Wireless Mesh Networks (WMNs) consist of a high-density of hundreds to thousands of mesh routers (MRs) deployed in corporate offices and university campuses. The main purpose of this deployment is to meet user demands for high bandwidth, mobility, and reliability. However, our recent consideration of such networks revealed that they are rarely used at their peak capacity besides the fact that the entire MRS remains active continuously. Thus, during lower traffic periods the energy consumption is the same as in busy hours, while it would be possible to save a large amount of power. Green networking has recently been proposed; consist of rethink how networks are constructed and operated so that not only the cost and performance are taken into consideration but also their energy consumption and carbon footprint. In this paper, we draw attention that a large part of idle MRs results in considerable energy losses. Thousands of WMNs worldwide jointly aggravate this problem, while raising serious worry about the energy wastage that will happen in the future. In response to this problem, we first propose an optimal approach called Optimal Energy Efficiency Management Design (OEEMD) by formulating the problem as a Mixed Integer Linear Program (MILP) model to investigate the power consumption in WMN. As this problem is known to be NP-hard, we then propose an efficient heuristic algorithm called Green Energy Efficiency Management Design (GEEMD) for wireless mesh networks. GEEMD uses a sleep mechanism to power on/off underutilized MRs, based on the traffic load and solar energy generation. For the performance evaluation, we used OEEMD and GEEMD to study the performance of WMN deployment scenario in the university and campus area of Tlemcen city in Algeria over dynamic traffic profiles. Illustrative numerical examples show that, with suitable design parameters, we can efficiently reduce energy consumption in WMN without significantly impacting the network performance.