An MHD Fluid Flow over a Porous Stretching/Shrinking Sheet with Slips and Mass Transpiration

In the present paper, an MHD three-dimensional non-Newtonian fluid flow over a porous stretching/shrinking sheet in the presence of mass transpiration and thermal radiation is examined. This problem mainly focusses on an analytical solution; graphene water is immersed in the flow of a fluid to enhance the thermal efficiency. The given non-linear PDEs are mapped into ODEs via suitable transformations, then the solution is obtained in terms of incomplete gamma function. The momentum equation is analyzed, and to derive the mass transpiration analytically, this mass transpiration is used in the heat transfer analysis and to find the analytical results with a Biot number. Physical significance parameters, including volume fraction, skin friction, mass transpiration, and thermal radiation, can be analyzed with the help of graphical representations. We indicate the unique solution at stretching sheet and multiple solution at shrinking sheet. The physical scenario can be understood with the help of different physical parameters, namely a Biot number, magnetic parameter, inverse Darcy number, Prandtl number, and thermal radiation; these physical parameters control the analytical results. Graphene nanoparticles are used to analyze the present study, and the value of the Prandtl number is fixed to 6.2. The graphical representations help to discuss the results of the present work. This problem is used in many industrial applications such as Polymer extrusion, paper production, metal cooling, glass blowing, etc. At the end of this work, we found that the velocity and temperature profile increases with the increasing values of the viscoelastic parameter and solid volume fraction; additionally, efficiency is increased for higher values of thermal radiation.

Production of Urea/Acetylated-ligninsulfonate Matrix as SRFs and Investigation the Effect of Hydrodynamic Conditions on the Release Rate Using Biot Number

Background: This study aimed to investigate the effect of the hydrodynamic condition on the release rate of urea/acetylated lignin sulfonate (Ac-LS) matrix as slow-release fertilizers (SRFs). Therefore, two models were developed using the mass transfer balance for the finite/infinite volume of fluids, solving finite integral transform/separation of a variable. In these models, the Biot number that verified the hydrodynamic condition appeared. Methods: In the experimental section, the urea/Ac-LS matrix fertilizer was produced. The morphological, thermal, chemical, and mechanical properties of the LS, Ac-LS, urea, and urea/Ac-LS matrix were analyzed using Fe-SEM, TGA, XRD, and SANTAM. Finally, the nitrogen release of the matrix fertilizer was investigated at 25°C for different impeller speeds. Results: The results showed that the thermal and mechanical resistance of urea/Ac-LS, with strong interaction, increased rather than pure urea or Ac-LS. The models were also validated using experimental data. The results further showed that in both states, the external resistance of the mass transfer decreased with increasing impeller speed, and the nitrogen release rate increased with increasing Biot number. Conclusion: It was also observed that, in a given hydrodynamic condition, initially, the release rate in the finite environment was less than the infinite; however, after a while, the type of environment did not affect the release rate

Study of 3-D Prandtl Nanofluid Flow over a Convectively Heated Sheet: A Stochastic Intelligent Technique

In this article, we examine the three-dimensional Prandtl nanofluid flow model (TD-PNFM) by utilizing the technique of Levenberg Marquardt with backpropagated artificial neural network (TLM-BANN). The flow is generated by stretched sheet. The electro conductive Prandtl nanofluid is taken through magnetic field. The PDEs representing the TD-PNFM are converted to system of ordinary differential equations, then the obtained ODEs are solved through Adam numerical solver to compute the reference dataset with the variations of Prandtl fluid number, flexible number, ratio parameter, Prandtl number, Biot number and thermophoresis number. The correctness and the validation of the proposed TD-PNFM are examined by training, testing and validation process of TLM-BANN. Regression analysis, error histogram and results of mean square error (MSE), validates the performance analysis of designed TLM-BANN. The performance is ranges 10−10, 10−10, 10−10, 10−11, 10−10 and 10−10 with epochs 204, 192, 143, 20, 183 and 176, as depicted through mean square error. Temperature profile decreases whenever there is an increase in Prandtl fluid number, flexible number, ratio parameter and Prandtl number, but temperature profile shows an increasing behavior with the increase in Biot number and thermophoresis number. The absolute error values by varying the parameters for temperature profile are 10−8 to 10−3, 10−8 to 10−3, 10−7 to 10−3, 10−7 to 10−3, 10−7 to 10−4 and 10−8 to 10−3. Similarly, the increase in Prandtl fluid number, flexible number and ratio parameter leads to a decrease in the concentration profile, whereas the increase in thermophoresis parameter increases the concentration distribution. The absolute error values by varying the parameters for concentration profile are 10−8 to 10−3, 10−7 to 10−3, 10−7 to 10−3 and 10−8 to 10−3. Velocity distribution shows an increasing trend for the upsurge in the values of Prandtl fluid parameter and flexible parameter. Skin friction coefficient declines for the increase in Hartmann number and ratio parameter Nusselt number falls for the rising values of thermophoresis parameter against Nb.

Effects of Non-Darcy Mixed Convection Over a Horizontal Cone With Different Convective Boundary Conditions Incorporating Gyrotactic Microorganisms On Dispersion

This paper discusses an investigation of the influence of dispersion impact on mixed convection flow over a horizontal cone within a non-Darcy porous medium subjected to convective boundary conditions. By imposing appropriate similarity transformations, the nonlinear partial differential equations governing flow, temperature, concentration, and microbe fields are reduced to a system of ordinary differential equations, which are then solved using the MATLAB BVP4C function. In a few circumstances, the research is brought to a strong conclusion by comparing the findings of the current study to previously published works. Mixed convection parameter λ, buoyancy parameters N1,N2, Lewis parameter Le, bioconvection lewis parameter Lb, Bioconvection peclet number Pe, Biot number Bi, Biot number of Mass transfer Bi,m and also Biot number of motile microorganism transfer Bi,n are all numerically calculated for various values of the dimensionless parameters of the problem. The results also reveal that, in the presence of dispersion effects, these parameters greatly influence the heat, mass, and motile microorganism transfer rates, as well as the corresponding velocity, temperature, concentration, and motile microorganism profiles.

Evaluation of a permissible roadbed thawing depth in permafrost

Roadbed thermal conditions in permafrost are subject to seasonal changes affecting roadway resilience. A roadbed thawing depth is important for road base processing, especially in permafrost. This research had the purpose of evaluation of a permissible roadbed thawing depth based on the Biot number reflecting general thermal resistance of roadbed layers. These results will contribute to understanding road bed thermal resistance and selection of roadway construction materials.

Soret and Dufour effects on a Casson nanofluid flow past a deformable cylinder with variable characteristics and Arrhenius activation energy

In this study, the effects of variable characteristics amalgamated with chemical reaction and Arrhenius activation energy are analyzed on a two-dimensional (2D) electrically conducting radiative Casson nanoliquid flow past a deformable cylinder embedded in a porous medium. The surface of the cylinder is deformable in the radial direction i.e., the z-axis. The impression of Soret and Dufour's effects boosts the transmission of heat and mass. The flow is analyzed numerically with the combined impacts of momentum slip, convective heat, and mass conditions. A numerical solution for the system of the differential equations is attained by employing the bvp4c function in MATLAB. The dimensionless protuberant parameters are graphically illustrated and discussed for the involved profiles. It is perceived that on escalating the velocity slip parameter and porosity parameter velocity field depreciates. Also, on escalating the radiation parameter and heat transfer Biot number a prominent difference is noticed in an upsurge of the thermal field. For growing values of Brownian motion and thermophoretic parameters, temperature field augments. On escalating the curvature parameter and porosity parameter, drag force coefficient upsurges. The outcome of the Soret number, mass transfer Biot number, and activation energy parameter is quite eminent on the concentration distribution for the sheet in comparison to the deformable cylinder. A comparative analysis of the present investigation with an already published work is also added to substantiate the envisioned problem.

A study of a computational BVP for heat transfer and friction drag in magnetohydrodynamics viscous flow of a nanofluid subject to the curved surface

The ongoing work investigates the features of Joule heating and convective condition over a magnetohydrodynamic stagnation point flow of [Formula: see text] nanofluid moving across a curved surface. Moreover, mass suction is supposed through the stretching/shrinking surface. The initially developed model of partial differential equations is transformed into the ordinary ones assisted by suitable similarity variables. Subsequently, the ultimate nonlinear model of ordinary differential equations is solved with the help of a built-in function bvp4c package in MATLAB. Several graphical results are plotted to see the influence of various dimensionless parameters over the velocity, temperature, heat transfer, and friction drag. We found that there exists an escalation in temperature with increasing values of curvature, Eckert number, Hartmann number, and Biot number; however, the velocity profile declines with large curvature, ratio parameter, and high concentration of nanoparticles. It is also important to note that the friction drag rises with the mass suction, and reduces with vast curvature, whereas the rate of heat transfer improves with suction and Biot number but lowers with Eckert number and Hartmann number.

The Effect of Biot Number on a One-Dimensional General Conduction Solution

Analytical solutions for thermal conduction problems are extremely important, particularly for verification of numerical codes. Temperatures and heat fluxes can be calculated very precisely, normally to eight or ten significant figures, even in situations involving large temperature gradients. It can be convenient to have a general analytical solution for a transient conduction problem in rectangular coordinates. The general solution is based on the principle that the three primary types of boundary conditions (prescribed temperature, prescribed heat flux, and convective) can all be handled using convective boundary conditions. A large convection coefficient closely approximates a prescribed temperature boundary condition and a very low convection coefficient closely approximates an insulated boundary condition. Since a dimensionless solution is used in this research, the effect of various values of dimensionless convection coefficients, or Biot number, are explored. An understandable concern with a general analytical solution is the effect of the choice of convection coefficients on the precision of the solution, since the primary motivation for using analytical solutions is the precision offered. An investigation is made in this study to determine the effects of the choices of large and small convection coefficients on the precision of the analytical solutions generated by the general convective formulation. Results are provided, in tablular and graphical form, to illustrate the effects of the choices of convection coefficients on the precision of the general analytical solution.