Effect Of Prandtl Number Research Articles

Two-dimensional Rayleigh–Bénard convection without boundaries

We study the effects of Prandtl number $\mathit {Pr}$ and Rayleigh number $\mathit {Ra}$ in two-dimensional Rayleigh–Bénard convection without boundaries, i.e. with periodic boundary conditions. For Prandtl numbers in the range $10^{-3} \leqslant \mathit {Pr} \leqslant 10^2$ , the viscous dissipation scales as $\epsilon _\nu \propto \mathit {Pr}^{1/2}\mathit {Ra}^{-1/4}$ , which is based on the observation that enstrophy $\langle {\omega ^2}\rangle \propto \mathit {Pr}^0 \mathit {Ra}^{1/4}$ , and the Nusselt number tends to follow the ‘ultimate’ scaling $\mathit {Nu} \propto \mathit {Pr}^{1/2}\mathit {Ra}^{1/2}$ for all values of $\mathit {Pr}$ considered. The inverse cascade of kinetic energy forms the power-law spectrum $\hat {E}_u(k) \propto k^{-2.3}$ , which is close to $k^{-11/5}$ proposed by the Bolgiano–Obukhov (BO) scaling. The potential energy flux is not constant, in contrast to one of the main assumptions underlying the BO phenomenology. So, the direct cascade of potential energy forms the power-law spectrum $\hat {E}_\theta (k) \propto k^{-1.2}$ , which deviates from the expected $k^{-7/5}$ . Finally, at $\mathit {Pr} \to 0$ and $\infty$ , we find that the dynamics is dominated by vertically oriented elevator modes that grow without bound, even at high Rayleigh numbers and with large-scale dissipation present.

Modelling and Simulation of the Effect of Prandtl and Soret Numbers on Mass Concentration with Magnetic Intensity in a Blood Channel

Modelling and Simulation of the Effect of Prandtl and Soret Numbers on Mass Concentration with Magnetic Intensity in a Blood Channel

Thermal study of single phase nanofluid model using radiative γAl2O3 nanomaterial under Hall current and momentum slip phenomena

The applications of nanofluids frequently occur in thermal insulation, cooling of electronic instruments, chemical engineering and to control the heat transfer during many experimental setups, interaction of nanoparticles with water for plants growth, crop improvement, crop protection, plant biology and biological sciences. Therefore, this research emphasis on the performance of radiated γAl2O3/H2O by adding the influential physical constraints (momentum slip and Hall current). The governing model for the flow through a disk with slippery surface is transformed into the final version via necessary mathematical operations and analyzed the problem numerically. Further, the thermal conductivity is computed using Effective Prandtl Number Model (EPNM) by taking nanoparticles amount up to 0.06%. After careful analysis of the problem, it is examined that when Al2O3 nanoparticles amount added in the range of 0.01%-0.06% then EPN increased from 100.398% to 102.636%, density from 100.298% to 101.786% and dynamic viscosity from 100.742% to 104.823%, respectively. Moreover, the electrical and thermal conductivities varied from 100.3% to 101.811% to 101.65%. The moving dynamics of Al2O3/water can be increased or controlled for [Formula: see text] and [Formula: see text], respectively. The Hall index n from 1.0, 3.0, 5.0, 7.0 strongly opposed the velocity and unsteadiness number slightly favor it. Further, the heat transport rate of Al2O3/water improved from 1.05371 to 1.41891 and the shear drag enhanced absolutely from [Formula: see text] to [Formula: see text] against the high nanoparticles amount.

Understanding the effect of Prandtl number on momentum and scalar mixing rates in neutral and stably stratified flows using gradient field dynamics

Recently, direct numerical simulations (DNS) of stably stratified turbulence have shown that as the Prandtl number ( $Pr$ ) is increased from 1 to 7, the mean turbulent potential energy dissipation rate (TPE-DR) drops dramatically, while the mean turbulent kinetic energy dissipation rate (TKE-DR) increases significantly. Through an analysis of the equations governing the fluctuating velocity and density gradients we provide a mechanistic explanation for this surprising behaviour and test the predictions using DNS. We show that the mean density gradient gives rise to a mechanism that opposes the production of fluctuating density gradients, and this is connected to the emergence of ramp cliffs. The same term appears in the velocity gradient equation but with the opposite sign, and is the contribution from buoyancy. This term is ultimately the reason why the TPE-DR reduces while the TKE-DR increases with increasing $Pr$ . Our analysis also predicts that the effects of buoyancy on the smallest scales of the flow become stronger as $Pr$ is increased, and this is confirmed by our DNS data. A consequence of this is that the standard buoyancy Reynolds number does not correctly estimate the impact of buoyancy at the smallest scales when $Pr$ deviates from 1, and we derive a suitable alternative parameter. Finally, an analysis of the filtered gradient equations reveals that the mean density gradient term changes sign at sufficiently large scales, such that buoyancy acts as a source for velocity gradients at small scales, but as a sink at large scales.

Unveiling the Triple Diffusion Bioconvective Applications for Couple Stress Nanofluid Due To an Oscillating Regime with Variable Thermal Features

Thermal engineering and industrial processes see various multidisciplinary applications due to the enhanced thermal performances of nanomaterials. The nanomaterials preserve a profound breakthrough in enhancing the heat transfer phenomenon. The objective of the current investigation is to address the thermal applications of couples-stress nanofluid in the presence of triple diffusion effects. The analysis is subject to the bioconvective significance of the suspension of microbes. The viscosity and thermal conductivity of a couple stress fluids are assumed to be variable. Moreover, we endorse linear thermal radiation effects and approach the problem with an effective Prandtl number. The source of flow is an oscillatory, porous stretching surface. Based on suggested flow assumptions, the model is represented via nonlinear couple partial differential equations (PDEs). We employ the homotopy analysis scheme to forecast the analytical simulations. The physical outcomes for the involved parameters are observed for the modeled problem. Various aspects based on the deduced results are claimed. Based on the performed analysis, it is observed that the magnitude of skin friction decreases due to variations in the couple-stress fluid parameter. The heat increases with the modified Dufour number and variable thermal conductivity coefficient. Furthermore, an increasing behavior of nanoparticle solutal concentration has been observed due to the Dufour-Lewis number.

Prandtl number effects on heat transfer in viscoelastic turbulent channel flow

Prandtl number effects on heat transfer in viscoelastic turbulent channel flow

Large eddy simulations of flow over additively manufactured surfaces: Impact of roughness and skewness on turbulent heat transfer

Additive manufacturing creates surfaces with random roughness, impacting heat transfer and pressure loss differently than traditional sand–grain roughness. Further research is needed to understand these effects. We conducted high-fidelity heat transfer simulations over three-dimensional additive manufactured surfaces with varying roughness heights and skewness. Based on an additive manufactured Inconel 939 sample from Siemens Energy, we created six surfaces with different normalized roughness heights, Ra/D=0.001,0.006,0.012,0.015,0.020, and 0.028, and a fixed skewness, sk=0.424. Each surface was also flipped to obtain negatively skewed counterparts (sk=−0.424). Simulations were conducted at a constant Reynolds number of 8000 and with temperature treated as a passive scalar (Prandtl number of 0.71). We analyzed temperature, velocity profiles, and heat fluxes to understand the impact of roughness height and skewness on heat and momentum transfer. The inner-scaled mean temperature profiles are of larger magnitude than the mean velocity profiles both inside and outside the roughness layer. This means, the temperature wall roughness function, ΔΘ+, differs from the momentum wall roughness function, ΔU+. Surfaces with positive and negative skewness yielded different estimates of equivalent sand–grain roughness for the same Ra/D values, suggesting a strong influence of slope and skewness on the relationship between roughness function and equivalent sand–grain roughness. Analysis of the heat and momentum transfer mechanisms indicated an increased effective Prandtl number within the rough surface in which the momentum diffusivity is larger than the corresponding thermal diffusivity due to the combined effects of turbulence and dispersion. Results consistently indicated improved heat transfer with increasing roughness height and positively skewed surfaces performing better beyond a certain roughness threshold than negatively skewed ones.

Double-Diffusive Natural Convection in L-Shaped Cavity by Lattice Boltzmann Method: Numerical Study

The double diffusive natural convection is studied numerically on an L-shaped cavity using lattice Boltzmann method (LBM). The top and right side of the cavity is insulated, the left and the bottom side of the cavity are maintained at high temperature, and remaining sides are considered as cold wall. This study is carried out using a two-dimensional nine-directional (D2Q9) lattice structure. Single relaxation time model is adopted to solve the LBM equations. The effects of different Rayleigh numbers (Ra = 103–105), aspect ratio (0.2–0.8), Prandtl number (Pr = 0.054, 0.7, 6.2, and 50), Lewis number (2), and buoyancy ratio (−2) on the temperature, concentration, and streamline contours are presented. For the selected range of operating parameters in this study, the heat and mass transfer are more pronounced for horizontal wall than vertical. At low Pr, the difference between horizontal wall to vertical wall average Nusselt number (Nu) is 11.2% and when Pr = 50, the same difference in average Nu is 37.5%. Similarly, the average Sherwood number between horizontal and vertical wall differences are 19.5% and 31.7%. For Ra = 105, the convection rate reduced by 46% and mass diffusion reduced by 52% between Pr = 0.054–50.

A comprehensive review on the Dynamical behavior of heat and fluid flow mechanism: Thermal performance across different geometries

The prominent novelty of current review is to exhibit the fluctuating and oscillatory convective heat transfer properties along various geometries with magnetic force, variable density, Prandtl number, buoyancy force and magnetic Prandtl number effects. The significance of present work is to illustrate a comprehensive review on transient convective heat transfer. Transient convective heat transfer plays an essential role in various technological and environmental applications, including climate control, structure safety, engines, thermal control, computer heating and cooling, and energy safety. The literature primarily focuses on steady temperature and velocity domains, with few studies exploring time-varying fluid flow in forced, natural, or mixed convective mechanisms with different methods. In current review, justification of results was performed by using oscillating stokes conditions directly in partial differential models. The similarity variables and stream functions are used in literature but in current review, the primitive variable transformation is used with implicit form of finite difference method and Gaussian elimination technique through FORTRAN and Tecplot-360 programming tools. The governing model is reduced into steady, real and imaginary form to explore steady and oscillating convective heat transmission. Transient flows have gained significance due to their ability to achieve large oscillating convective heat transfer rates. Compared with steady movement, oscillating flows exhibit higher velocity variations along the heated surface. Periodic flow produces an improved transient surface heat transmission rate than steady flow. Predicting and controlling transients in thermal exchangers requires a concept of transient forced convection heat transport. Transient convective thermal transmission solutions are important for ensuring the effectiveness and reliability of electrical components, nuclear and thermal power stations, heat-generating engines, steam turbines, condensation systems, catalytic converters, heat shielding for spacecraft, electrical devices, internal combustion engines, air conditioning and refrigerator components, cooling networks for batteries, generators, and transformers. It is found that the frequency of convective heat transport enhances through periodic and oscillating stokes variables. It was depicted that the higher amplitude in convective heat transfer was displayed for each choice of magnetic force parameter around two angles π/4 and π of circular magnetized surface. It was depicted that the maximum transient convective heat transmission was reported along vertical angle π/2 with buoyancy force, Prandtl and magnetic Prandtl values.

Fractional numerical analysis of γ-Al2O3 nanofluid flows with effective Prandtl number for enhanced heat transfer

Abstract Nanoparticles have gained recognition for significantly improving convective heat transfer efficiency near boundary layer flows. The characteristics of both momentum and thermal boundary layers are significantly influenced by the Prandtl number, which holds a crucial role. In this vein, the current study conducted a detailed computational analysis of the mixed convection flow of $\gamma$Al$_2$O$_3$-H$_2$O and $\gamma$Al$_2$O$_3$-C$_2$H$_6$O$_2$ nanofluids over a stretching surface. This research integrates an effective Prandtl number, utilizing viscosity and thermal conductivity models based on empirical findings. Additionally, a unique double-fractional constitutive model is debuted to accurately evaluate the effective Prandtl number’s function in the boundary layer. The equations were solved using a numerical technique that combined the finite-difference method with the L$_1$ algorithm. This investigation presents numerical findings related to the velocity, temperature distributions, wall shear stress coefficient, and heat transfer coefficient, contrasting scenarios with and without the effective Prandtl number. The research shows that integrating nanoparticles into the base fluids reduces the temperature of the nanofluid with an effective Prandtl number while enhancing the heat transfer rate irrespective of its presence. Nonetheless, the introduction of a fractional parameter reduced the heat transfer efficiency within the system. Notably, the $\gamma$Al$_2$O$_3$-C$_2$H$_6$O$_2$ nanofluid demonstrates superior heat transfer enhancement capabilities compared to its $\gamma$Al$_2$O$_3$-H$_2$O counterpart but also exacerbates the drag coefficient more significantly. Many practical applications of this study include electronics cooling, industrial process heat exchangers, and rotating and stationary gas turbines in power plants, and efficient heat exchangers in aircraft.

Application of discrete symmetry to natural convection in vertical porous microchannels

Abstract This work focuses on the study of natural convection in a flat porous microchannel with asymmetric heating. The novelty of the work lies in the fact that for the first time the method of discrete symmetries was used to analyze the complete system of Navier–Stokes and energy equations in a two-dimensional approximation. Analytical solutions for velocity and temperature profiles have been derived based on symmetry analysis, taking into account boundary conditions such as slip and temperature jump at the channel walls. The effect of Grashof, Knudsen, Darcy, and Prandtl numbers on the flow characteristics in the microchannel and heat transfer coefficients was elucidated. At high Grashof numbers, an ascending flow near the hot wall and a descending flow near the cold wall arise. Increasing the Knudsen number leads to an increase in the velocity, temperature jump at the walls and a decrease in heat transfer coefficients. As the Darcy number increases, velocities amplify in both ascending and descending flows. The temperature jump at the hot wall grows up, while it remains unchanged at the cold wall. In the same time, the heat transfer coefficient at the hot wall decreases.

Dominant heat transfer mechanism with conical roughness in a cubical box in turbulent Rayleigh–Bénard convection

In the present study, we numerically investigate the effect of Prandtl number on the heat transfer mechanism in turbulent Rayleigh–Bénard convection inside a cubical box endowed with conical roughness elements. The Rayleigh number is kept fixed at Ra=108, while the Prandtl number (Pr) varies from 1 to 50. In contrast to the monotonic increasing trend of the Nusselt number (Nu∼Pr0.27) in the two-dimensional (2D) roughness explored previously [Sharma et al., “Influence of Prandtl number in turbulent Rayleigh-Bénard convection over rough surfaces,” Phys. Rev. Fluids 7, 104609 (2022)], it assumes an invariant behavior (∼Pr0.012) for three dimensional (3D), though it is approximately 50% higher than its smooth counterpart. Flow intensity, measured in terms of Reynolds number (Re), drops with increasing Pr showing consistently lower magnitude for the 3D configuration. The addition of roughness elements is observed to disrupt the preferred orientation of large-scale circulation (LSC). The effect is predominant for lower Pr, where the roughness interferes most with the natural bias of LSC toward the diagonal planes of the cubical box. The analysis of plume statistics reveals that both coverage and intensity of plumes are augmented for the roughened cell. Increased homogeneity in the flow at higher Pr is reflected by the emergence of a more pronounced and distinguishable peak in probability density functions of temperature and velocity. Temporal spectra and variance data substantiate augmented intensity of fluctuations in the rough cell, while behavioral differences in the flow at different Pr are elucidated by using cross correlation of vertical velocity and temperature fluctuations.

Flow instabilities driven by Prandtl number effect and rotation-depth coupling effect in the cylinder with a top disk

We employed linear stability analysis to investigate the Prandtl number (Pr) effect and rotation-depth coupling effect on the complex flow instability in a cylinder with a top disk. The dependence of the critical Rayleigh number on the Pr number, as well as the relationship between the critical disk rotation rate and the aspect ratio at Pr = 6.7, were obtained. Results reveal that the flow stability increases with increasing Pr number, and the convection instability stems from the inertial mechanism for 0.011 ≤ Pr ≤ 0.0258 and thermal buoyancy mechanism for 1.4 ≤ Pr ≤ 28.01. Regarding the rotation-depth coupling effect for the melt with Pr = 6.7, a decreasing melt level leads to a general increase in the critical disk rotation rate. Furthermore, within the interval of aspect ratio (ratio of depth to cylinder radius) 0.7 ≤ Γ ≤ 1.62, multiple transitions of the flow state from stable to unstable and then back to stable were observed with increasing disk rotation rate before finally becoming unstable. Energy analysis reveals that multiple transitions in the flow state are attributed to the competition between thermal buoyancy and inertial mechanisms.

Effects of turbulent Prandtl number on supercritical carbon dioxide turbulent flow with high heat flux in vertical round tube

Supercritical carbon dioxide (sCO2) is a promising working medium for coal-fired power plants, high-temperature solar power systems, nuclear reactor systems, and fuel cells owing to its high efficiency and inertness. In these cases, the sCO2 is in a round tube under high temperature and pressure, far from the pseudo-critical point. Here, the thermophysical properties of sCO2 changes, resulting in large prediction errors. In this study, a conjugate heat transfer model with the k-ε turbulent model was created to analyze the tube performance of the sCO2, and the effects of turbulent Prandtl number (Prt) on the sCO2 turbulent flow with high heat flux were examined through experimental and numerical investigations. Prt had a considerable effect on the performance of the sCO2 turbulent flow far from the pseudo-critical point. The mean relative errors of the inner wall temperature and convective heat transfer coefficient were reduced by approximately 13% and 27%, respectively, when Prt was decreased from 1 to 0.55. For the sCO2 turbulent flow with a high heat flux, constant Prt values of 0.55–0.6 were applicable. The findings afford key insights for the development of sCO2 turbulent flow with high heat flux.

Numerical analysis of thermal improvement in hydrogen‐based host fluids under buoyancy force and EPNM effects: Study for vertical cylinder

AbstractThe nanofluids became much of interest due to their superior heat mechanism over the conventional fluids. The addition of nanoparticles in the host solvent enhances the internal ability of the liquid to store and transmit heat. Therefore, these fluids are widely used in biomedical engineering, detergents, medication, applied thermal engineering, mechanical, and chemical engineering and so forth. Keeping in mind the significance of nanofluids, this study is conducted to investigate the comparative heat transmission in and under the Effective Prandtl Number Model (EPNM) effects over a vertical permeable cylinder. Formulation of the model is carried out over a vertical cylinder about the stagnation point and the heat transport model is achieved after the successful implementation of the cylindrical stream function, nanofluids effective characteristics, and cylindrical similarity equations. The mathematical treatment was done via RK technique and furnished the results. The nanofluids have the capacity to control the fluid motion more effectively than ordinary fluid and combined convection is better where rapid fluid movement is desired. In the existence of EPNM, higher heat transmission is achieved and is prominent for based on their thermophysical values. Further, the skin friction and Nusselt number are optimum for against .

Prandtl number effects on extreme mixing events in forced stratified turbulence

Relatively strongly stratified turbulent flows tend to self-organise into a ‘layered anisotropic stratified turbulence’ (LAST) regime, characterised by relatively deep and well-mixed density ‘layers’ separated by relatively thin ‘interfaces’ of enhanced density gradient. Understanding the associated mixing dynamics is a central problem in geophysical fluid dynamics. It is challenging to study LAST mixing, as it is associated with Reynolds numbers $Re := UL/\nu \gg 1$ and Froude numbers $Fr :=(2{\rm \pi} U)/(L N) \ll 1$ ( $U$ and $L$ being characteristic velocity and length scales, $\nu$ the kinematic viscosity and $N$ the buoyancy frequency). Since a sufficiently large dynamic range (largely) unaffected by stratification and viscosity is required, it is also necessary for the buoyancy Reynolds number $Re_{b} := \epsilon /(\nu N^{2}) \gg 1$ , where $\epsilon$ is the (appropriately volume-averaged) turbulent kinetic energy dissipation rate. This requirement is exacerbated for oceanically relevant flows, as the Prandtl number $Pr := \nu /\kappa = {O}(10)$ in thermally stratified water (where $\kappa$ is the thermal diffusivity), thus leading (potentially) to even finer density field structures. We report here on four forced fully resolved direct numerical simulations of stratified turbulence at various Froude ( $Fr=0.5, 2$ ) and Prandtl ( $Pr=1, 7$ ) numbers forced so that $Re_{b}=50$ , with resolutions up to $30\,240 \times 30\,240 \times 3780$ . We find that, as $Pr$ increases, emergent ‘interfaces’ become finer and their contribution to bulk mixing characteristics decreases at the expense of the small-scale density structures populating the well-mixed ‘layers’. However, extreme mixing events (as quantified by significantly elevated local destruction rates of buoyancy variance $\chi _0$ ) are always preferentially found in the (statically stable) interfaces, irrespective of the value of $Pr$ .

Effect of Prandtl number and free-stream orientation on global parameters for flow past a heated square cylinder

In this study, an in-depth examination of the aerodynamic parameters involving forced and mixed convection around a heated square cylinder is presented. The ranges of Prandtl number (Pr), Richardson number (Ri), and flow orientation (α) are kept as 0.71 ≤ Pr ≤ 1000, 0 ≤ Ri ≤ 1.6, 0° ≤ α ≤ 90°, while the Reynolds number (Re) and the cylinder orientation (ϕ) are kept fixed as Re = 100 and ϕ = 0°, respectively. The flow is considered as two-dimensional (2D), steady, laminar, incompressible, and viscous. The buoyancy effects are taken into account through the Boussinesq approximation. At lower Pr, the flow shifts from unsteady to steady with increasing Ri. This transition persists at higher Ri with increasing Prandtl values. The flow remains consistently unsteady at α = 90°. Isotherm crowding intensifies with higher Pr and/or Ri across all flow inclinations. Across the complete spectrum of flow angles, it is noted that the mean lift coefficient rises as the Richardson number increases. Additionally, the mean drag coefficient reaches its peak at Ri = 1.6 when Pr = 0.71. The findings reveal that the Strouhal number (St) rises as the Richardson number (Ri) increases, and it decreases as the Prandtl number (Pr) increases. The mean Nusselt number (Nu¯) demonstrates an upward trend as the Prandtl number increases, with Ri held constant. It is also observed that Nu¯ is more sensitive to the Prandtl number than the Richardson number and is maximum at Pr = 1000 for the selected range of flow orientations.

Heat and mass exchanger analysis for Ree-Eyring hybrid nanofluid through a stretching sheet utilizing the homotopy perturbation method

An investigation is being carried out to describe the flow of a Ree-Eyring hybrid nanofluid by a stretch flow. SiO2 and GO are being examined for use as hybrid nanoparticles in the accumulation with carboxymethyl cellulose (CMC) water at low concentrations. A concentration of between 0.0 and 0.4 % is suggested for use as a base fluid (CMC− water). The model equations are firstly converted into ordinary differential equations through suitable alteration. The Homotopy Perturbation Method (HPM) and R–K method were applied to governing (ODEs). The produced results were identified by the R–K numerical technique. Both of these methods of approval demonstrate that our approach achieves an acceptable level of accuracy. The obtained results are numerical data for the behaviours of the velocity, temperature, and concentration of nanoparticles about other physical factors. Multiple graphs illustrating the conclusions of physical significance are shown and thoroughly analyzed. The most important findings from this research show that the stretching sheet has a role in determining the depth of the boundary layer. By raising the Weissenberg number, the thickness of the boundary layer will be enhanced, which will lead to an augmentation in the velocity of the non-Newtonian fluid. Moreover, the Prandtl number was a second crucial variable that was explored, it follows that enhancing the Prandtl number effect in a lessening in the thermal layer. The last parameter was the Schmidt number, and increasing in Schmidt number caused a significant reduction in the mass of the fluid.

Numerical and optimal thermal analysis of non-Newtonian fluids flow over a wedge by using response surface methodology (RSM): Sensitivity analysis

The numerical and optimal thermal analysis of Casson fluid flow over a wedge is investigated in this work. To perform numerical and sensitivity analysis we have convert third order non-linear PDEs into set of ODEs by using similarity transformations along with boundary conditions. These equations are simulated using numerical technique Keller Box method and then compared the values of skin friction coefficient and Nusselt number with those existing in literature and found excellent agreement. Then by using these numerical data we have performed sensitivity analysis by using Response Surface Methodology (RSM). ANOVA tables are generated and developed a correlations between input parameters and output responses. The coefficient of determination for output responses skinfriction coefficient and Nusselt number are 96.50% and 99.51% respectively which shows the best fitted correlations. Finally, we have performed sensitivity analysis which reflects that skinfriction coefficient is more sensitive to Falkner–Skan exponent (m) and there is no effect of Prandtl number (Pr) on skinfriction coefficient. It is also concluded that Nusselt number is sensitive to Prandtl number (Pr) and obtains its optimum value with variation in Prandtl number (Pr).

Analysis of MHD and Heat Transfer Characteristics of Thermally Radiative Upper-Convected Maxwell Fluid Flow between Moving Plates: Semi-Analytical and Numerical Solution

The current paper studies the MHD and heat transfer characteristics of radiative upper-convected Maxwell fluid flow between two plates approaching or receding from each other with injection at the fixed lower porous plate. The governing momentum and energy equations are reduced into non-linear ordinary differential equations employing similarity transformations. With the help of the Homotopy Perturbation Method (HPM), an approximate analytic solution is obtained. This work aims to determine the effects of Reynolds number (R), Deborah number (De), Radiation parameter (Rd), Magnetic parameter (M), and Prandtl number (Pr) on the velocity and temperature profiles. It is observed that the Deborah number has a direct impact on the velocity profile when there is a squeezed flow. It is also observed that the magnetic parameter shows an indirect impact on the temporal distribution for both the upper plate moving away and towards the lower. The variations in the significant physical parameters on the coefficient of skin friction and heat transfer rates are also calculated. The results are then compared with the classical finite difference method and are in excellent agreement. It is found that larger the magnetic parameter, the dominance of viscous forces retards the velocity in the core region, and the increase in radiation parameter suppresses the heat transfer rates. This study is helpful in industrial applications, specifically in polymer processing.