Study of Heat Transfer under the Impact of Thermal Radiation, Ramped Velocity, and Ramped Temperature on the MHD Oldroyd-B Fluid Subject to Noninteger Differentiable Operators

Syed Tauseef Saeed,Muhammad Bilal Riaz,Ilyas Khan,Syed Muhammad Husnine

doi:10.1155/2020/8890820

Abstract

This theoretical study explores the impact of heat generation/absorption with ramp wall velocity and ramp wall temperature on the magnetohydrodynamic (MHD) time-dependent Oldroyd-B fluid over an unbounded plate embedded in a porous surface. The mathematical analysis of fractional governing partial differential equations has been established using systematic and powerful techniques of Laplace transform with its numerical inversion algorithms. The fractionalized solutions have been traced out separately through all fractional differential operators. Nondimensional parameters along with Laplace transformation are used to find the solution of temperature and velocity profiles. Fractional time derivatives are used to analyze the impact of fractional parameters (memory effect) on the dynamics of the fluid. While making a comparison, it is observed that the fractional-order model is the best to explain the memory effect as compared to classical models. The obtained solutions are plotted graphically for different values of physical parameters. Our results suggest that the velocity profile decreases by increasing the effective Prandtl number. Furthermore, the existence of an effective Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity.

Highlights

Academic Editor: George Psihoyios is theoretical study explores the impact of heat generation/absorption with ramp wall velocity and ramp wall temperature on the magnetohydrodynamic (MHD) time-dependent Oldroyd-B fluid over an unbounded plate embedded in a porous surface. e mathematical analysis of fractional governing partial differential equations has been established using systematic and powerful techniques of Laplace transform with its numerical inversion algorithms. e fractionalized solutions have been traced out separately through all fractional differential operators
Different valuable work has been discussed for modeling fluid dynamics, signal processing, viscoelasticity, electrochemistry, and biological structure through fractional time derivatives. is fractional differential operator found useful conclusions for experts to treat cancer cells with a suitable amount of heat source and has compared the results to see the memory effect of the temperature function
The noninteger differentiable operator is chosen for the fractional MHD Oldroyd-B model which is developed under thermal radiation, ramp velocity, and ramp temperature associated with physical initial and boundary conditions. e model is solved via the Laplace transform technique and inversion algorithm. e required results are displayed in graphs with physical arguments

Summary

Introduction

Academic Editor: George Psihoyios is theoretical study explores the impact of heat generation/absorption with ramp wall velocity and ramp wall temperature on the magnetohydrodynamic (MHD) time-dependent Oldroyd-B fluid over an unbounded plate embedded in a porous surface. e mathematical analysis of fractional governing partial differential equations has been established using systematic and powerful techniques of Laplace transform with its numerical inversion algorithms. e fractionalized solutions have been traced out separately through all fractional differential operators. Nondimensional parameters along with Laplace transformation are used to find the solution of temperature and velocity profiles. Our results suggest that the velocity profile decreases by increasing the effective Prandtl number. Tiwana et al [21] and Anwar et al [22] analyzed the MHD Oldroyd-B fluid under the effect of ramped temperature and velocity.

Results

Conclusion