A Simplified Finite Difference Method (SFDM) Solution via Tridiagonal Matrix Algorithm for MHD Radiating Nanofluid Flow over a Slippery Sheet Submerged in a Permeable Medium

In this paper, we turn our attention to the mathematical model to simulate steady, hydromagnetic, and radiating nanofluid flow past an exponentially stretching sheet. A numerical modeling technique, simplified finite difference method (SFDM), has been applied to the flow model that is based on partial differential equations (PDEs) which is converted to nonlinear ordinary differential equations (ODEs) by using similarity variables. For the resultant algebraic system, the SFDM uses the tridiagonal matrix algorithm (TDMA) in computing the solution. The effectiveness of numerical scheme is verified by comparing it with solution from the literature. However, where reference solution is not available, one can compare its numerical results with the results of MATLAB built-in package bvp4c. The velocity, temperature, and concentration profiles are graphed for a variety of parameters, i.e., Prandtl number, Grashof number, thermal radiation parameter, Darcy number, Eckert number, Lewis number, and Brownian and thermophoresis parameters. The significant effects of the associated emerging thermophysical parameters, i.e., skin friction coefficient, local Nusselt number, and local Sherwood numbers are analyzed and discussed in detail. Numerical results are compared from the available literature and found a close agreement with each other. It is found that the Eckert number upsurges the velocity curve. However, the dimensionless temperature declines with the Grashof number. It is also shown that the SFDM gives good results when compared with the results obtained from bvp4c and results from the literature.

Analysis of calendering process of non-isothermal flow of non-Newtonian fluid: A perturbative and numerical study

This paper numerically solves the third-order fluid flow during calendering with slip condition at the rolls. The basic equations are transformed into dimensionless forms and simplified by adopting LAT (Lubrication Approximation Theory). The flow equations are then solved with the perturbation technique. Whereas a finite difference scheme along with TDMA (Tridiagonal Matrix Algorithm) is implemented to solve the energy equation. Engineering parameters like power input, exit distance, and roll separating force are computed. The impact of slip parameter [Formula: see text] and material parameter [Formula: see text] on the velocity profile, pressure, pressure gradient, temperature profile, power input, detachment point, and roll separating force is portrayed through graphs and discussed. It is noticed that both the parameters [Formula: see text] and [Formula: see text] exhibit opposite behaviors and give insight to the mechanisms that control the physical and engineering parameters.

Performance Optimization of Tridiagonal Matrix Algorithm [TDMA] on Multicore Architectures

Fast and efficient tridiagonal solvers are highly appreciated in scientific and engineering domain, but challenging optimization task for computer engineers. The state-of-the-art developments in multi-core computing paves the way to meet this challenge to an extent. The technical advances in multi-core computing provide opportunities to exploit lower levels of parallelism and concurrency for inherently sequential algorithms. In this article, the authors present an optimal performance pipelined parallel variant of the conventional Tridiagonal Matrix Algorithm (TDMA), aka the Thomas algorithm, on a multi-core CPU platform. The implementation, analysis and performance comparison of the proposed pipelined parallel TDMA and the conventional version are performed on an Intel SIMD multi-core architecture. The results are compared in terms of elapsed time, speedup, cache miss rate. For a system of ‘n' linear equations where n = 2^36 in presented pipelined parallel TDMA achieves speedup of 1.294X with a parallel efficiency of 43% initially and inclines towards linear speed up as the system grows.

Isothermal free jets in high-temperature surroundings

Two types of isothermal free jets, named positively and negatively buoyant, have been studied numerically to discern the effect of surrounding temperatures on their flow dynamics. Turbulence closure in those jets was achieved by standard k - ε model. The governing equations were solved using Implicit θ-Scheme and Tridiagonal Matrix Algorithm. Calculations were made for the jets having constant temperature at 20 °C and by varying surrounding temperatures from 20°C to 1000°C. It is clear that negatively buoyant jets but not the positively buoyant jets are nearly invariant to the change in surrounding temperatures compared to non-buoyant jet. Change in fluid dynamical behaviour of positively buoyant jets due to surrounding temperature change seems promising as it may offer the advantages of fuel jets in high-temperature air combustion.

Influence of Partition Location on Natural Convection in a Partitioned Enclosure

In this study, Natural convection heat transfer and fluid flow of square partitioned enclosure with two partitions protruding centrally from the end walls of an enclosure have been analysed numerically using finite element method. The enclosure has opposite isothermal walls at different temperatures. The thickness and length of the partitions is fixed and equal to 1/10 and 1/4 of width of the enclosure respectively. Computation for Rayleigh number in the range of 104 to 106 has been conducted. The influence of different thermal boundary conditions at the end walls and at the partitions is included in the investigation. ‘Standard’ boundary conditions are introduced as more appropriate to simulate situations of practical engineering interest. To solve the relevant governing equations a segregated sequential solution algorithm is used after employing Boussinesq approximation. These equations after discretization were solved by using the tridiagonal matrix algorithm. Results clearly demonstrate that partition location has a significant effect on heat transfer.