S ≤ 3, the friction factor exhibits a decline, with rates of 0.306201851 (for Platelet shape) and 0.304466755 (for Spherical shape). An intriguing observation reveals an augmentation in the generation of entropy as the volumetric fraction of TiO 2 rises. Upon investigation, it has been determined that when the Eckert number (Ecn) increases within the range of 0 ≤ Ecn ≤ 0.3, there is a significant reduction in the Nusselt number. Specifically, the decline is measured to be 0.328685192 for the platelet shape and 0.308939422 for the spherical shape. The utility of the Forchheimer number in regulating the fluid’s motion has been unveiled.

Thermal analysis of the water-based micropolar hybrid nanofluid flow comprising diamond and copper nanomaterials past an extending surface

This research demonstrates that hybrid nanofluids are superior to traditional fluids in terms of their capacity to transmit heat. An intensive investigation of hybrid nanofluids is needed to fill gaps in knowledge of heat transmission improvement methods. Therefore, scientists and researchers are combining different solid particles in various base fluids to boost the material's thermal conductivity. That's why the author has combined diamond and copper nanoparticles in a water solvent to examine the two-dimensional, steady, and incompressible magnetohydrodynamic (MHD) hybrid micropolar nanofluid flow over a permeable extending surface through the porous media. The Cattaneo-Christov heat and mass flux model is used to assess the heat and mass diffusion occurrences in temperature and concentration distributions. The similarity transformations are used to convert the PDEs along with their related boundary constraints into a set of nonlinear ODEs. A semi-analytical method known as HAM is used with the help of MATHEMATICA software to perform an analytical analysis on the set of nonlinear ODEs. The impacts of many important factors on the velocity, microrotation, thermal, and concentration functions are demonstrated through graphs and discussed in detail. The study results demonstrate that velocity distribution is a declining function of the magnetic field and porosity parameter. The magnetic field, Brownian motion, heat source, thermophoresis, and radiation parameters have positively influenced the thermal profile, while the thermal relaxation parameter has a negative influence on it. Nanoparticle volume fraction improves the Nusselt and Sherwood numbers. Heat transfer and skin friction are both amplified by the magnetic field. The skin-friction coefficient improves with an increase in the permeability parameter and the volume percentage of nanoparticles. Also, nanoparticles volume fraction enhances the mass transfer rate. Hybrid nanofluids have superior thermal characteristics over regular fluids.

Lie group analysis on EMHD Jeffrey nanofluid flow with exponential heat source: Heat transfer optimization using RSM

The present research examines the behavior of a Jeffrey nanofluid flow across a stretching sheet under the effect of electric and magnetic fields. It comprises the Buongiorno model as well as an exponential heat source. The impact of chemical reaction has also been taken into consideration. While assuming no mass flux, the study considers boundary conditions for thermal convection and velocity slip. Lie group transformations are employed to transform the set of governing equations into a dimensionless system and later simulated using the finite difference scheme. It is found that the velocity profile rises as the Deborah number is enhanced whereas the ratio of relaxation to retardation time parameter has an inverse effect on the velocity profile. It is noted that per unit change in the Deborah number descends the drag coefficient by 31.29%. In this study, the response surface methodology and sensitivity analysis have been conducted by choosing heat transport as the dependent variable and the electric-field parameter ( 0.01 ≤ E ≤ 0.03 ) , exponential heat source parameter ( 0.02 ≤ Qe ≤ 0.06 ) , and Biot number ( 0.15 ≤ Bi ≤ 0.25 ) as the independent variables. The Nusselt number escalates when the Bi number is increased and drops as the E values are raised. In the instance of the Biot number, the Nusselt number exhibits the maximum sensitivity.

Solar photothermal utilization of coupled latent heat storage: A numerical and optimization study

The combination of Organic Rankine Cycle (ORC) and Latent Heat Thermal Energy Storage (LHTES) is a novel approach for effectively utilizing solar energy. However, the influence of solar energy fluctuations on the heat transfer process of LHTES systems is not yet clear. In this study, a sinusoidal heat source is applied to a rotating triple-tube LHTES system, and numerical analysis and model verification are conducted. The parameters of the sinusoidal heat source are optimized using the response surface method. The effects of heat source amplitude, half period, and rotation speed on the heat release time and heat release rate of LHTES are investigated, and corresponding quadratic regression equations are fitted. The optimized structure (rotation speed = 0.5 rpm, amplitude = 7.5 K, half-cycle = 100) obtained through the response surface method reduced the solidification time by 12.45% compared to the initial structure (rotation speed = 0.3 rpm, amplitude = 7.5 K, half-cycle = 100). The average temperature response and heat release rate increased by 28.34% and 16.25%, respectively. The sensible heat and total heat release within one solidification cycle increased by 12.17% and 1.87%, respectively. This study lays the foundation for the optimization design of LHTES systems and the integrated application of Organic Rankine Cycle.

Research on Off-Design Characteristics and Control of an Innovative S-CO2 Power Cycle Driven by the Flue Gas Waste Heat

Recently, supercritical CO2 (S-CO2) has been extensively applied for the recovery of waste heat from flue gas. Although various cycle configurations have been proposed, existing studies predominantly focus on the steady analysis and optimization of different S-CO2 structures under design conditions, and there is a noticeable deficiency in off-design research, especially for the innovative S-CO2 cycles. Thus, in this work aimed at the proposed novel S-CO2 power cycle, off-design characteristics and corresponding control strategies are investigated for the waste heat recovery. Based on the design parameters of the S-CO2 cycle, structural dimensions of printed circuit heat exchangers (PCHEs) and shell-and-tube heat exchangers are determined, and design values of turbines and compressors are specified. On this basis, off-design models for these key components are formulated. By manipulating variables such as cooling water inlet temperature, cooling water mass flow rate, flue gas inlet temperature and flue gas mass flow rate, cycle performances of the system are analyzed under off-design conditions. The simulation results show that when the inlet temperature and the mass flow rate of cooling water vary separately, the thermal efficiency both can reach the maximum value of 28.43% at the design point. For the changes in heat source parameters, the optimum point is slightly deviated from the design condition. Amidst the fluctuations in flue gas inlet temperature, the thermal efficiency optimizes to a peak of 28.56% at 530 °C. In the case of variation in the flue gas mass flow rate, the highest thermal efficiency 28.75% can be obtained. Furthermore, to maintain the efficient and stable operation of the S-CO2 power cycle, the corresponding control strategy of the cooling water mass flow rate is proposed for the cooling water inlet temperature variation. Generally, when the inlet temperature of cooling water increases from 23 °C to 27 °C, the cooling water mass flow should increase from 82.3% to 132.7% of the design value to keep the system running as much as possible at design conditions.

Thermodynamic Analysis of Magnetized Carbon Nanotubes (CNTs) Conveying Ethylene Glycol (EG) Based Nanofluid Flow Through Porous Convergent/Divergent Channel in the Existence of Lorentz Force and Solar Radiation

Due to higher thermal features, carbon nanotubes (CNTs) have significant uses in heating frameworks, medical, hyperthermia, industrial cooling, process of cooling in heat exchangers, electronic and pharmaceutical administration systems, heating systems, radiators, electrical, electronic device batteries, and engineering areas. The main concern of present study is to inspect the EG based CNTs nanomaterials flow in a porous divergent/convergent channel with the application of Lorentz force. The Darcy-Forchheimer theory is utilized to investigate the nanofluid motion and thermal features. Mathematical modeling is further developed by considering Joule heating, solar radiation and heat source. Ordinary differential equations (ODEs) are obtained by employing the proper transformations (obtained from symmetry analysis). The numerical computations are executed through NDSolve technique using Mathematica tool. The upshots of distinct significant parameters on different profiles are displayed via numerical data and sketches. The major outcome is that, enhancement in nanoparticles volume fraction and in inertia coefficient escalate the nanofluids motion for both divergent and convergent. Furthermore, drag forces exerted by the channel is more for higher porosity parameter and inertia coefficient. Also heat transfer rate is significantly enhances against radiation and heat source parameter and is more in case of stretching wall than the shrinking one. Overall, the effect of MWCNT is about 3% is more than that of CWCNT.

Non-similar analysis of micropolar magnetized nanofluid flow over a stretched surface

The study of micropolar nanofluids unveils intriguing applications, propelled by their exceptional heat transfer capabilities in comparison to conventional fluids. This investigation focuses on analyzing the behavior of magnetized micropolar nanofluid flow over a stretched surface, taking into account crucial factors such as viscous dissipation and heat source. The chosen base fluid is blood, with Copper [Formula: see text] nanoparticles serving as the selected material. Incorporating the single-phase (Tiwari-Das) model with boundary layer assumptions for micropolar nanofluid flow, we introduce the volume fraction of nanoparticles to assess heat transport. The governing system undergoes transformation into a set of dimensionless non-linear coupled differential equations through appropriate transformations. This transformation involves the utilization of a combination of the local non-similarity technique and bvp4c (MATLAB tool) to derive the system of nondimensional partial differential equations (PDEs) for micropolar nanofluid. Our systematic exploration delves into the consequences of nondimensional parameters on velocity, microrotation, and temperature profiles within the boundary layer, including the Eckert number, micropolar parameter, magnetic field parameter, heat source, Prandtl number, and microorganism parameter. Graphical representations vividly demonstrate that the velocity and temperature of micropolar nanofluid increase with the rise in material parameter values, while the microrotation profile decreases. Increasing the magnetic field parameter leads to a reduction in the velocity profile. Moreover, the micropolar temperature profile shows an increase with the rising Eckert number. Crucially, the research emphasizes that factors like the heat source and Eckert number play a role in decreasing the local Nusselt number. In contrast, an increase in the local Nusselt number is observed for material parameters. Furthermore, the skin friction coefficient decreases as micropolar parameter values increase, whereas an increase in the skin friction coefficient is noted for the magnetic field. The primary focus of this research lies in the development of suitable non-similar transformations for the investigated problem, aiming to yield authentic and efficient results. These results hold substantial promise to make meaningful contributions to future research on nanofluid flows.

On viscous stratified Darcy–Forchheimer flow in a horizontal porous layer with thermal anisotropy and variable permeability

This study analyzes the effect of anisotropy and the internal heat source in a Darcy–Forchheimer porous layer. It is well known that the variations in viscosity can be attributed to the temperature. Therefore, in the present problem, we consider a linear variation in viscosity with temperature for simplicity. We first derived the linear instability theory and then established global stability using the energy functional approach. In the global stability analysis, we show that working with the L2 norm fails to give a sufficient condition for global stability by exhibiting that the associated maximization problem is unbounded in the underlying stability measure space. Then, we show that a conditional stability bound can be achieved by restricting the internal heat source parameter Q with higher-order norms. The eigenvalue problems obtained in linear and nonlinear theories were integrated numerically. The linear and nonlinear instability thresholds are then compared to identify the potential regions of sub-critical instabilities. It is observed that the system is stabilized when the horizontal component of thermal diffusivity dominates and is unstable when the vertical component of thermal diffusivity dominates. We also found that increasing the variable permeability parameter λ destabilized the system. It is observed that increasing viscosity stabilizes the system, and decreasing viscosity encourages the start of convection. It is also interesting that, in the presence of an internal heat source, the region of subcritical instability increases with increasing viscosity effect but reduces with increasing vertical permeability λ.

Analysis of Magnetohydrodynamic Free Convection in Micropolar Fluids over a Permeable Shrinking Sheet with Slip Boundary Conditions

The convective micropolar fluid flow over a permeable shrinking sheet in the presence of a heat source and thermal radiation with the magnetic field directed towards the sheet has been studied in this paper. The mathematical formulation considers the partial slip condition at the sheet, allowing a realistic representation of the fluid flow near the boundary. The governing equations for the flow, heat, and mass transfer are formulated using the conservation laws of mass, momentum, angular momentum, energy, and concentration. The resulting nonlinear partial differential equations are transformed into a system of ordinary differential equations using suitable similarity transformations. The numerical solutions are obtained using robust computational techniques to examine the influence of various parameters on the velocity, temperature, and concentration profiles. The impact of slip effects, micropolar fluid characteristics, and permeability parameters on the flow features and heat transfer rates are thoroughly analyzed. The findings of this investigation offer valuable insights into the behavior of micropolar fluids in free convection flows over permeable shrinking sheets with slip, providing a foundation for potential applications in various industrial and engineering processes. Key findings include the observation that the velocity profile overshoots for assisting flow with decreasing viscous force and rising magnetic effects as opposed to opposing flow. The thermal boundary layer thickness decreases due to buoyant force but shows increasing behavior with heat source parameters. The present result agrees with the earlier findings for specific parameter values in particular cases.

The detrimental effect of thermal exposure and thermophoresis on MHD flow with combined mass and heat transmission employing permeability

We look at the viscous free-convective transitional magnetohydrodynamic thermal and mass flow over a plate that is always perforated and standing upright through permeable media while thermal radiation, a thermal source, and a chemical reaction are all going on. There is additional consideration for the Soret effect. The plate receives a normal application of a transversely consistent magnetic field. The magnetic Reynolds number is considerably lower considering the axial applied magnetic field instead of the induced magnetic field. The models that control mass, heat, and fluid flow are turned into two-dimensional shapes, and the answers are found by running numerical simulations using the MATLAB algorithm bvp4c. In realistic circumstances, the outcomes have been illustrated graphically. Several fluid properties have been found to have an impact on velocity, temperature, and concentration profiles. There is noticeable increase in velocity along with the growth of the permeability parameter and Soret number. Other dimensionless parameters have a significant impact on the fluid velocity. Likewise, the temperature profile diminishes as the radiation parameter has increased. The concentration distribution falls as the heat source parameter expands. Also, the analysis is encompassed in tabular form for the shearing stress, Nusselt number, and Sherwood number. The combined knowledge of heat and mass moving through viscous flows can be used to make a wide range of mechanisms and processes. These include biological reactors, therapeutic delivery systems, methods of splitting, aerodynamic aircraft design, and modeling for sustainability. It also optimizes automotive radiators and engine efficiency, and it improves cooling systems.

Influence of Plastic Strain on Heat Capacity of L485ME Pipe Steel Grade

The aim of this work is an experimental evaluation of a specific heat capacity as a function of plastic strain for thermo-mechanically rolled pipe material, with application of an infrared thermographic camera. The tensile load tests of samples prepared of L485ME (X70M) steel grade were performed with the use of a strength machine. Based on other known material thermophysical properties, the determination of heat source parameters was conducted with the use of an infrared thermography and with an optimization task solution. A linear regression equation describing the specific heat capacity as a function of plastic percentage elongation for L485ME steel grade was determined. The experimental results of the present study showed a linear increase in the specific heat capacity in the range of the analyzed tensile deformation up to 16%. The presented methodology is suitable for assessment of the material specific heat capacity as a function of strain up to the occurrence of the sample narrowing in a direction perpendicular to the tensile force.

Electroosmotic and Gyrotactic Microorganisms Effects on MHD Al2O3-Cu/Blood Hybrid Nanofluid Flow through Multi-Stenosed Bifurcated Artery.

The purpose of this study is to investigate the electroosmotic flow of a hybrid nanofluid (Al2O3-Cu/Blood) with gyrotactic microorganisms through a bifurcated artery with mild stenosis in both parent and daughter arteries. The flow is subjected to a uniform magnetic field, viscous dissipation, and a heat source. The governing equations undergo the non-dimensional transformation and coordinate conversion to regularize irregular boundaries, then solve the resulting system using the Crank-Nicolson method. In both sections of the bifurcated artery (parent and daughter artery), the wall shear stress (WSS) profile decreases with increasing stenotic depth. Nusselt profile increases with an increase in the heat source parameter. The present endeavour can be beneficial for designing better biomedical devices and gaining insight into the hemodynamic flow for therapeutic applications in the biomedical sciences.

Multieffect bioconvective transport of oxytactic microorganisms with thermal radiation, Lorentz force, heat source, and chemical reaction over a flexible cylinder

AbstractThe multieffect bioconvective heat transfer in porous media is essential for many technological applications. However, the literature governing practical applications is very scarce. The bioconvective transport of magnetohydrodynamic cross nanofluid carrying oxytactic microorganisms across a flexible cylinder with velocity slip, viscous dissipation, thermal radiation, and chemical reaction with a heat source in Darcy–Forchheimer porous medium is predicted in this piece of work. The random movement and thermophoresis processes are revealed by the Buongiorno model. Using a suitable similarity transformation and boundary layer approximation, the simplified model equations are converted into coupled highly nonlinear ordinary differential equations (ODEs). The resulting ODEs are dealt with numerically utilizing the BVP4C and the shooting method with predetermined thermal radiation, heat source, chemical reaction, and so forth parameters. The velocity field is inversely influenced by the Forchheimer number and porosity parameter. The Sherwood number is significantly influenced by chemical reactions. For heat source parameter (S) and increasing radiation parameter (Rd), the Nusselt number increases and convection is shown for the value of Rd near about 3. Overall, this study will help researchers in science and engineering to understand the intricate and multieffective dynamic system and industrial applications like microbiology, and biodynamical systems, biological tissues, biofilms, soil, or filter media.

Analytical simulation of Darcy–Forchheimer flow of hybrid nanofluid through cone with nonlinear heat source and chemical reaction

This paper intends to discuss the hybrid nanofluid flow through a cone in a Darcy–Forchheimer porous media, containing base fluid Methanol (CH3OH), nanoparticles of titanium oxide (TiO2) and copper (Cu). We have examined the flow under the influences of mixed convection, viscous dissipation, chemical reaction, and nonlinear heat source. In hybrid nanofluid flow, viscous dissipation and mixed convection play a crucial role in heat exchangers. By accounting for both mixed convection and viscous dissipation, the addition of nanoparticles into a base fluid improves the transfer of heat and optimizes the performance of the cooling system. Using the laws of conservation, governing equations have been constructed. The flow model is converted using the appropriate similarity transformations from partial differential equations to ordinary differential equations. The homotopy analysis method is used to solve the updated system of equations. When Forchheimer inertial drag parameter is increased, the velocity profile decreases, but it rises when the Darcy number is increased. As the value of exponential heat source parameter rises, the temperature profile increases as well. The result exposes that with an increment in nanoparticle volume fraction, temperature profile also rises but velocity profile decreases.

Numerical simulation for radiative hybrid nanofluid (TiO2+Fe3O4∕H2O) flow due to a non-uniform stretching sheet with variable permeability

Variable permeability plays a crucial role in various manufacturing and technical applications such as fixed-bed catalytic reactors, heat exchangers, and dying, among others. The primary focus of this paper is to investigate the impacts of variable permeability on hybrid nanofluid (HNF) flow due to nonlinear sheet stretching with thermal heat flux. The HNF is made up of a mixer of [Formula: see text] and [Formula: see text] nanoparticles and water serving as the base fluid. Using efficient similarity transformations, the flow-governing equations are converted into a set of ordinary differential equations, and the resulting system is computationally solved by using the MATLAB program (bvp4c). The impact of various physical variables on the fluid velocity and heat transfer characteristics is analyzed via graphs. It is found that as the permeability parameter rises, the velocity of the HNF diminishes while the temperature amplifies. The drag force coefficient declines with an intensification of the volume fraction of the [Formula: see text] nanoparticles. The HNF [Formula: see text] exhibits 0.45–0.75% increase in heat transfer rate when compared to a nanofluid [Formula: see text] for different values of heat source parameter. The current investigation is compared to the existing literature, revealing a good level of agreement.