Unsteady laminar slip flow along an infinite vertical plate with ramped plate temperature and concentration in the presence of thermal radiation and buoyancy is investigated. Approximated Navier–Stokes equation along with the energy and species equations are solved analytically by adopting the Laplace transform technique. The dependencies of the flow, heat and mass transfer characteristics on time (t), space (y) and nondimensional governing parameters, namely, slip (λ), radiation (R), buoyancy forces ratio (N), Prandtl number (Pr) and Schmidt number (Sc), are explored for both ramped and constant plate temperature and concentration conditions. The results show that radiation effect is appreciable at a lower range of R and found to be greater for the constant than that for the ramped condition. A strong flow near to the plate is generated by radiation and buoyancy effects, and accelerated by slip effect. Finally it is also shown logically and mathematically that in the absence of radiation and presence/absence of slip the flow should be brought to stationary flow when two buoyancies are opposite and equal in magnitude with equal solutal and thermal diffusions.

中文翻译：

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在存在热辐射和浮力的情况下，经过无限垂直板的非定常滑流，其板温度和浓度均升高

研究了在存在热辐射和浮力的情况下，沿无限垂直板的非稳态层滑流，其中板温度和浓度呈斜坡状增长。近似的Navier–Stokes方程以及能量和物种方程通过采用Laplace变换技术进行解析求解。流量，传热和传质特性对时间（t），空间（y）和无量纲控制参数的依赖性，即滑移（λ）），研究了斜率和恒定板温和浓度条件下的辐射（R），浮力比（N），普朗特数（Pr）和施密特数（Sc）。结果表明，在较低的R范围内，辐射效应是明显的，并且发现该常数比倾斜条件下的辐射效应更大。辐射和浮力效应会在板附近产生强烈流动，而滑动效应会加速流动。最后，从逻辑和数学上也表明，在不存在辐射和存在/不存在滑动的情况下，当两个蓝度相对且大小相等且具有相同的溶质和热扩散时，应将流动转换为平稳流动。