This study explains the transient free convection phenomenon in a vertical porous channel subject to nonlinear thermal radiation. The infinite vertical channel encloses magnetohydrodynamic (MHD) flow of an Oldroyd-B fluid. The left channel wall possesses time-dependent velocity , while the right wall exhibits no motion. The momentum and temperature field equations are developed on the bases of momentum conservation law and Fourier’s principle of heat transfer. Laplace transformation technique and Durbin’s numerical inversion method are jointly incorporated to compute the solutions of the formulated problem. The influences of flow and material parameters on heat transfer and fluid velocity are graphically scrutinized with physical aspects. The numerical computations for skin friction and temperature gradient are tabularized to comprehensively examine the wall shear stress and heat transfer rate. Finally, velocity fields for Maxwell fluid, second grade fluid, and viscous fluid are traced out as limiting cases and their comparison is drawn with the velocity field of an Oldroyd-B fluid. Besides this, some newly published results are also deduced from the acquired solutions. It is observed that increasing the magnitude of radiation parameter Rd rapidly enhances the rate of heat transfer at the right channel wall while an inverse behavior of Nusselt number is witnessed at the left channel wall. The Maxwell fluid and second grade fluid indicate the swiftest and slowest channel flow rates respectively. The shear stress specifies dual nature for relaxation and retardation parameters subject to static and moving wall. Additionally, it is found that the flow of an Oldroyd-B fluid is retarded by a magnetic field.

本研究解释了受非线性热辐射影响的垂直多孔通道中的瞬态自由对流现象。无限的垂直通道包围着 Oldroyd-B 流体的磁流体动力学 (MHD) 流。左通道壁具有随时间变化的速度，而右壁没有运动。动量和温度场方程是根据动量守恒定律和傅立叶传热原理建立的。拉普拉斯变换技术和杜宾数值反演方法联合起来计算公式化问题的解。流动和材料参数对传热和流体速度的影响通过物理方面进行了图形化检查。表皮摩擦和温度梯度的数值计算被制成表格，以综合检验壁面剪应力和传热速率。最后，麦克斯韦流体、二级流体和粘性流体的速度场被描绘为极限情况，并将它们与 Oldroyd-B 流体的速度场进行比较。除此之外，一些新发表的结果也是从获得的解决方案中推导出来的。据观察，增加辐射参数的幅度Rd迅速提高了右通道壁处的传热速率，而在左通道壁处观察到了 Nusselt 数的逆行为。Maxwell 流体和二级流体分别表示最快和最慢的通道流速。剪切应力指定了受静态和移动壁影响的松弛和延迟参数的双重性质。此外，还发现 Oldroyd-B 流体的流动受到磁场的阻碍。