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This article investigates the visualizations of heatlines in a natural convection magnetohydrodynamic flow from a vertical cylinder via heat function concept. Fluid is electrically conducting in the existence of an applied magnetic field. The constitutive equations of time-dependent, coupled and highly nonlinear Jeffrey fluid model are evaluated mathematically by utilizing well-organized unconditionally stable finite-difference Crank–Nicolson method. Simulated results are given for several values of Deborah number and Hartmann number to present interesting aspects of the solution of the flow variables, friction factor and heat transfer rate. Results specify that required time to achieve time-independent state rapidly rises with the boosting values of Hartmann number. Boundary-layer flow visualization has been made using heatlines, isotherms and streamlines to perceive the understanding of heat and fluid flow. It is noticed that heat function value reduces for augmenting Hartmann number and also for all smaller physical parameter values and these heatlines become closer to the hot wall. It is also remarked that the hydromagnetic flow-field profiles concerning the Newtonian fluid show a different pattern from that of non-Newtonian Jeffrey fluid. [ABSTRACT FROM AUTHOR]

This article studies the pattern of heat lines in free convection non-Newtonian flow from a semi-infinite vertical cylinder via Bejan's heat function concept. The viscoelastic Jeffrey fluid model is employed. The time-dependent, coupled, nonlinear conservation equations for momentum and energy (heat) are solved computationally with the unconditionally stable finite difference Crank–Nicolson method. Extensive graphical results are presented for the influence of Deborah number (viscoelastic parameter) and Prandtl number (with ranges 0–0.8 and 0.68–7.2, respectively) on thermal and flow characteristics including time histories of overall skin friction and heat transfer rate. Lower values of Deborah number indicate that the material acts in a more fluid-like manner, whereas the higher values of Deborah number correspond to the material showing characteristics more associated with a solid. The solutions indicate that the time taken for the flow-field variables to achieve the steady state is increased with higher values of Deborah number. Boundary flow visualization is presented using heat lines, isotherms and streamlines. It is observed that as Deborah number increases the intensity of heat lines increases and they tend to deviate from the hot cylindrical wall. Furthermore, the flow-field variables for the Newtonian fluid case exhibit a significantly different pattern from that of Jeffrey fluid. [ABSTRACT FROM AUTHOR]

Entropy generation is an important aspect of modern thermal polymer processing optimization. Many polymers exhibit strongly non‐Newtonian effects and dissipation effects in thermal processing. Motivated by these aspects in this study, a numerical analysis of the entropy generation with viscous dissipation effect in an unsteady flow of viscoelastic fluid from a vertical cylinder is presented. The Reiner‐Rivlin physical model of grade 2 (second‐grade fluid) is used, which can envisage normal stress variations in polymeric flow‐fields. Viscosity variation is included. The obtained governing equations are resolved using implicit finite difference method of Crank‐Nicolson type with well imposed initial and boundary conditions. Key control parameters are the second‐grade viscoelastic fluid parameter (β), viscosity variation parameter (γ), and viscous dissipation parameter (ε). Also, group parameter (BrΩ−1), Grashof number (Gr), and Prandtl number (Pr) are examined. Numerical solutions are presented for steady‐state flow variables, temperature, time histories of friction, wall heat transfer rate, entropy, and Bejan curves for distinct values of control parameters. The results specify that entropy generation decreases with augmenting values of β, γ, and Gr. The converse trend is noticed with increasing Pr and BrΩ−1. Furthermore, the computations reveal that entropy and Bejan lines only occur close to the hot cylinder wall. [ABSTRACT FROM AUTHOR]

Radiative–convective flow studies find wide range of applications in furnace design, solar fans, photochemical reactors, turbid water bodies, etc. The present article focusses on unsteady radiative–convective hydromagnetic couple stress fluid (CSF) flow from a vertical cylinder using the thermodynamic concept. The obtained governing equations of the present model are resolved by a well-organised numerical scheme. The unsteady nature of friction, entropy, coefficients of heat and mass transfer (HMT) along with the time-independent state pattern of flow-field profiles, are shown graphically for distinct values of governing radiation parameter, magnetic parameter, concentration parameter, and constant parameter to display important aspects of the solution. To analyse the HMT process in a 2D domain, Bejans flow visualisation is considered along with isotherms, streamlines, and isoconcentration lines. The Bejans HMT flow visualisation shows that the heat and mass function contours are denser in the foremost verge of the hot surface of the cylinder compared to other contours. The result indicates that the entropy generation (EG) parameter increases with decreasing values of radiation and magnetic parameters. Also, the entropy parameter increases for increasing values of concentration parameter or constant parameter. [ABSTRACT FROM AUTHOR]

In the present research article, the transient radiative free convective hydromagnetic Casson fluid flow past a vertical cylinder with entropy heat generation is analysed numerically. The mathematical model of this problem is constituted by highly time-dependent non-linear coupled equations and they are resolved by an efficient unconditionally stable implicit scheme. The time histories of average values of momentum and heat transport coefficients, entropy generation and Bejan number, as well as the steady-state flow variables are discussed for several values of non-dimensional parameters arising in the flow equations. The results indicate that entropy generation parameter and Bejan number upsurges with rising values of Casson fluid parameter, viscous dissipation parameter, group parameter and Grashof number, whereas the reverse trend is observed for radiation and magnetic parameters. Also, it is viewed that the variation of entropy and Bejan lines occurs in the proximity of the hot cylindrical wall only. Finally, a comparison between the Casson and Newtonian fluid is made based on the obtained numerical results of the present study and this has important implications in industrial thermal materials processing operations. [ABSTRACT FROM AUTHOR]