Dimensionless Form Research Articles

A Fractional Study of MHD Casson Fluid Motion With Thermal Radiative Flux and Heat Injection/Suction Mechanism Under Ramped Wall Condition: Application of Rabotnov Exponential Kernel

Abstract The primary objective of this research is to extend the concept of fractionalized Casson fluid flow. In this study, a comprehensive analysis of magnetohydrodynamic (MHD) natural convective flow of Casson fluid is conducted, focusing on obtaining analytical solutions using the non-integer-order derivative known as the Yang–Abdel-Aty–Cattani (YAC) operator. The YAC operator utilized in this research possesses a more generalized exponential kernel. The fluid flow is examined in the vicinity of an infinitely vertical plate with a characteristic velocity denoted as u 0. The mathematical modelling of the problem incorporates partial differential equations, incorporating Newtonian heating and ramped conditions. To facilitate the analysis, a suitable set of variables is introduced to transform the governing equations into a dimensionless form. The Laplace transform (LT) is then applied to the fractional system of equations, and the obtained results are presented in series form and also expressed in terms of special functions. The study further investigates the influence of relevant parameters, such as α, β, Pr , Q, Gr, M, Nr and K, on the fluid flow to reveal interesting findings. A comparison of different approaches reveals that the YAC method yields superior results compared to existing operators found in the literature. Graphs are generated to illustrate the outcomes effectively. Additionally, the research explores the limiting cases of the Casson and viscous fluid models to derive the classical form from the YAC fractionalized Casson fluid model.

Semi-Analytical Approach and Green's Function Method: A Comparison in the Analysis of the Interaction of a Moving Mass on an Infinite Beam on a Three-Layer Viscoelastic Foundation at the Stability Limit-The Effect of Damping of Foundation Materials.

In this paper, the interaction of a mass moving uniformly on an infinite beam on a three-layer viscoelastic foundation is analyzed with the objective of determining the lowest velocity at the stability limit, called, in this context, the critical velocity. This issue is important for rail transport and, in particular, for the high-speed train, because the moving mass is the basic model of a vehicle, and the infinite beam on a three-layer viscoelastic foundation is the usual mechanical representation of the railway track. In addition to this, the advantages and disadvantages of the two implemented methods, namely, the semi-analytical approach and the Green's function method, are summarized in terms of computational time, the precision of the obtained results, limitations, and the feasibility of implementation. All results are presented in a dimensionless form to cover a wide range of possible scenarios. Some results may be considered academic, however, results related to a particular railway track are also included. Particular attention is paid to the influence of the damping of materials in the foundation upon the critical velocity of the moving mass. Regarding the semi-analytical approach, it is demonstrated that the critical velocities can be obtained in an exact manner by tracing the branches of the so-called instability lines in the velocity-moving-mass plane. This analysis can be maintained within the real domain. As for the time series, they can be determined by a numerical inverse Laplace transform. Moreover, thanks to the analytical form of the final result in the Fourier domain, each value corresponding to a specific time instant can be obtained directly, that is, without the previous time history. Regarding the Green's function method, this is used to verify a few points delimiting the stable and unstable regions of the moving mass with the help of the D-decomposition approach. Additionally, a numerical algorithm based on the Green's function and convolution integral written for dimensionless quantities is used to calculate the time series of the moving mass. In addition to identifying the critical velocity of the moving mass, its connection with the critical velocity of the moving force is emphasized, and the possibility of validating the results on long finite beams using modal expansion is presented and described.

MHD Casson Fluid Flow in Stagnation-Point over an Inclined Porous Surface

Motivated by the need to comprehend and optimize complex fluid flow phenomena in various engineering and industrial applications, this paper investigates the magnetohydrodynamic (MHD) Casson fluid flow characteristics in the vicinity of a stagnation point over an inclined porous surface. The study addresses the interplay of permeability, viscous dissipation, buoyancy, and volumetric heat source, chemical reaction of the diffusion species, thermal slip, and obliqueness at the bounding surface. The governing equations are transformed into a dimensionless form using appropriate similarity transformations. The resulting nonlinear ordinary differential equations are solved numerically using the fourth-order Runge-Kutta method, coupled with the shooting technique as coded into the bvp4c solver of MATLAB 2021a. Findings from this study show that instability arises due to reduced velocity at low permeability, and Biot number enhances the Newtonian cooling at the surface, a requirement for the design of heat exchangers.

Illustration of activation energy and exponential heat source on the conducting viscous fluid through an expanding surface

In the current scenario, this investigation deal with the illustration of the advanced heat source properties influenced by exponential distribution for the inclusion of activation energy in the flow of viscous conducting fluid over an expanding surface. The flow through porous matrix is also characterized by the heat dissipation formulated due to viscous, Joule, and Darcy effects. Due to the consideration of the transverse magnetic field, and porous matrix, the effect of Joule and Darcy dissipations cannot be neglected. However, the novelty arises for the investigation that characterizes its key role to optimize the transport properties in numerous industrial application that be governed by the external heat source, which is beneficial for the better shape of the product and size of the manufacturing products. The dimensionless form of the proposed model associated with various flow properties is solved numerically employing shooting based “ Runge-Kutta fourth-order.” The illustration of the features of the various components associated in the present profiles is deployed graphically and the numerical computation of shear rate vis-a-vis other rate coefficients are presented in the tabular form. Finally, the important outcomes of the study deployed as; the velocity profile augments with the increasing thermal buoyancy as well as the ratio of the volumetric coefficient and the enhanced Lewis number combined with the reaction coefficient augments the solutal rate.

Dynamics of magnetized hybrid solid particles in a rotating cone with gradient descent optimization

Background Recent developments in nanoscience and nanotechnology have led to innovative hybrid nanofluids with superior thermal attributes to traditional nanofluids. These developments act as inspiration for the current framework, which focuses on an unsteady Casson hybrid nanofluid flow over a rotating cone in the presence of nonuniform heat source/sink factor. Methodology Two distinct shaped hybrid nanoparticles-hosted water is emphasized in the present work, namely spherical shaped CoF e 2 O 4 and cylindrical shaped Cu . The contribution of the heat source/sink variable is incorporated into the regulating equations utilizing boundary layer approximations. The resulting expressions of dimensionless forms of transmuted ODEs are computed through an NDSolve scheme. The performance of the pertinent parameters is accentuated to exhibit the relevance of the considered flow model. Furthermore, Multiple Linear Regression is introduced to generate appropriate formulations for the prediction of physical quantities on nanofluid and hybrid nanofluid. Core findings The volume fraction particles have a propensity to boost the temperature distribution, while the azimuthal and tangential factor follows the opposite trend in both the nanofluid and hybrid nanofluid. The skin friction coefficients rise for unsteady parameters, but the Nusselt number gets diminished due to the unsteadiness. The heat transfer rate of CoF e 2 O 4 nanoparticles hosted H 2 O is increased in Rudyak model than the Brinkman viscosity model by the involvement of an effective viscosity coefficient in terms of volume concentration of dispersed particles in nanofluid. Validation The outcomes are validated by comparing the present exploration with previously published investigations in certain instances. The multiple linear regression accurately anticipated the physical quantities with minimal error 10 − 2 . Applications An implementation of machine learning as an approach to do thermal evaluation with reliability and precision has emerged as a growing trend. The results of this investigation will benefit plenty of heat transfer applications, such as heat exchangers, heat pipes, and micro-channels.

Analysis of the Thermal Regime of a Residential Building Premises after an Emergency Shutdown of the Heating System

Maintaining favorable microclimatic conditions in a residential dwelling is directly related to the stable operation of the heating system. An emergency shutdown of the heating system, especially in the winter season, can lead to serious negative consequences: disruption of thermal comfort for people in the residential building, rupture of pipelines and heating devices, flooding of adjacent premises, etc. Thus, the issue of predicting the thermal regime of a residential dwelling after the termination of heat supply is of practical relevance. The object of study: Residential premises in buildings. Subject of study: Patterns of change in the temperature of the indoor air (in dimensional and dimensionless forms), the rate of temperature drop, and the loss of thermal energy during an emergency shutdown of the heating system. Objective of the study: To forecast the thermal regime of a room in a residential building after an emergency shutdown of the heating system. Research methods: Classical theory of thermal stability of building enclosures; theory of regular thermal regime, according to which the temperature field at all points of the cooled body (in this case, the heating system) changes in the same way, obeying the exponential law; software computer calculations. Research results: In a room of a residential building, the indoor air temperature will reach the dew point (12.5 ℃) within 8 hours 42 minutes after an emergency shutdown of the heating system and zero value - after 23 hours 42 minutes. Based on the conducted scientific research, it can be stated that the thermal storage capacity of external enclosures, due to their design features, plays a primary role in preserving the thermal regime of a residential dwelling after the heating system is turned off.

Mathematical modelling and heat transfer observations for Jeffrey nanofluid with applications of extended Fourier theory and temperature dependent thermal conductivity

The suspension of non-Newtonian materials with nanoparticles is important to enhance the thermal phenomenon in various engineering and industrial processes. The versatile research in nanomaterials provide different applications in thermal processes, heat exchangers, thermoelectric devices, HVAC systems, energy processes etc. Following to such novel motivations in mind, current research endorsed the enhancement in heat transfer due to suspension of Jeffrey nanofluid comprising the variable thermal conductivity. The cause of flow is associated to two disks attaining fixed distance. The modified developed relations for Fourier's hypothesis are utilized to model the problem. The flow problem is modeled with appliance of fundamental novel laws. By applying suitable transformations, corresponding differential equations are renovated into dimensionless forms which are solved with applications of analytic homotopic algorithm. The behavior of temperature and velocity due to various parameters is discussed. The numerical calculations have been done for wall shear force and Nusselt number. The results show that the velocity profile boosted due to variation of stretching ratio constant. The enhancement in heat transfer is observed due to Reynolds number. Moreover, the increasing observations for wall shear force in upper and lower disk surfaces are obtained against larger material parameter. The simulated results may find applications in improving heat transfer phenomenon, manufacturing systems, recovery processes, cooling systems, chemical phenomenon, fuel cells etc.

Решение краевой задачи тепломассопереноса методом конечного интегрального преобразования Фурье для условий лучистого обогрева почвы

The purpose of the research is to find, predict and regulate the temperature and humidity regime of the soil for the conditions of radiant heating of cultivation facilities using dark-type ceiling infrared radiators. In the work, without intermediate mathematical transformations, a generally accepted system of differential equations (both in dimensional and dimensionless forms) is presented, taking into account the main and cross processes of heat and mass transfer in dispersed media. For this system of equations, a particular analytical solution is considered, which takes into account not only the main phenomena of heat and mass transfer that occur independently of each other, but also the effect of water vapor transfer on the formation of the temperature field of the soil layer. Using the example of milling peat, the results of solving this problem are presented in the form of one-dimensional unsteady fields of temperature and moisture content. Taking into account the given unambiguity conditions (geometric, physical, initial and boundary conditions), it is established that the required values of moisture content and temperature will be reached in six hours. At the same time ,there is practically no change in moisture content during the time period under consideration on the coordinate segment z ∈[0;6,0] sm. The solution of the mathematical problem, implemented in a software environment, allows you to control the thermal and humidity conditions of the soil by regulating the heat flow on its surface (in the case of an obvious relationship between the magnitude of the heat flux and the intensity of evaporation from the soil surface). Due to the fact that the solution proposed in the article is a particular one and does not take into account thermal diffusion in the soil layer, i.e.the influence of temperature differences on moist ure transfer seems appropriate and of scientific interest to consider further the general solution of the system of differential equations of interrelated heat and mass transfer.

LANDAU LEGENDRE WAVELET GALERKIN METHOD APPLIED TO STUDY TWO-PHASE MOVING BOUNDARY PROBLEM OF HEAT TRANSFER IN FINITE REGION

In this paper, we developed a mathematical model of solidification where specific heat and thermal conductivity are temperature dependent. This model is a two-phase moving boundary problem (MBP) of heat transfer in finite region and represents as MBP of system of parabolic nonlinear second-order partial differential equations (PDEs). We developed a Landau Legendre wavelet Galerkin method for finding the solution of the problem. The MBP of a system of PDEs is transformed into a variable boundary value problem of nonlinear ordinary defferential equations (ODEs) by the use of dimensionless variables and the Landau transform. The problem is converted into a system of algebraic equations with the application of Legendre wavelet Galerkin method. In particular case, we compared present solution with Laplace transform solution and found approximately the same. The whole investigation has been done in dimensionless form. When the specific heat and thermal conductivity exponentially vary in temperatures, it is the effect of dimensionless parameters: thermal diffusivity (α<sub>12</sub>), ratio of thermal conductivity (<i>k</i><sub>12</sub>), dimensionless temperature (θ<sub><i> f</i></sub>), Fourier number (F<sub>0</sub>), Stefan number (Ste), and ratio of densities (ρ<sub>1</sub> / ρ<sub>2</sub>) are discussed in detail.

An exact asymptotic solution for a non-Newtonian fluid in a generalized Couette flow subject to an inclined magnetic field and a first-order chemical reaction

<abstract><p>Understanding generalized Couette flow provides valuable insights into the behavior of fluids under various conditions, contributing to the advancement of more accurate models for real-world applications including tribology and lubrication, polymer and food processing, water conservation and oil exploration, microfluidics, biological fluid dynamics (blood flow in vessels), and electrohydrodynamic, and so on. The present study provided the exact asymptotic solution for the generalized Couette flow of a non-Newtonian Jeffrey fluid in a horizontal channel immersed in a saturated porous medium.The governing partial differential equations were transformed into a dimensionless form using the similarity technique and the resulting system of equations is solved by the Perturbation technique, as well as the method of the separation of variables, and computed on MATLAB (ode15s solver).The behavior of fluid velocity was investigated and presented through 2-D and 3-D graphs for two cases (ⅰ) when the implication of the magnetic field was strengthened and (ⅱ) when the magnitude of the magnetic field was fixed but its degree of inclination was altered. The first-order chemical reactions and thermal radiation were also considered. Additionally, the effect of numerous emerging quantities on momentum, temperature, and concentration contours characterizing the fluid flow was depicted graphically and discussed. Furthermore, the skin friction (at different angles of inclination and magnetic strength), Nusselt number, and Sherwood number (at different time intervals) were evaluated at both boundaries and presented tabularly. The findings revealed that there was a decrease in the velocity profile with an increasing degree of inclination and strength of the magnetic field. Moreover, we observed an increment in thermal and mass flux when it was measured over time at both of the channels. Also, the outcomes predicted an oscillatory nature of shear stress at both of the boundries.</p></abstract>

IMPACT OF POROUS AND MAGNETIC DISSIPATION ON DISSIPATIVE FLUID FLOW AND HEAT TRANSFER IN THE PRESENCE OF DARCY-BRINKMAN POROUS MEDIUM

In this article, the boundary layer flow of an electrically-conducting fluid through a porous medium attached with a radiative permeable stretching sheet is analyzed. Following the Brinkman theory, an extended Darcy model (Darcy-Brinkman model) is utilized for the model momentum equation. Heat transfer analysis is also performed in the presence of viscous and Joule dissipation. Moreover, in the modeling of the energy equation, the effects of internal heating resulting from the mechanical effort required to squeeze out the fluid through the porous medium are also included in porous dissipation. Suitable dimensionless variables are introduced to convert the governing boundary layer equations into a dimensionless form, which are then converted into self-similar, nonlinear ordinary differential equations by utilizing similarity transformations. The exact solution of the nonlinear self-similar momentum equation is obtained in the form of the exponential function. In contrast, the solution of the energy equation is computed through the Laplace transform technique in the form of Kummer confluent hypergeometric functions. Effects of involved physical parameters on the momentum boundary layer (MBL), thermal boundary layer (TBL), wall shear stress, and local Nusselt number are explored through graphs and tables. Moreover, the slope linear regression (SLR) technique is used to calculate the rate of decrease/increase in shear stress and the rate of heat transfer at the boundary. The velocity and momentum boundary layer decreases for large values of porosity parameter and increases by increasing the viscosity ratio. The shear stress increases by increasing the porosity parameter, Hartman number, and suction parameter, while the opposite effect is examined with increasing values of viscosity ratio parameter. Heat transfer rate also enhances by increasing the Brinkman viscosity ratio parameter and wall suction velocity.

Unsteady MHD Free Convection Flow of Fluid in Micro Channel in the Presence of Viscous Dissipation Between Vertical Parallel Two Walls

Convection is a process by which heat is transferred by movement of a heated water. The phenomenon where heat transfer process is driven by natural fluid motion due to temperature and density gradients is called free convection. The effect of slip velocity on thermal behaviours of MHD free convection flow over a vertical parallel two walls is the focus of this research. The mathematical equations which described the phenomenom includes momentum, magnetic field and energy equations. Condition for the existence and uniqueness of solution of the model equations were established using the approach of Lipschitz continuity. The model equations in dimensionless form were solved using Olayiwola’s generalized polynomial approximation method (OGPAM). The results obtained which contains the dimensionless parameters were presented graphically and discussed. It was observed that increase in Reynolds number and Knudsen number both enhanced the velocity distribution at the two walls. Also, magnetic field and temperature field were enhanced by magnetic prandtl number and Eckert number respectively.

Optimization of system parameters during conjugate mixed convective flow in a square domain with an oscillating spinning cylinder

A computational analysis has been executed to analyze the combined conduction-mixed convection heat transfer of a rotationally oscillating solid cylinder in a differentially heated square box filled with air. The conjugate mixed convective flow initiates the heat transfer process, where the left-side boundary is isothermally kept to a higher temperature, and the right-side boundary is maintained at a lower temperature. Conduction heat transfer takes place inside the solid cylinder. Navier-Stokes and heat energy conservation equations model the system in the dimensionless pressure-velocity formulation. All these equations are solved via the Galerkin finite element approach. Three different combinations of Grashof (103-105), Reynolds (32–316), and Richardson (0.1–10) numbers are examined to systematically investigate the variations of governing parameters on instantaneous Nusselt numbers and the respective time-averaged values along the hot wall. In each combination, the impacts of the oscillating amplitude and frequency and the variation of cylinder diameter are examined to perform the optimization study. Power spectrum analysis is also done using the Fast Fourier Transform in the frequency domain to visualize the principal frequency of the system. The instantaneous values of the Nusselt number exhibit a wavering pattern over time owing to the recurrent waning and waxing of the thermal boundary layer. For all the cases, the maximum diameter and oscillating amplitude of the cylinder are found to maximize the heat transfer. However, the optimized frequency of the oscillation strongly depends on the selection of the governing parameters. In addition, the principal thermal frequency of the system is determined to be independent of the oscillation frequency.

ОСОБЛИВОСТІ РОБОТИ НАПІРНИХ ПОХИЛЬНИХ ЗБІРНИХ ДРЕНАЖНИХ ТРУБОПРОВОДІВ ЗА НАЯВНОСТІ ПОХИЛУ РІВНЯ ҐРУНТОВИХ ВОД

The development of a reliable methodology for calculating drainage pipelines in reclamation systems is crucial for en-hancing agricultural production efficiency and optimizing the use of water and land resources.Many existing calculation methods do not consider the simultaneous influence of pipe slope and groundwater level slope on the characteristics and operating conditions of collecting drainage pipelines. Addressing this issue will contribute to the advancement of modern hydraulic engineering and hydromelioration.The purpose of the article is to develop a methodology for calculating the parameters of pressure collecting drainage pipelines in reclamation systems, which are laid with a slope and operate in the presence of a groundwater level slope.A system of differential equations describing the liquid motion in collecting drainage pipelines laid with a slope and operating with a certain groundwater level slope is presented in the article. This system includes a variable mass hydraulicsequation and a modified filtration equation. The original system is reduced to a dimensionless form by introducing new vari-ables. The solution to the equations system results in straightforward and easy-to-use analytical dependencies for calculating the main hydraulic and structural characteristics of precast drainage pipes.The analysis employs the concept of an infinitely long drainage pipeline operating with a groundwater level slope, equivalent to an inclined pipeline with an infinitely filtering capacity of the side surface walls. The impact of drainage pipe geometric slope and groundwater level on its design charac-teristics is evaluated.The obtained dependencies for calculating collecting drainage pipelines will enhance the efficiency and reliability of drainage systems, improve resistance to extreme weather conditions, reduce energy consumption and enhance adaptation to various operating conditions

An artificial neural network analysis of the thermal distribution of a fractional-order radial porous fin influenced by an inclined magnetic field

<abstract><p>Fins and radial fins are essential elements in engineering applications, serving as critical components to optimize heat transfer and improve thermal management in a wide range of sectors. The thermal distribution within a radial porous fin was investigated in this study under steady-state conditions, with an emphasis on the impact of different factors. The introduction of an inclined magnetic field was investigated to assess the effects of convection and internal heat generation on the thermal behavior of the fin. The dimensionless form of the governing temperature equation was utilized to facilitate analysis. Numerical solutions were obtained through the implementation of the Hybrid Cuckoo Search Algorithm-based Artificial Neural Network (HCS-ANN). The Hartmann number (M) and the Convection-Conduction parameter (Nc) were utilized in the evaluation of heat transfer efficiency. Enhanced efficiency, as evidenced by decreased temperature and enhanced heat removal, was correlated with higher values of these parameters. Residual errors for both M and Nc were contained within a specified range of $ 10^{-6} $ to $ 10^{-14} $, thereby offering a quantitative assessment of the model's accuracy. As a crucial instrument for assessing the performance and dependability of predictive models, the residual analysis highlighted the impact of fractional orders on temperature fluctuations. As the Hartmann number increased, the rate of heat transfer accelerated, demonstrating the magnetic field's inhibitory effect on convection heat transport, according to the study. The complex relationship among Nc, fractional order (BETA), and temperature was underscored, which motivated additional research to improve our comprehension of the intricate physical mechanisms involved. This study enhanced the overall understanding of thermal dynamics in radial porous fins, providing significant implications for a wide array of applications, including aerospace systems and heat exchangers.</p></abstract>

Experimental surface runoff hydrographs from linear impervious subcatchments for rainfalls of extremely high intensity

This study focuses on lab-scale experimental runoff hydrographs from a linear completely impervious plane subcatchment. An improved method of surface runoff physical modelling was developed, allowing for expanded laboratory hydrograph simulations up to a linear scale of 10. Model rains of different intensities and durations were applied, and digital online data processing techniques were employed to ensure high time resolution and accurate flow rate determination. The experimental hydrographs were analyzed in a dimensionless form to facilitate generalization and comparison with widely used nonlinear reservoir method and unit hydrograph method. Wave-like fluctuations of the flow rate were observed in most experimental hydrographs as they approached the maximum runoff. The dimensionless phase time of the experimental hydrographs showed an increasing trend with higher rainfall intensity, and a power-law equation was derived to approximate this relationship. An averaged dimensionless runoff hydrograph was obtained by processing individual hydrographs, and it was approximated by the DR-Hill-Zerobackground model for the initial stage during the rainfall and by the Weibull model for the later stage, after the rainfall stopped. The findings of this study have significant implications for modelling surface runoff from small urban subcatchments, particularly under critical rainfall events with extremely high intensity.

Impact of Convection and Rotation on Advanced Thermal Energy Storage Using Nanoencapsulated Phase Change Materials in Wavy Enclosures

Free convection heat transfer in hybrid nanofluids in a differentially heated wavy enclosure is studied. The wavy enclosure moves at a constant counterclockwise rotational speed along its longitudinal axis. The enclosure is filled with a hybrid nanofluids consisting of water (H2O) and nanoencapsulated phase change materials (NEPCMs). These NEPCMs consist of a polyurethane coating and a core of N‐nonadecane, which undergoes a phase transition and has the capacity to retain or emit a significant quantity of latent heat. The dimensionless forms of the governing equations have been solved using finite element method. The validity of the present code is demonstrated by comparing its predictions with published results. The governing parameters under consideration are the corrugated number, 0 ≤ N ≤ 3, the volume fraction of hybrid nanoparticles, 0.0 ≤ ϕ ≤ 0.05, the Taylor number, 8 × 102 ≤ TaH2O ≤ 2 × 104. Changing the rotation speed is found to alter the melting and solidification zones in terms of pathways and size zones. The melting zone has a large size at moderate wave number, and its size shrinks and shifts downward as the wave number increases. An increase in the heat transfer rate values up to 38% is obtained when the concentration is adjusted from 1% to 5% for N = 1.

Response of Non-local and Heat Source in Moore-Gibson-Thompson Theory of Thermoelasticity with Hyperbolic Two Temperature

A new mathematical model of the Moore–Gibson–Thompson (MGT) theory of thermoelasticity under non-local and hyperbolic two-temperature (HTT) has been developed. The preliminary equations are put in two-dimensional form and are converted into dimensionless form. The obtained equations are simplified by applying potential functions. The Laplace transform w.r.t time variable and Fourier transforms w.r.t space variable are employed in the resulting equations. The assumed model has been used to explore the outcome of heat source in the form of a laser pulse decaying with time and moving with constant velocity in one direction. The problem is further examined with normal distributed force and ramp type thermal source. In the transformed domain, the physical field quantities like displacements, stresses, conductive temperature, and thermodynamic temperature are obtained. The resulting expressions are obtained numerically with the numerical inversion technique of the transforms. In simulation, various impacts such as non-local, heat source velocity-time, and HTT are examined and presented in the form of figures. Unique results are also deduced.

Significance of Melting Heat Transfer, Inclined Magnetic Field, and Thermal Radiation on the Dynamics of Williamson Nanofluid Above a Stretching Sheet

This study investigates the melting heat transfer in MHD flow that occurs when the flow is past a stretched sheet. With the use of the boundary layer concept, a set of non-linear ODEs is derived from a system of PDEs of motion and energy. After transforming the non-linear ODEs and their boundary conditions into dimensionless form with the use of appropriate similarity conversions, the equations are then numerically solved by employing the MATLAB inbuilt solver bvp4c method in conjunction with the shooting methodology. Through the use of a variety of charts and tables, the authors analyze and describe in depth the effects that relevant factors have on a variety of flow fields. As melting factor (Me) increases, it is discovered that the effect of Me on fluid temperature and velocity distributions decreases. Williamson parameter and inclined magnetic profile are shown to have decreasing impact on velocity and momentum parameter. After that, the findings are compared with the earlier published findings in limited situations of the issue, and it is discovered that they are in exceptional specify with those findings.

Unsteady MHD Free Convection Flow of a Second Grade Casson Fluid with Ramped Wall Temperature

The present study delves into the analysis of unsteady free convection flow involving a non-Newtonian Casson fluid adjacent to an infinitely tall vertical plate. The primary objective of this article is to examine the flow behaviour of a second-grade Casson fluid under varying critical parameters. The plate exhibits a gradual increase in wall temperature and is situated within a porous medium. The governing equations are transformed into a dimensionless form, using non dimensionless variables. The method of Laplace transform (MOLT) is employed to derive accurate solutions for the temperature and velocity within the flow field. To enhance comprehension of the issue, The impact of different physical parameters on the flow field has been examined through the utilization of graphs and tables. Outcome of the problem was compared with existing one which was in good agreement. The study revealed that the velocity magnitude was lower in the scenario with ramped temperature compared to the scenario with isothermal temperature. Finally, skin friction and Nusselt numbers of the present work are tabulated. The significant outcome of the present work is that the flow field for the present phenomena is same as that of the existing one in absence of radiation parameter and heat source parameter when, u(0,t)=0, β=∞.