Relaxation Parameters Research Articles

Computational heat transfer analysis of ternary hybrid nanofluid flow over a rotating disk using the Cattaneo-Christov model: Application of the Lobatto-III formula

This work investigated the impact of ternary nanoparticles on the flow dynamics across a revolving disk. This study examines the nanoparticles of magnesium oxide (MgO), titanium dioxide (TiO2), and CoFe2O4 that were dispersed in different liquids -water and ethylene glycol (EG). This study examines the joint impacts of a varying inclined magnetic field and CattaneoChristov heat and mass flux on the flow of two ternary nanofluids across a spinning disk. Problems of this nature predominantly arise in symmetrical phenomena through the use of similarity transformations and are relevant to engineering, physics, and applied mathematics. The phenomena were expressed as partial differential equations, which were subsequently transformed into an ordinary differential equation within the existing system. Subsequently, this work is computed with the bvp4c scheme in MATLAB. Graphical results are employed to evaluate the examination of mass and heat transfer. The velocities increase with the inclined magnetic impression for both ternary nanofluids. The temperature increases and concentration declines with the increasing volume fraction of TiO2 and CoFe2O4 for both ternary nanofluid flows. The Nusselt number declines for I-ternary nanofluid flow and increases for II-ternary nanofluid flow with the thermal and solutal relaxation parameter along with the increasing volume fraction of TiO2 and MgO. In addition, the alterations in concentration, temperature, and velocity graphs for different dimensionless parameters are briefly examined through related diagrams. The Nusselt number declines with the I-ternary group and increases with the II-ternary group for the nanoparticle MgO concentration.

Scaling Effects of the Weissenberg Number in Electrokinetic Oldroyd-B Fluid Flow Within a Microchannel.

This study attempts to extend previous research on electrokinetic turbulence (EKT) in Oldroyd-B fluid by investigating the relationship between the Weissenberg number ( ) and the second-order velocity structure function ( ) under applied electric fields. Inspired by Sasmal's demonstration in Sasmal (2022) of how heterogeneous zeta potentials induce turbulence above a critical , we develop a mathematical framework linking to turbulent phenomena. Our analysis incorporates recent findings on AC (Zhao & Wang, 2017) and DC (Zhao & Wang 2019) EKT, which have defined scaling laws for velocity and scalar structure functions in the forced cascade region. Our finding shows that and , for a length scale , and , where is a velocity fluctuations quantity and denotes the time relaxation parameter. This work establishes a positive correlation between and turbulent flow phenomena through a rigorous analysis of velocity structure functions, thereby offering a mathematical foundation for building the design and optimization of EKT-based microfluidicdevices.

A Closed-Form Expression for Analysis of Dark State Exchange Saturation Transfer (DEST) NMR Experiments.

Closed-form expressions for the analysis of Dark state Exchange Saturation Transfer (DEST) NMR experiments, a powerful experimental tool for characterizing exchange processes involving the interaction of NMR visible species with very high molecular weight partners, is presented. Essentially identical exchange and relaxation parameters are derived from the analytical and numerical best fits of the DEST profiles obtained for a protein construct derived from huntingtin exon-1, comprising the N-terminal amphiphilic sequence followed by a seven-residue glutamine repeat, httNTQ7, in the presence of small (SUV) and large (LUV) unilamellar lipid vesicles. The use of analytical expressions significantly speeds up the fitting of experimental DEST profiles to a two-state exchange model and simplifies the analysis of the DEST effects.

The STRIPAK associated kinase MST4 is a novel mediator in heart failure pathogenesis

Abstract Heart failure still poses substantial challenges in understanding its underlying molecular pathways. We recently found the mammalian STE20-like kinase 4 (MST4) significantly upregulated in human failing hearts (5.7-fold in DCM and 3.8-fold ICM) as well as in heart failure animal models (i.e. 2.5-fold in Calsarcin-1-KO, 2.5-fold in MLP-KO). MST4 is a member of striatin interacting phosphatases and kinases complexes (STRIPAK), an emerging group of multiprotein complexes responsible for integrating cellular signalling pathways. We provide the first evidence of functional STRIPAK complexes containing MST4 by co-immunoprecipitation and interactomics experiments in cardiomyocytes. Moreover, we found MST4 to interact with several intercalated disc proteins like beta-Catenin or Desmin. Adenoviral overexpression of MST4 in neonatal rat ventricular cardiomyocytes (NRVCM) results in a significant increase in cell size (+13%). This was not accompanied by the activation of fetal genes such as NPPA, NPPB or RCAN1.4, but rather by an increase in phosphorylation of Protein kinase B (PKB/Akt, 3.3-fold). Akt is usually associated with physiological hypertrophy, indicating that MST4 may be involved in protective pathways in cardiomyocytes. In support of this notion, MST4 overexpression reduced apoptotic activity (cleavage of Caspase 3 -69%, Caspase 7 -80%, Parp1 -27%) and improved both contractility (fractional shortening cell +23%, fractional shortening sarcomere +30%, time to max. contraction cell -10%, time to max. contraction sarcomere -12%) and relaxation parameters (time to max. relaxation velocity cell -12%) in isolated adult rat ventricular cardiomyocytes. In order to identify cardiac targets of MST4, we performed a comprehensive analysis of the phosphoproteome of NRVCM overexpressing MST4 compared with control-virus +/- pharmacological inhibitor at two time points. We identified more than 70,000 peptides including more than 20,000 phosphopeptides in more than 4,000 protein groups. Using linear modelling with a reduced data set containing regulated features selected by thresholds for p-value and fold change, we observed a consistent MST4 effect and a number of enriched gene ontology terms. Here, we found several potential MST4 targets and effects on protein expression levels associated with intercalated disc proteins. In human heart samples, MST4 was also localized to the intercalated disc region by immunostaining. Interesting proteins in that context that might help explain some of the observed cardioprotective MST4 effects are Connexin 43, Desmin, Ryanodine receptor, Phospholemman, Junctophilin2, Myozap or Frizzled 1. Taken together, our data imply that MST4 upregulation in human heart failure serves an adaptive role which may offer translational opportunities.Graphical Abstract

Investigation of heat generation and radiation effects on boundary layer flow of Prandtl liquid with Cattaneo–Christov double diffusion models

In this analysis, a bidirectional stretched sheet is used to produce a 3D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{D}$$\\end{document} flow of Prandtl liquid with improve mass diffusion and heat conduction models. This study advances knowledge of magnetohydrodynamics, radiation impacts, and heat production in fluid dynamics and transport processes. The Prandtl fluid model is critical for modeling non-Newtonian fluids, capturing its viscoelastic features, and allowing for precise simulation in industrial applications. It gives a mathematical foundation for analyzing complex fluid behaviors, which is necessary for optimizing operations utilizing such fluids. It uses the boundary layer method to simplify the fundamental equations and Cattaneo–Christov double diffusion models. The optimal homotopy analysis method is used to solve nonlinear ODEs caused by non-dimensional similarity variables. This investigation undertakes the calculation of drag coefficient for surfaces mass transfer rates and heat transfer rates proximate to the solid boundary. Furthermore, it conducts a comprehensive analysis of the influences exerted by various parameters on concentration and temperature profiles employing graphical representations for a rigorous examination. The Prandtl fluid model describes the viscoelastic characteristics of non-Newtonian fluids through constitutive equations, dimensional evaluation, and numerical simulations, which are frequently validated by experiments. The results show that changes in thermal and concentration relaxation parameters are accompanied by a decline in temperature. Temperature field rises as the thermal radiation parameter and heat generation increases. The work's novelty consists in its advanced modeling of Prandtl non-Newtonian fluids via Cattaneo–Christov double diffusion models, which incorporate magnetohydrodynamics and radiation effects and use optimal homotopy analysis for accurate parametric analyses of heat and mass transfer.

Exploring slip flow and heat transfer of power-law fluid past an induced magnetic stretching regime subject to Cattaneo-Christov flux theory

This work investigates the heat transmission and boundary layer (BL) slip flow of a power-law fluid induced by stretching surfaces. The power-law fluid, induced magnetic field, and finite thermal relaxation have significant applications in a variety of industrial settings, including thin-layer growth, cooling systems, the extrusion process, and coating and shaping operations in a heat transfer mechanism. With these significant industrial applications, the current study explores BL flow and heat transfer in the context of the of the Cattaneo-Christov theory against the backdrop of an induced magnetic field over a stretching surface. The shear-thinning and thickening features are captured by the power-law fluid model, while the Cattaneo-Christov theory solves the deficiencies of Fourier's law. The BVP4c technique is used to construct and solve BL equations numerically. The surface drag and heat transmission rates at the wall are studied using statistical multi-regression analysis. The findings clarify that the magnetic and power law indices have a favorable effect on the Nusselt number, while their influence on skin friction is conflicting. A lower heat transmission is predicted with thermal relaxation as compared to Fourier's law in the energy equation. The accumulated thermal relaxation parameter produces a non-equilibrium state, delaying the internal thermal processes.

Optimized Accelerated Over-Relaxation Method for Robust Signal Detection: A Metaheuristic Approach

Massive MIMO technology is recognized as a key enabler for beyond 5G (B5G) and next-generation wireless networks. By utilizing large-scale antenna arrays at the base station (BS), it significantly improves both system capacity and energy efficiency. Despite these advantages, the deployment of a high number of antennas at the BS presents considerable challenges, particularly in the design of signal detectors that can operate with low computational complexity. While the minimum mean square error (MMSE) detector offers optimal performance in these large-scale systems, it suffers from the computational burden that makes its practical implementation challenging. To mitigate this, various iterative methods and their improved versions have been introduced. However, these iterative methods often converge slowly and are less accurate. To address these challenges, this study introduces an improved variant of traditional accelerated over-relaxation (AOR), called optimized AOR (OAOR). AOR is an over-relaxation method, and its performance is highly dependent on its relaxation parameters. To find the optimal parameters, we have developed an innovative approach that integrates a nature-inspired meta-heuristic algorithm known as Particle Swarm Optimization (PSO). Specifically, we introduce a novel variant of PSO that improves upon basic PSO by enhancing the cognitive coefficients to optimize the relaxation parameters for OAOR. These key modifications to the standard PSO improve its ability to explore various solutions efficiently and help to find the optimal parameters more quickly for signal detection. It facilitates the OAOR with faster convergence towards the optimal solution by reducing the error rate, resulting in high detection accuracy and simultaneously decreasing computational complexity from O(K3) to O(K2) making it suitable for modern wireless communication systems. We conduct extensive simulations across various configurations of massive MIMO systems. The results indicate that our proposed method achieves better performance compared to existing techniques. This improvement is particularly evident in terms of both computational complexity and error rate.

Synergistic effect of ceramic filler in polymer salt complex for improved ion dissociation and migration mechanism

Abstract Use of Ceramic filler is one of the most common approaches to improve the conductivity and stability properties of a solid polymer electrolyte (SPE) cum separator. Among them, active fillers like Garnet have been extensively used to enhance the stability and conductivity of SPE. However, SPE suffers from limited ion migration at room temperature acting as a bottleneck for their application in all solid-state batteries. An extensive study on these fillers' role in ion dissociation and migration can be a stepping stone for advanced SPE. In the present work, an FTIR analysis has primarily been used to identify and evaluate cation coordinate site-cation, and ion pair interactions in a Li6.5La3Zr1.75Te0.25O12 loaded polyethylene oxide-LiCF3SO3 matrix with varying ceramic concentrations. Further, the Trukhan model has been used to calculate diffusion coefficient, mobility, and charge carrier density to interpret relaxation parameters, conductivity, and FTIR results in the SPE samples. Finally, an ion migration model has been proposed based on the results obtained in experimental studies.

Fitting Quality of NMR Relaxation Data to Differentiate Asphalt Binders

Asphalt binder performance grades (PGs) are important metrics in designing pavements for effective transportation infrastructure. The PG system relies on the binder’s stiffness and is determined through energy- and time-intensive physical testing. Physical properties, like stiffness, can also be determined by spin–lattice NMR relaxometry, a non-destructive chemical method. NMR relaxometry can quantify the molecular mobility of materials by determining relaxation times from exponential decays of excited nuclear magnetization. While relaxation times have been used to determine physical properties of materials, a quantitative relation to the PG grades of asphalt binder is yet to be established. In this study, T1 NMR relaxation analyses were used to differentiate between solid asphalt binders and determine the fastest yet still-reliable method of modeling exponential decay data. Algorithms that fit exponential decay relaxation data using one, two, or three independent relaxation times were compared with a 128-coefficient discrete inverse Laplace transformation to determine the best mathematical fit for a comparative analysis. The number of data points was then reduced from 256 to 64 to 16 and finally to 8 data points on a relaxation curve to reduce the testing time and determine the minimum number of data points needed for comparison. Two batches of PG 64-22 asphalt binder, along with samples of PG 76-22 and 94-10 binders, were investigated. The best compromise between measuring time and data reliability was found by acquiring 64 data points and then using a biexponential model to fit the experimental data. The PG 64-22 sources provided similar results, indicating similar physical properties. The PG 64-22 and PG 76-22 binders could also be compared via monoexponential data fits, but the PG 94-10 samples required an additional relaxation parameter for comparison. To differentiate all three binder grades, the primary relaxation times, along with their relative ratios, were utilized.

Charge transport in organic semiconductors from the mapping approach to surface hopping.

We describe how to simulate charge diffusion in organic semiconductors using a recently introduced mixed quantum-classical method, the mapping approach to surface hopping. In contrast to standard fewest-switches surface hopping, this method propagates the classical degrees of freedom deterministically on the most populated adiabatic electronic state. This correctly preserves the equilibrium distribution of a quantum charge coupled to classical phonons, allowing one to time-average along trajectories to improve the statistical convergence of the calculation. We illustrate the method with an application to a standard model for the charge transport in the direction of maximum mobility in crystalline rubrene. Because of its consistency with the equilibrium distribution, the present method gives a time-dependent diffusion coefficient that plateaus correctly to a long-time limiting value. The resulting mobility is somewhat higher than that of the relaxation time approximation, which uses a phenomenological relaxation parameter to obtain a non-zero diffusion coefficient from a calculation with static phonon disorder. However, it is very similar to the mobility obtained from Ehrenfest dynamics, at least in the parameter regimes we have investigated here. This is somewhat surprising because Ehrenfest dynamics overheats the electronic subsystem and is, therefore, inconsistent with the equilibrium distribution.

Relaxation RKN-type integrators that preserve two invariants for second-order (oscillatory) systems

Recently, the relaxation technique has been widely used to impose conservation of invariants while retaining the full accuracy of the original method. So far, only a single invariant of a system has been considered. In this work, by a mild generalization of the relaxation technique, the Runge–Kutta–Nyström (RKN) integrators are modified to preserve two invariants for second-order system of Ordinary Differential Equations (ODEs). The proposed integrators can be explicit and of arbitrarily high order. The accuracy of the relaxation RKN integrators and the existence of valid relaxation parameters have been proved. The construction of the new integrators is under the framework of adapted RKN (ARKN) integrators which are specially designed for numerical solving second-order oscillatory systems. Therefore, the proposed integrators could be oscillation-preserving in the sense that they exactly integrate homogeneous oscillatory system q′′+Kq=0. Some numerical experiments are conducted to show the advantage and efficiency of the proposed integrators in comparison with the standard (A)RKN integrators.

Structural and dynamics characterization of the Zika virus NS2B using nuclear magnetic resonance and RosettaMP: A challenge for transmembrane protein studies

Zika virus (ZIKV) is an emergent flavivirus that represents a global public health concern due to its association with severe neurological disorders. NS2B is a multifunctional viral membrane protein primarily used to regulate viral protease activity and is crucial for virus replication, making it an appealing target for antiviral drugs. This study presents the structural elucidation of full-length ZIKV NS2B in sodium dodecyl sulfate (SDS) micelles using solution nuclear magnetic resonance experimental data and RosettaMP. The protein structure has four transmembrane α-helices, two amphipathic α-helices, and a β-hairpin in the hydrophilic region. NS2B presented secondary and tertiary stability in different concentrations of SDS. Furthermore, we studied the dynamics of NS2B in SDS micelles through relaxation parameters and paramagnetic relaxation enhancement experiments. The findings were consistent with the structural calculations. Our work will be essential in understanding the role of NS2B in viral replication and screening for inhibitors against ZIKV.

The SOR and AOR Methods with Stepwise Optimized Values of Parameters for the Iterative Solutions of Linear Systems

We modify the successive overrelaxation (SOR) method and accelerated overrelaxation (AOR) method for solving linear equations systems. The optimal value of the acceleration parameter is determined, using the maximal reduction method of the residual vector’s length, or equivalently an orthogonality condition. Rather than the constant value, the MAOR method endows a step-by-step varying acceleration parameter to possess the property of absolute convergence and the orthogonality of consecutive residual vector. In SOR, the relaxation parameter is also optimized by using the orthogonality condition. Numerical examples ensure that the MSOR and MAOR iterative schemes converge faster than the original SOR and AOR iterative schemes. They are easily implemented with low computational cost, and without needing of a detailed spectral analysis to determine the optimal values of parameters has a great advantage.

Study of molecular interaction between benzaldehyde and methanol using microwave dielectric relaxation spectroscopy and radial distribution function

A microwave dielectric relaxation study was conducted for mixtures of benzaldehyde (BZ) and methanol (MeOH) over a frequency range of 200 MHz to 20 GHz at seven different temperatures, ranging from 293.15 K to 323.15 K. The dielectric relaxation parameters, obtained through a fitting process, were used to examine their dependence on concentration and temperature. Thermodynamic parameters, such as Gibbs free energy (ΔG), molar enthalpy of activation (ΔH), and molar entropy of activation (ΔS), were evaluated using the temperature dependence of the dipolar relaxation time. The study provided valuable insights into the molecular interactions and dynamic behavior of the components in the binary mixture system. Additionally, a molecular dynamics (MD) simulation study was conducted on the binary mixture of BZ and MeOH to determine the Radial Distribution Function (RDF) and coordination number for different pairs of molecules and atoms, which revealed information about the binding and arrangement of the local structure.

Spirocyclic pyrrolidinyl nitroxides with exo-methylene substituents.

Nitroxides are stable organic radicals with exceptionally long lifetimes, which render them uniquely suitable as observable probes or polarising agents for spectroscopic investigation of biomolecular structure and dynamics. Radical-based probes for biological applications are ideally characterized by both robustness towards reductive degradation and beneficial electron spin relaxation parameters. These properties are largely influenced by the molecular structure of the nitroxide scaffold, and also by the conformations it prefers to adopt. In this study we present the synthesis of the first nitroxides based on a spirocyclic pyrrolidine scaffold with an exocyclic methylene substituent. The conformations adopted by these nitroxides were evaluated by X-ray crystallography, both with single nitroxide crystals and by inclusion of nitroxides in a microporous crystalline sponge. The kinetic and thermodynamic stability of the new nitroxides towards reduction was investigated by electron paramagnetic resonance (EPR) spectroscopy and cyclic voltammetry (CV). In combination with EPR measurements of electron spin relaxation properties, these results suggest that this new family of nitroxides can provide access to multifunctionalized probes and polarising agents suitable for use in biological environments at elevated temperatures.

Enhancing superconductivity in CoSi2 films with laser annealing

Laser annealing was employed to trigger the solid-state reaction of a thin Co film (2.5 nm) with undoped Si. A metastable disilicide layer was obtained after one laser pulse close to the melt threshold. Its diffraction pattern, relaxed lattice parameter, and residual resisitivity are consistent with the formation of the defective CsCl structure. The CoSi2 phase was found after prolonging the thermal treatment with additional pulses or rapid thermal annealing. Because CoSi is skipped in the phase sequence, CoSi2 layers are more uniform in thickness, have an increased superconductivity and a reduced formation temperature. This approach is compatible with the SALICIDE process and can be used to form smooth contacts in superconducting or regular transistors.

Quasi-one-dimensional non-equilibrium method for shock tube and stagnation line flows

Shock tube experiments are used to investigate non-equilibrium thermochemistry and radiative processes in reacting gas hypersonic flows. Boundary layer and shock structure are known to influence the spatial variation of the test slug state properties. This work derives and validates a novel method for viscous, quasi-one-dimensional, non-equilibrium flow in a shock tube assuming constant shock speed. The proposed method fully resolves the shock structure. Mirels' estimate for boundary layer growth around the test slug determines the dilation rate at the centerline. This, along with relevant boundary conditions, appropriately models core flow in a shock tube. The flow equations are discretized by finite differences on a staggered grid. The resulting highly non-linear set of algebraic equations is solved by Newton iterations. The Jacobian matrix is block tridiagonal with a Schur complement, allowing efficient inversion. This culminates in a unique and computationally efficient quasi-one-dimensional method offering improved modeling of the physical characteristics of shock tube experiments. Results of a 3 km/s, 66.6 Pa argon test case solved by a viscous, axisymmetric Navier–Stokes solution had agreement with the proposed method in temperature and pressure profiles to within 2% and post-shock velocity to within 15%. Reacting gas shock tube experiments in synthetic air and synthetic Titan atmospheres were analyzed. Radiance values in the non-equilibrium and equilibrium regions were compared under various assumptions for the shock structure and radial velocity distribution. These results highlight the necessity of a dedicated shock tube solver when analyzing shock tube thermochemistry, particularly when determining reaction rates and relaxation parameters.

A new local and explicit kinetic method for linear and non-linear convection-diffusion problems with finite kinetic speeds: II. Multi-dimensional case

We extend to multi-dimensions the work of [1], where new fully explicit kinetic methods were built for the approximation of linear and non-linear convection-diffusion problems. The fundamental principles from the earlier work are retained: (1) rather than aiming for the desired equations in the strict limit of a vanishing relaxation parameter, as is commonly done in the diffusion limit of kinetic methods, diffusion terms are sought as a first-order correction of this limit in a Chapman-Enskog expansion, (2) introducing a coupling between the conserved variables within the relaxation process by a specifically designed collision matrix makes it possible to systematically match a desired diffusion. Extending this strategy to multi-dimensions cannot, however, be achieved through simple directional splitting, as diffusion is likely to couple space directions with each other, such as with shear viscosity in the Navier-Stokes equations. In this work, we show how rewriting the collision matrix in terms of moments can address this issue, regardless of the number of kinetic waves, while ensuring conservation systematically. This rewriting allows for introducing a new class of kinetic models called regularized models, simplifying the numerical methods and establishing connections with Jin-Xin models. Subsequently, new explicit arbitrary high-order kinetic schemes are formulated and validated on standard two-dimensional cases from the literature. Excellent results are obtained in the simulation of a shock-boundary layer interaction, validating their ability to approximate the Navier-Stokes equations with kinetic speeds obeying nothing but a subcharacteristic condition along with a hyperbolic constraint on the time step.

Solving Mathematical Programs with Complementarity Constraints Arising in Nonsmooth Optimal Control

AbstractThis paper examines solution methods for mathematical programs with complementarity constraints (MPCC) obtained from the time-discretization of optimal control problems (OCPs) subject to nonsmooth dynamical systems. The MPCC theory and stationarity concepts are reviewed and summarized. The focus is on relaxation-based methods for MPCCs, which solve a (finite) sequence of more regular nonlinear programs (NLP), where a regularization/homotopy parameter is driven to zero. Such methods perform reasonably well on currently available benchmarks. However, these results do not always generalize to MPCCs obtained from nonsmooth OCPs. To provide a more complete picture, this paper introduces a novel benchmark collection of such problems, which we call . The problem set includes 603 different MPCCs and we split it into a few representative subsets to accelerate the testing. We compare different relaxation-based methods, NLP solvers, homotopy parameter update and relaxation parameter steering strategies. Moreover, we check whether the obtained stationary points allow first-order descent directions, which may be the case for some of the weaker MPCC stationarity concepts. In the best case, the Scholtes’ relaxation (SIAM J. Optim. 11, 918–936, 2001) with (Math. Program. 106, 25–57, 2006) as NLP solver manages to solve 73.8% of the problems. This highlights the need for further improvements in algorithms and software for MPCCs.

Entropy optimization in ternary hybrid nanofluid flow over a convectively heated bidirectional stretching sheet with Lorentz forces and viscous dissipation: A Cattaneo–Christov heat flux model

Bidirectional stretching sheet models can represent surfaces in heat exchangers where fluids flow under continuous deformation. Ternary hybrid nanofluids could be employed in these systems to increase heat transfer rates between fluids in heat exchangers and improve the efficiency of energy conversion processes. In this work, we explore the novel application of a ternary hybrid nanofluid (water with titanium dioxide, cobalt ferrite, and magnesium oxide nanoparticles) for enhanced heat transfer in heat exchangers modeled by a bidirectional stretching sheet. This approach offers a potential advancement over traditional nanofluids (with one or two nanoparticles). Furthermore, we present a comprehensive analysis that incorporates ohmic heating, Cattaneo–Christov heat flux, thermal radiation, viscous dissipation, and irreversibility. The governing equations are transformed into a system of nonlinear ordinary differential equations using appropriate similarity transformations and then solved using the bvp4c solver, a MATLAB built-in function. This study's findings reveal that the Eckert number and radiation parameter increase fluid temperature, while the thermal relaxation parameter leads to a reduction in the temperature of the fluid. It is detected that an increase in magnetic field parameter and volume fraction of [Formula: see text] results in a decline of the skin friction factors in both directions. It is revealed that there is a reduction in the Nusselt number with the rise in Eckert number ([Formula: see text]), and the same number declines at a rate of 0.8252 when [Formula: see text]. It is noticed that the skin friction coefficient declines at a rate of 0.62179204 (in case of x-direction) and 0.621791816 (in case of y-direction), respectively, when the values of magnetic field parameter lie between 0 and 3.5. Furthermore, it is noticed that an upsurge in thermal relaxation parameter results in a fall in the temperature of the fluid.