This paper presents the parametric study for the flow characteristic and heat transmission of MHD $\mathit{Ti}{O}_2-$water nanofluid (NF) in a permeable channel with expanding or contracting walls with thermal radiation. The slip condition is imposed on the lower wall of the channel. The Tiwari-Das (TD) NF model is used to study the properties of the nanoparticles (NPs) considering water as base fluid (BF). Similarity transformations are used to transform the governing momentum and energy equations into non-linear ordinary differential equations (ODEs) which are then solved by homotopy analysis and shooting methods. The influence on flow fields of velocity, temperature, surface friction factor and Nusselt number due to several parameters representing slip, porosity, radiation, magnetic field and suction/injection are studied graphically. It is examined that velocity profile and skin friction are decreased by slip parameter and magnetic parameter. It is also remarked that the temperature profile increases and Nusselt number decreases for radiation parameter.

本文对MHD的流动特性和传热进行了参数研究 $\mathit{钛}{Ø}_2--$水纳米流体（NF）在具有热辐射的膨胀或收缩壁的可渗透通道中。滑移条件强加在通道的下壁上。Tiwari-Das（TD）NF模型用于研究以水为基础液（BF）的纳米颗粒（NPs）的性能。相似变换用于将控制动量和能量方程式转换为非线性常微分方程（ODE），然后通过同伦分析和射击方法求解。图形化地研究了由于滑移，孔隙率，辐射，磁场和吸/注几个参数对速度，温度，表面摩擦系数和努塞尔数对流场的影响。检查了滑动参数和磁参数降低了速度分布和皮肤摩擦。