Theoretical analysis of heat transfer in a multilayer body is relevant for several engineering applications where heat transfer occurs through a stack of thermally dis-similar materials. In most of such literature, a constant convective heat transfer coefficient is assumed as a boundary condition at one end of the body. In contrast, there is a lack of work to model a problem with spatial variation in the convective heat transfer coefficient. This paper presents an analytical solution for thermal conduction in a multilayer rectangular body with spatially varying convective heat transfer coefficient at one end. In addition, this solution also accounts for internal heat generation and inter-layer thermal contact resistance and spatially varying heat flux on the other end of the body. The solution is derived in a series form, and it is shown that the coefficients of the series can be determined by solving a well-defined set of linear algebraic equations. The analytical solution is verified by comparison with numerical simulations, as well as with standard solution for a simplified special case. The impact of spatially varying cooling provided by jet impingement is analyzed using the analytical solution. A resource optimization problem pertaining to the optimal use of jet cooling is solved. Results presented here may benefit thermal management analysis of a broad variety of engineering applications involving heat transfer in multi-layer bodies.

多层体中传热的理论分析与几种工程应用相关，其中传热通过一组热不相似的材料发生。在大多数此类文献中，恒定的对流传热系数被假定为主体一端的边界条件。相比之下，缺乏对流换热系数空间变化问题建模的工作。本文提出了一种多层矩形体中热传导的解析解，其中一端具有空间变化的对流传热系数。此外，该解决方案还考虑了主体另一端的内部发热和层间热接触电阻以及空间变化的热通量。该解决方案以系列形式导出，结果表明，可以通过求解一组明确定义的线性代数方程来确定级数的系数。解析解通过与数值模拟以及简化特殊情况的标准解进行比较来验证。使用解析解来分析由射流冲击提供的空间变化冷却的影响。解决了与优化使用射流冷却有关的资源优化问题。此处介绍的结果可能有益于涉及多层体传热的各种工程应用的热管理分析。以及用于简化特殊情况的标准解决方案。使用解析解来分析由射流冲击提供的空间变化冷却的影响。解决了与优化使用射流冷却有关的资源优化问题。此处介绍的结果可能有益于涉及多层体传热的各种工程应用的热管理分析。以及用于简化特殊情况的标准解决方案。使用解析解来分析由射流冲击提供的空间变化冷却的影响。解决了与优化使用射流冷却有关的资源优化问题。此处介绍的结果可能有益于涉及多层体传热的各种工程应用的热管理分析。