Finite Difference Technique Research Articles

Unsteady MHD Casson fluid flow past a vertical plate in the presence of viscid dissipation and Dufour effects

PurposeThis research investigates the impact of Dufour effects and viscous dissipation on unsteady magnetohydrodynamic (MHD) natural convection in an incompressible, viscous, and electrically conductive fluid over a vertically oscillating flat plate. The study highlights the significance of magnetic fields in influencing thermal and mass transfer, particularly in the context of thermal radiation. Computational fluid dynamics method including finite difference or finite element techniques can be used to crack the governing equations of the fluid flow. In this work, we used the finite element method (FEM) numerical technique to analyze the numerical behavior of unsteady boundary layer flow of Casson fluid with natural convection past an oscillating vertical plate. Key parameters such as skin friction, temperature, concentration, velocity and Sherwood numbers are derived and analyzed. The results demonstrate that viscous dissipation significantly elevates the fluid temperature, while an increase in the radiation parameter is associated with a decrease in internal friction at the plate. These findings provide critical insights into the interplay between thermal radiation and magnetic fields in MHD flows, with potential applications in engineering systems involving heat and mass transfer, such as cooling systems and material processing. This study underscores the importance of understanding these dynamics for optimizing the performance of MHD applications in various industrial settings.Design/methodology/approachThe mainly authorized and energetic FEM to explain the non-linear, dimensionless partial differential equations (11–13) via equation with boundary conditions (14) makes use of Bathe (36), Reddy (37), Connor (38) and Chung (39). Following are the key steps that make up the method: discretize the domain, derivation of element equation, assembly of element equation, imposition of boundary condition and solution of assembly equation.FindingsThis study examined the impact of viscid dissipative radiation and the Dufour effect on unsteady one-dimensional MHD natural convective flow of a viscous, incompressible, electrically conducting fluid past an infinite moving vertical flat plate with a chemical reaction. Numerically solving the governing equations using the FEM approach is efficient and precise, aiming to be applied to fluid mechanics and related problems. Along with their effects on temperature, concentration and velocity, the following parameters are included: the mass Grashof number, the Soret number, the Grashof number, the Prandtl number, chemical reaction, the Schmidt number, radiation and the Casson parameter. Both the Grashof numbers of thermal and mass rates (Gr, Gm) make an increment in the velocity region. The velocity decreases with an increase in the magnetic parameter. The velocity increases with an increase in the permeability of the porous medium parameter. The temperature flow rate is higher for both Dufour and Viscid dissipation, while a decrement is noted of both Prandtl number and radiation effects. The decrementing behavior of the concentration region is observed at supreme inputs of chemical reaction coefficient and Schmidt number.Originality/valueThis is an original paper and not submitted anywhere.

Exploration of Arrhenius activation energy and thermal radiation on MHD double-diffusive convection of ternary hybrid nanofluid flow over a vertical annulus with discrete heating

The primary objective of this article is to examine the effect of discrete heating on MHD double-diffusive convection and thermal radiation of ternary hybrid nanofluid flow heat and mass transfer in a vertical cylindrical annulus along with Arrhenius activation energy and chemical reaction. In this study, the cavity inner wall has two distinct flush-mounted heat sources, while the outer wall is isothermally cooled at a lower temperature. The top and bottom walls are thermally insulated. The ensuing equations that govern the physical framework are solved using the implicit Crank-Nicholson finite difference technique. As the heater advances upward, the flow intensity decreases, leaving a part of the fluid static at the bottom of the cylinder. Because more heat induces high buoyant flow in the annulus, the absolute value of axial velocity and wall temperature rises as the length of the heat source rises. Enhancing the activation energy parameter values drops the Arrhenius energy function, elevating the pace of the generative chemical process and hence the concentration. Increasing the thermal radiation parameter lowers the surface heat flux while enhancing the nanofluid temperature. The Brownian motion parameter corresponds to the random motion of nanoparticles in a fluid, and this irregular movement augments the collision of nanoparticles with fluid particles, causing the particle's kinetic energy which leads to thermal energy and hence increases temperature, a 10% increment in Brownian motion parameter leads to 26% rise in the temperature. Also, the heat and mass transfer characteristics are forecasted and analyzed by considering the Levenberg–Marquardt backpropagating artificial neural network technique.

Mathematical Modeling and Applications of Differential Equations in Science and Engineering

Analytically, differential equations are a means of developing relationships between functions that define rates of changes and these rates in terms of the underlying function. They are crucial in modeling diverse, evolutive systems within various domains, to list but a few: physics, engineering, biology, and economics. The fundamentals of differential equations are categorized mainly into Two types of Differential Equations are Ordinary Differential Equations and Partial Differential Equations. Most of the differential equations are solved analytically and numerically techniques such as separation of variables, Fourier series and finite difference techniques. In situations, where exact solutions are tough to come across, computational tools like MATLAB, Maple and the Python libraries help towards approximations. Because they help to explain how systems behave, as well as predicting and improving them, differential equations are an essential tool for expanding the body of scientific and engineering knowledge.

Computational study on entropy generation in Casson nanofluid flow with motile gyrotactic microorganisms using finite difference method

The present study reveals the phenomenon of flow and thermal variations of non-Newtonian nanofluids flow of Copper (Cu) nanoparticles through two orthogonal permeable porous discs. Additionally, the study delves into the significance of liquid solid interfacial layer and nanoparticle diameter is studied to optimize the thermal conductivity. Gyrotactic Microorganisms are also considered to optimize the nanoparticles stability inside the fluid, and the entropy generation caused to system disorder, so entropy analysis is also calculated. Using appropriate dimensionless variables, the controlling PDEs are converted into dimensionless forms. These dimensionless PDEs are solved using the Finite Difference technique, which yields very accurate and stable solutions. Higher values of the Rayleigh bio-convection and mixed convection terms enhance the flow velocity field in both porous discs. The less thickness of nanolayer has significance effect to optimize the temperature. Enhancing the values of bioconvection Lewis number leads to a decrease in motile microorganism concentration in both permeable discs, and entropy generation rate increases against rising power of Eckert number and thermal radiation rise. The finite difference method outcomes have been thoroughly validated against already published research, and showing an excellent correlation. This research holds significant potential for applications in the fabrication and electromagnetic control of advanced magnetic nanofluid materials, relevant to biomedical, energy, thermal management, and aerospace technologies.

A simplified approach for simulating pollutant transport in small rivers with dead zones using convolution

Abstract In the paper an alternative method to solve the one-dimensional advective-diffusive equation describing the pollutants transport in river with dead zones is presented. Because very often transport in a small river can be treated as a 1D issue, then instead of numerical solution of the advection-diffusion equation an equivalent approach based on the convolution technique can be used. Consequently, for a given impulse response function the numerical calculations are required to compute a convolution only. The impulse response function is obtained as an analytical solution of the linear advection-diffusion equation for the Dirac delta function imposed as the boundary condition at the upstream end. Therefore, it represents the Gauss distribution and consequently, this approach is unreliable when the dead zones occur. To reproduce an asymmetric distribution of concentration along the channel axis an approximation of analytical impulse response function using the asymmetric Gumbel distribution is proposed. This approach valid for solution of the transport equation with constant coefficients is extended for piecewise constant coefficients. Convolution approach does not produce any numerical dissipation and dispersion errors typically generated by the methods based on the finite difference technique. Validation of the method using the results of field measurements confirmed its effectiveness.

A compact finite-difference and Haar wavelets collocation technique for parabolic volterra integro-differential equations

Abstract In this paper, a numerical investigation of a class of parabolic Volterra integro-differential equations (parabolic-VIDEs) is conducted. The approach focuses on semi-discretizing parabolic-VIDEs by utilizing a second-order compact finite difference method O ( δ t 2 ) for the time variable and approximating the integral term using the trapezoidal rule. Further, the spatial derivative is approximated by Haar wavelet method. This hybrid methodology leverages the strengths of both techniques to solve the equations more efficiently and accurately. The error analysis, using L 2 and L ∞-norms, shows low computational costs. Numerical experiments show that second-order accuracy in both time and space, respectively. Stability and convergence of the proposed method are given through Sobolve space. Some numerical examples are tested for the effectiveness and accuracy of the proposed method. Furthermore, the presented numerical approach is compared with standard finite difference numerical methods and the results are reported in a table.

Photonic hook shaping achieved by the micro-nano fiber array based Janus cylindrical metalens

Abstract Near-field focusing of an electromagnetic wave on the assembly of hexagonally asymmetric arranged close-contact nanofibers into a cylindrical Janus metalens is considered for different fiber sizes and optical properties. We propose combining the meta-material concept with a photonic hook based on the finite-difference time-domain technique. Simulation results show that the cylindrical meta-photonic Janus structure produces the focal region of enhanced optical intensity, which exists in the spatial form of a localized structured light known as a photonic hook. A detailed study of all key parameters of a photonic hook depending on the Janus metalens topology and optical properties of the fiber filling is carried out. The structure conditions have been determined for the beam waist of a photonic hook that is less than the diffraction limit. This Janus cylindrical metalens may contribute to the versatile control of photonic hook generation in the applications of bio-photonics and optical microscopes.

Advancement of nanoparticles in blood flow with non-linear radiation and optimisation of irreversibility within the microchannel using analysis of variance and Taguchi approach

Nanoparticles in blood flow play a pivotal role because of their extensive use in biomedicine, tissue engineering, and blood coagulation. Gold and Zinc nanoparticles have been proven to be stable and non-toxic to humans. Also, gold nanoparticles are biocompatible with less cytotoxicity, which makes them best suited for therapeutic drug delivery. Both gold and zinc nanoparticles in the blood are allowed to flow through an inclined microchannel, anticipating the couple stresses experienced by the fluid particles. The non-linear radiation and heat source components are contemplated in the study. The modelled equations are solved numerically with the aid of the finite difference technique. Analysis of variance and Taguchi optimization technique are applied to the entropy generated during the flow in the system. This method has proposed the optimal values for the parameters to achieve the least entropy. Outcomes have reported that as the effects of couple stress inverse parameter increase, the velocity of the fluid increase. Additionally, the flow profiles show an increase over time. The thermal field increases with the convection-radiation parameter, and declines with an increasing nanoparticle volume fraction. We observe an increase in irreversibility with enhanced radiation and the temperature difference parameter. The nanofluid phase's velocity and temperature are high in comparison to the hybrid nanofluid phase. The ANOVA-Taguchi method reveal that the couple stress inverse parameter has a 0.5 % impact, whereas the temperature gradient parameter has the highest impact on entropy generation, which is 56.14 %. Manipulation of the temperature gradient parameter is critical in regulating the irreversibility generated in the channel.

Flowing Liquid Crystal Torons Around Obstacles.

Liquid crystal torons, localized topological structures, are known for their stability and dynamic behaviour in response to external stimuli, making them attractive for advanced material applications. In this study, we investigate the flow of torons in chiral nematic liquid crystals around obstacles. We simulate the fluid flow and director field interactions using a hybrid numerical method combining lattice Boltzmann and finite difference techniques. Our results reveal that the toron dynamical behaviour depends strongly on the impact parameter from the obstacle. At impact parameters smaller than half cholesteric pitch, the flowing toron is destabilized by the interaction with the obstacle; otherwise, the flowing toron follows a trajectory with a deflection which decays exponentially with the impact parameter. Additionally, we explore the scattering of torons by multiple obstacles, providing insights into how the dynamics of these structures respond to complex environments.

Analysis of thermophoretic and Brownian diffusions in hydromagnetic curvilinear flow of Carreau nanofluid with activation energy and heat generation

This study presents a theoretical analysis of the thermophoretic and Brownian diffusion effects on the magnetized flow of Carreau nanofluid over a stretchable curved surface. The investigation includes the impact of heat generation and activation energy, which are incorporated into the energy and concentration equations, respectively. The mathematical model of the boundary layer flow is formulated as a set of nonlinear partial differential equations using curvilinear coordinates. These equations are transformed into ordinary differential equations through the application of appropriate similarity variables. The resulting system is solved numerically by using the shooting method along with the Runge-Kutta technique. The accuracy of the numerical results is further verified by the Keller-box method, a finite difference technique. The obtained results are also checked by giving a comparison table with the published data in the literature. Furthermore, the convergence of the solutions is also checked by a convergent series method known as the homotopy analysis method (HAM). The study examines the influence of several key parameters, including the radius of curvature, Weissenberg number, Prandtl number, Lewis number, Brownian and thermophoretic diffusions parameters, Hartmann number, heat generation parameter, activation energy parameter, temperature difference parameter, chemical reaction parameter, and power law index. The effects of these parameters on momentum, temperature, concentration distributions, mass and heat transfer rates, and as well as the skin friction coefficient are examined through graphs and tables. Graphical observations declare that the velocity field diminishes against the rising values of the Hartmann number and Weissenberg number. However, the velocity profile rises with improved values of the radius of curvature parameter and power law index parameter. It is also noticed that the magnitude of the concentration field rises with growing values of the Brownian parameter, activation energy parameter and Lewis number, whereas it shows a decreasing manner against the enhanced values of the thermophoresis parameter and temperature difference parameter.

Robust and accurate numerical framework for multi-dimensional fractional-order telegraph equations using Jacobi/Jacobi-Romanovski spectral technique

This paper presents a novel spectral algorithm for the numerical solution of multi-dimensional fractional-order telegraph equations, a critical model used to capture the combined effects of diffusion and wave propagation. The core innovation of this work is the application of Jacobi-Romanovski polynomials as the basis functions for spectral discretization. These polynomials offer unique advantages, including the ability to handle nonstandard domains and boundary conditions, making them particularly suitable for partial differential equation (PDE) applications. A comprehensive error analysis is conducted, providing deep insights into the convergence rates and factors affecting the accuracy of the numerical solutions. Extensive numerical experiments further demonstrate the superior performance of the proposed spectral algorithm in solving a wide range of multi-dimensional fractional-order telegraph equation models. The results show a significant improvement in accuracy and computational efficiency compared to traditional numerical methods, such as finite difference or finite element techniques. This research advances the field of computational science by offering a robust, efficient, and versatile numerical framework for the precise solution of complex multi-dimensional PDEs.

Enhancing valuation of variable annuities in Lévy models with stochastic interest rate

This paper extends the valuation and optimal surrender framework for variable annuities with guaranteed minimum benefits in a Lévy equity market environment by incorporating a stochastic interest rate described by the Hull-White model. This approach frames a more dynamic and realistic financial setting compared to previous literature. We exploit a robust valuation mechanism employing a hybrid numerical method that merges tree methods for interest rate modeling with finite difference techniques for the underlying asset price. This method is particularly effective for addressing the complexities of variable annuities, where periodic fees and mortality risks are significant factors. Our findings reveal the influence of stochastic interest rates on the strategic decision-making process concerning the surrender of these financial instruments. Through comprehensive numerical experiments, and by comparing our results with those obtained through the Longstaff-Schwartz Monte Carlo method, we illustrate how our refined model can guide insurers in designing contracts that equitably balance the interests of both parties. This is particularly relevant in discouraging premature surrenders while adapting to the realistic fluctuations of financial markets. Lastly, a comparative statics analysis with varying interest rate parameters underscores the impact of interest rates on the cost of the optimal surrender strategy, emphasizing the importance of accurately modeling stochastic interest rates.

High-Performance Visible-to-SWIR Photodetector Based on the Layered WS2 Heterojunction with Light-Trapping Pyramidal Black Germanium.

This study presents a layered transition metal dichalcogenide/black germanium (b-Ge) heterojunction photodetector that exhibits superior performance across a broad spectrum of wavelengths spanning from visible (vis) to shortwave infrared (SWIR). The photodetector includes a thin layer of b-Ge, which is created by wet etching of germanium (Ge) wafer to form submicrometer pyramidal structures. On top of this b-Ge layer, the WS2 thin film is deposited using pulsed laser deposition. In comparison to conventional germanium, b-Ge absorbs about 25% more light between 850 and 1750 nm wavelengths. The WS2/b-Ge photodetector has a peak photoresponsivity of 0.65 A/W, which is more than twice the photoresponsivity of the WS2/Ge photodetector at 1540 nm. Additionally, it shows better responsivity and response speed compared with other similar state-of-the-art photodetectors. Such an improvement in the performance of the device is credited to the light-trapping effect enabled by the germanium pyramids. Theoretical simulations employing the finite-difference time-domain technique help validate the concept. This novel photodetector holds promise for efficient detection of light across the vis to SWIR spectrum.

Improved numerical schemes to solve general fractional diabetes models

In this article, we propose a new class of nonlinear fractional differential equations of diabetes disease based on the concept of Caputo fractional derivative. Two numerical techniques are introduced to analyse the solution of the general fractional diabetes model, that describes glucose homeostasis. The first method, which constructed using the nonstandard finite difference technique involves an asymptotically stable difference scheme. This method maintains important properties of the solutions of the studied system, such as the positivity and boundedness. The second method is the Jacobi-Gauss–Lobatto spectral collocation approach, known for its exponential accuracy. By employing this collocation method, the problem is transformed into a set of algebraic nonlinear equations, simplifying the overall task. Numerical simulations were conducted to compare the performance of these two techniques with other standard methods and the analytic solution in specific cases. Our findings show that the Jacobi-Gauss–Lobatto spectral collocation technique provides higher accuracy in solving the fractional diabetes model system, while the nonstandard finite difference approach requires lower computational duration.

Dynamics of Fourier's and Fick's laws on the convectively heated oscillatory sheet under Arrhenius kinetics: The finite-difference technique

The significance of chemical reaction with activation energy and convective boundary conditions on the fluid flow via an oscillatory stretchy surface in the presence of permeable media and radiation is analyzed in this study. This inspection presents Fourier and Fick's laws-based equations for heat, mass transport, and liquid flow through an oscillating stretchy sheet. Understanding these dynamics aids in the optimisation of catalytic reaction settings, where gradients greatly influence reaction rates in concentration and temperature. The governing differential equations of the current study are modelled and changed into their non-dimensional form by employing suitable similarity variables. The finite difference method (FDM) is also used to numerically solve the obtained dimensionless equations. The influence of many factors on the several profiles is portrayed with graphical representations. The outcome of the unsteadiness and porosity parameters on the velocity profile with time coordinate is depicted. The increase in the radiation parameter and Biot number upsurges the thermal profile. The temperature reduces as the unsteadiness parameter and temperature relaxation time parameter grow. The upsurge in the activation energy parameter intensifies the mass transport. The rise in concentration relaxation time parameter diminishes the concentration profile.

Finite difference analysis for entropy optimized nanomaterial Darcy-Forchheimer flow with homogeneous and heterogeneous reactions

Hybrid nanoliquids are not underestimated for their involvement in microelectronics, transportation, coolant processes, ships, biological processes and power generation. Hence motivation for current work is to examine homogeneous-heterogeneous reactions in entropy optimized flow by curved sheet stretched with nonlinear velocity. Trihybrid nanoliquid is synthesized through 2 % of ferrous oxides(Fe3O4), 2 % of silver(Ag) and 2 % of copper(Cu). Kerosene oil is employed as the base fluid. These specific kinds of nanoparticles are taken into consideration because of their numerous applications in heat dissipation, air filters, dynamic sealing, biosensors and catalysts process. Kerosene oil may have applications in many different domains such as energy storage, cleaning agent, portable heaters, fuel additive and industrial lubricants. Darcy-Forchheimer model is employed. Analysis in presence of radiation, dissipation, Ohmic heating, entropy generation and heat generation/absorption are organized. Unlike the previous considerations, the thermal expression here consists of impacts through Darcy-Forchheimer relation. Adequate transformations are implemented. Computations have been arranged by applying finite difference technique (FDM) using MATLAB. Quantities for physical interest are addressed. The presented analysis may have relevance for solar systems, chemical reacting processes, cooling towers and polymer data processes. The conclusions are also organized for important key findings. It is noticed that trihybrid nanomaterial has more entropy rate when compared with hybrid and classical nanoliquids when volume fraction is chosen as 2 % for trihybrid fluid. It is proposed that the ability to transfer heat is enhanced when nanoparticles are added to conventional fluids. Decay in concentration is noticed for both homogeneous and heterogeneous parameters. Reduction for Bejan number is noticed through homogeneous diffusion factor. Comparison with previous study is also presented and found great consensus between them.

Investigating new solutions for a general form of q$$ \mathfrak{q} $$‐deformed equation: An analytical and numerical study

SummaryThis paper contributes to the study of a new model called the ‐deformed equation or the ‐deformed tanh‐Gordon model. To understand physical systems with violated symmetries. We utilize the ‐expansion approach to solve the ‐deformed equation for specific parameter values. This method generates solutions that provide valuable insights into the system's dynamics and behavior. To verify the accuracy of our solutions, we also apply the finite difference technique to obtain numerical solutions to the ‐deformed equation. This dual approach ensures the reliability of our results. We present our findings using tables and graphics to enhance clarity and facilitate comparison between the analytical and numerical solutions. These visual aids help readers better understand the similarities and differences between the two approaches. The ‐deformation is significant as it models physical systems with nonstandard symmetry features, like extensivity, offering a more accurate representation of real‐world phenomena. The growing significance of this equation across various disciplines highlights its potential in advancing our understanding of complex physical systems. This paper contributes valuable knowledge about the ‐deformed equation, demonstrating its potential for accurately modeling physical systems with violated symmetries. Through both analytical and numerical techniques, we offer comprehensive solutions and validate their accuracy, with graphical representations enhancing the clarity and understanding of our results. This exploration of ‐deformation advances modeling techniques, providing a more precise depiction of real‐world processes with nonstandard symmetry features.

Numerical Method for Predicting Transient Aerodynamic Heating in Hemispherical Domes

In this research, a streamlined numerical approach designed for the quick estimation of temperature profiles across the finite thickness of a hemispherical dome subjected to aerodynamic heating is introduced. Hemispherical domes, with their advantageous aerodynamic, structural, and optical properties, are frequently utilized in the front sections of objects traveling at supersonic velocities, including missiles or vehicles. The proposed method relies on one-dimensional analyses of fluid dynamics and flow characteristics to approximate the local heat flux across the exterior surface of the dome. By calculating these local heat flux values, it is also possible to predict the temperature variations within the thickness of the dome by employing the finite difference technique, to solve the heat conduction equation in spherical coordinates. This process is iterated over successive time intervals, to simulate the entire flight duration. Unlike traditional Computational Fluid Dynamics (CFD) simulations, the proposed strategy offers the benefits of significantly lower computational time and resource demands. The primary objective of this work is to provide an efficient numerical tool for evaluating aerodynamic heating impact and temperature gradients on hemispherical domes under specific conditions. The effectiveness of the proposed method will be validated by comparing the temperature profiles derived for a standard flight scenario against those obtained from 2-D axisymmetric transient CFD simulations performed using ANSYS-Fluent 2022 R2.

Entropy generation analysis of oscillatory magnetized darcian flow of mixed thermal convection and mass transfer with joule heat over radiative sheet

Significance of this work is to examine enhanced thermal efficiency of magnetic nanofluid in the presence of Joule heating and radiation in missile technological devices, nuclear energy plants, rockets, solar energy systems and enhancing cyclic processes. Prominent aim of current investigation is to demonstrate the amplitude and oscillating analysis of mixed convective heat rate of Darcian magnetic nanoparticle movements with entropy generation, thermal radiation and Joule heat impact through porous stretching sheet. The magnetic layer along stretching surface plays important role to control thermal performance. Governing mathematical equations are reduced in convenient form by using non-dimensional analysis. The primitive mathematical form of steady and oscillating model is calculated through oscillatory stokes and primitive variables. Using Gaussian elimination and finite differences techniques, the geometrical and numerical outcomes of steady and oscillatory models are obtained by applying FORTRAN lahey-95 programming tool. The novelty of this problem is to study the oscillatory thermal and concentration profiles of Darcian magnetic nanoparticles with Joule heating and radiations. It is examined that momentum and temperature distribution grows as radiant-energy increases but decreases for maximum Joule heating. It is found that temperature and concentration distributions enhances as magnetic force decreases. Prominent enhancing amplitudes in heat and mass transfer are obtained for maximum Schmidt and thermophoresis parameter. Heat and mass transfer decreases as magnetic factor increases due to insulating magnetic nanoparticles.

Impacts of thermally stratified medium on transient convective heat transfer between co‐axial horizontal fixed pipes: Applications of the thermal stratification

AbstractThermal stratification improves coaxial pipe systems’ efficiency and stability. Thermal stratification enables accurate temperature maintenance, reduces thermal stress, optimizes heat transmission performance, and minimizes usage of energy to guarantee the system's long‐term performance. The main aim of the current study is to investigate the impacts of thermal stratification on buoyancy force flow and thermal transmission between coaxial fixed pipes. In the present research, the applications of thermally stratified medium on transient convective heat transfer between two coaxial fixed pipes are studied. A two‐dimensional mathematical formulation in terms of mutually nonlinear partial differential equations is used to analyze the unsteady flow and temperature field between the co‐axial pipes, when the internal pipe is uniformly heated and the outer wall of the external pipe is placed at infinity from the surface of the inner fixed pipe. Flow is assumed along the axial direction of the internal pipe and stationary boundary condition is assumed at the surface of the inner pipe. The coupled equations of the simulated model are solved numerically by applying the Implicit Finite Difference Technique. The computed outcomes in the form of geometrical interpretation are highlighted by using the technically advanced software TECHPLOT‐360. Comprehensive detail of the obtained results for the non‐dimensional parameters included in the flow formulation is predicted for steady state velocity, temperature distribution, time‐dependent surface shearness and time‐dependent energy shearness in results and discussion section of the manuscript. The emphasis is placed on the thermal stratification parameter in the above mentioned chief quantities. From the obtained results, it is predicted that the fluid flow pattern and thermal distribution are both reduced for rising values of the thermal stratification parameter S = 0.001, 0.03, 0.05, and 0.07. Minimum flow and thermal profile are observed at S = 0.07. Further, the amplitude of the time‐dependent surface shearness is uniformly distributed throughout the medium and the amplitude of the time‐dependent energy shearness is reduced effectively for S = 1.0, 5.0, and 10.0.