This article presents a numerical study to investigate boundary-layer heat transfer fluid associated with a moving flat body in cooperation of variable plate and streaming-free velocity along the boundary surface in the laminar flow. The thermal conductivity is supposed to vary linearly with temperature. Similarity transformations are applied to render the governing partial differential equations for mass, momentum and energy into a system of ordinary differential equations to reveal the possible existence of dual solutions. MATLAB package has been used to solve the boundary value problem numerically. We present the effects of various parameters such as velocity ratio, thermal conductivity and variable viscosity on velocity and temperature distribution. The analysis of the results concerning Skin friction and Nusselt number near the wall is also presented. It is focused on the detection and description of the dual solutions. The study reveals that the undertaken problem admits dual solutions in particular range of values of different physical parameters. It can be seen that for the first branch solution, the fluid velocity decreases near the sheet, but it increases far away from the sheet for velocity ratio parameter, whereas the opposite effect is induced for second branch solution. Skin friction coefficient and rate of heat transfer increase due to increase in thermal conductivity parameter.

本文提供了一个数值研究，以研究与移动平板相关联的边界层传热流体，这些流体与可变板和层流中沿边界表面的自由流动速度共同作用。热导率应随温度线性变化。应用相似变换将质量，动量和能量的控制性偏微分方程转换为一个常微分方程组，以揭示对偶解的可能存在。MATLAB软件包已用于数值求解边界值问题。我们介绍了各种参数（例如速度比，导热系数和可变粘度）对速度和温度分布的影响。还提出了关于壁附近的皮肤摩擦和努塞尔数的结果的分析。它专注于双重解决方案的检测和描述。研究表明，所承担的问题允许在不同物理参数值的特定范围内采用双重解。可以看出，对于第一分支溶液，流体速度在片材附近降低，但是对于速度比参数，它远离片材增加，而对于第二分支溶液则产生相反的效果。皮肤摩擦系数和热传递速率由于导热系数的增加而增加。研究表明，所承担的问题允许在不同物理参数的特定值范围内采用双重解。可以看出，对于第一分支溶液，流体速度在片材附近降低，但是对于速度比参数，它远离片材增加，而对于第二分支溶液则产生相反的效果。皮肤摩擦系数和热传递速率由于导热系数的增加而增加。研究表明，所承担的问题允许在不同物理参数的特定值范围内采用双重解。可以看出，对于第一分支溶液，流体速度在片材附近减小，但是对于速度比参数，它远离片材增加，而对于第二分支溶液则产生相反的效果。皮肤摩擦系数和热传递速率由于导热系数的增加而增加。