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Steady natural convection Couette flow with wall conduction and thermal boundary condition of third kind
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-05-18 , DOI: 10.1002/zamm.201900095 Abiodun O. Ajibade 1 , Ayuba M. Umar 1
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-05-18 , DOI: 10.1002/zamm.201900095 Abiodun O. Ajibade 1 , Ayuba M. Umar 1
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This study theoretically investigates the effects of viscous dissipation and boundary plate thickness on an incompressible heat generating/absorbing fluid with non‐uniform internal temperature unlike lumped heat capacitance assumption. The flow, which is laminar is induced by free convection caused by asymmetric heating of the channel boundaries and internally generated energy caused by viscous dissipation. In addition, convection through the boundary plates is also considered in the flow formation. One of the plates channel moves along the flow direction while the other is stationary. Due to the non‐linear and coupling nature of the governing flow equations, homotopy perturbation method (HPM) has been adopted to analytically find the approximate solution to the problem. The effects of thermodynamic and hydrodynamic parameters are depicted in graphs and tables. It is discovered from the investigation that, both the velocity and temperature profiles increase with increase in viscous dissipation. Velocity distribution decreases with increase in Biot number while the temperature distribution near the heated plate increases with increase in Biot number. The increase in boundary plate thickness d causes a boost in the fluid flow across the medium and reduces the temperature of the fluid near the heated plate. It is further discovered that the rate of heat transfer on both plates increase with increase in Biot number while they drastically dropped when the boundary plate thickness d is increased. The shear stresses on the surface of both plates increase with increase in heat generation while reverse cases were observed with increase in heat absorption . It is further observed that the volume flow rate within the channel increases with increase in viscous dissipation .
中文翻译：
具有第三种壁传导和热边界条件的稳态自然对流库埃特流
这项研究从理论上研究了粘性耗散和边界板厚度对内部温度不均匀的不可压缩生热/吸收流体的影响，这与集总热容假设不同。层流是由通道边界的不对称加热引起的自由对流以及由粘性耗散引起的内部产生的能量引起的。另外，在流动形成中还考虑了通过边界板的对流。一块板通道沿流动方向移动，而另一块板固定。由于控制流方程的非线性和耦合性质，已采用同伦摄动法（HPM）来分析找到该问题的近似解。在图表中描述了热力学和流体力学参数的影响。从调查中发现，速度和温度曲线都随粘性耗散的增加而增加。速度分布随Biot数的增加而降低，而加热板附近的温度分布随Biot数的增加而增加。边界板厚度的增加d会增加流经介质的流体流量，并降低加热板附近流体的温度。进一步发现，当边界板厚度d增加时，两块板上的传热速率都随着Biot数的增加而增加，而随着它们的数量急剧下降。两块板表面的剪应力随着热量的产生而增加 反之则观察到热量吸收增加 。进一步观察到，通道内的体积流速随着粘性耗散的增加而增加。
更新日期：2020-05-18
中文翻译：
具有第三种壁传导和热边界条件的稳态自然对流库埃特流
这项研究从理论上研究了粘性耗散和边界板厚度对内部温度不均匀的不可压缩生热/吸收流体的影响，这与集总热容假设不同。层流是由通道边界的不对称加热引起的自由对流以及由粘性耗散引起的内部产生的能量引起的。另外，在流动形成中还考虑了通过边界板的对流。一块板通道沿流动方向移动，而另一块板固定。由于控制流方程的非线性和耦合性质，已采用同伦摄动法（HPM）来分析找到该问题的近似解。在图表中描述了热力学和流体力学参数的影响。从调查中发现，速度和温度曲线都随粘性耗散的增加而增加。速度分布随Biot数的增加而降低，而加热板附近的温度分布随Biot数的增加而增加。边界板厚度的增加d会增加流经介质的流体流量，并降低加热板附近流体的温度。进一步发现，当边界板厚度d增加时，两块板上的传热速率都随着Biot数的增加而增加，而随着它们的数量急剧下降。两块板表面的剪应力随着热量的产生而增加 反之则观察到热量吸收增加 。进一步观察到，通道内的体积流速随着粘性耗散的增加而增加。
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