Abstract
In this paper, we formulate a four step computational algorithm to solve nonlinear Burger’s equation with source terms whose occur in aerodynamics engineering which play a major roles in convection and diffusion whose present in viscous fluid flow engineering problems. Numerical assessment was carried out to study effect of source term which represents the heat released in the boundary layer. Increase the source term and decrease in kinematic viscosity which play a major roles in obtaing velocity . Eventually, we subject the nonlinear Burger’s equation with source terms to initial and boundary conditions available in the literature. The results revealed that the new algorithm is capable and realiable to solve similar nonlinear partial differential equations occur in applied physics and engineering.
Highlights
In this paper, we consider nonlinear Burgers’ equation with source terms in aerodynamics engineering of the form (Mayur et al, 2018): ∂φ ∂φ ∂φ∂t + φ ∂x = v ∂x x − λφ x, v, λ > 0 (1)with initial and boundary conditions given (Chandrasekharan Nair, & Awasthi, 2019).https://www.acseusa.org/journal/index.php/aijser American International Journal of Sciences and Engineering Research Vol 4, No 1; 2021 x φ(x, t0) = + 1 c0 x2 e4v
The objective of this paper is to modified the algorithm presented by (Falade & Tiamiyu, 2020) and to investigate behavior of parameters on Burgers’ equation (1) which explains the role of diffusion and convection when a non-autonomous reaction term produces heat constantly in a viscous flow (Mohamed, 2019), we present 3D plots, 2D plots and densityplots for the heat distrubution profiles of NEW FOUR STEPS ALGORITHM (NFSA) we present a four steps algorithm using MAPLE18 codes software package to solve equation (1) with initial conditions (2) as follows: restart: Step 1: Digits ≔ 23; N ≔ 4; 1 C[0] ≔ 2 ; v ≔ {[0.0[10,.100.0,001.2, 00,.000.3001,00..40000]01] ; λ ≔ {[0.0[10,.100.0,001.2, 00,.000.3001,00..40000]01]; x φ(x, 0)
We axamined and obtained velocity φ(x, t) when kinematics viscosity v is less than λ source term and vice-versa
Summary
We consider nonlinear Burgers’ equation with source terms in aerodynamics engineering of the form (Mayur et al, 2018): ∂φ ∂φ ∂φ
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