Impacts of Thermal Radiation and Heat Consumption/Generation on Unsteady MHD Convection Flow of an Oldroyd-B Fluid with Ramped Velocity and Temperature in a Generalized Darcy Medium

Abstract

This article analyzes the time-dependent magnetohydrodynamic flow of Oldroyed-B fluid in the presence of heat consumption/generation and thermal radiation. The flow is restricted to a vertical infinite plate saturated in porous material along with ramp wall velocity and ramp wall temperature conditions. This flow also incorporates the generalized Darcy’s law. In this paper, accurate equation of velocity field is presented first and then solutions of mass and energy equation are derived in Laplace domain. Real-time domain solutions are obtained by tackling the complexity of Laplace domain expressions through numerical Laplace inversion. Skin friction coefficient and Nusselt number are also calculated. A comparison for ramp wall temperature condition and isothermal temperature condition is also drawn to investigate the difference. A graphical study is conducted to analyze the influence of parameters on fluid flow and heat transfer. It is found that radiation parameter and heat generation elevate the energy profile, while flow is accelerated by increasing the retardation time and porosity parameter and an opposite behavior is noted for increasing relaxation time and magnetic parameter. Furthermore, heat transfer rate is higher for increasing Prandtl number and velocity on plate decreases with increase in relaxation time λ 1 .

Thermophysical Investigation of Oldroyd-B Fluid with Functional Effects of Permeability: Memory Effect Study Using Non-Singular Kernel Derivative Approach

“…Figure 1. Geometrical formation of the flow model.The constitutive flow equations for an Oldroyd-B fluid are given as[46,47] …”

Thermophysical Study of Oldroyd-B Hybrid Nanofluid with Sinusoidal Conditions and Permeability: A Prabhakar Fractional Approach

“…The pored plate vibrates with some constant velocity 𝑈 𝐶𝑜𝑠(𝜔𝑡) in which 𝜔 is the vibration rate of the inclined plane, as configured in Figure 1. The basic partial differential equations are provided below, taking into account the following assumptions and ignoring the pressure gradient, viscous dissipation, and the use of Boussinseq's and Rosseland approximations [36,37],…”

Shape effect on MHD flow of time fractional Ferro-Brinkman type nanofluid with ramped heating

“…(17) yield to or where β * = α d /ρ is the Brinkman type fluid parameter which corresponds to the drag force of highly non-Darcy's porous medium. The energy equation together with thermal radiation and heat generation is given by 37 The radiative heat flux q r in Eq. (22) is formulated by using via the Roseland approximation as 38 The T 4 is expanded along T ∞ by using the Taylor series as The temperature gradient is assumed to be small enough so, the higher-order terms are neglected which yield to…”

“…( 17 ) yield to or where is the Brinkman type fluid parameter which corresponds to the drag force of highly non-Darcy’s porous medium. The energy equation together with thermal radiation and heat generation is given by 37 …”