Analytical models for heat transfer around a single ground heat exchanger in the presence of both horizontal and vertical groundwater flow considering a convective boundary condition

Energy ◽  
2022 ◽  
pp. 123159
Author(s):  
Yang Zhou ◽  
Zhi-xiang Zheng ◽  
Guang-si Zhao
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Exchanger ◽  
Groundwater Flow ◽  
Convective Boundary Condition ◽  
Analytical Models ◽  
Ground Heat Exchanger ◽  
Convective Boundary

Analytical Solution for Solid Cylindrical Heat Source Model With Convective Boundary Condition

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Yang Zhou ◽  
Cheng Xu ◽  
David Sego ◽  
Dong-hai Zhang
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Analytical Solution ◽  
Heat Source ◽  
Groundwater Flow ◽  
Convective Boundary Condition ◽  
Convective Boundary ◽  
Energy Pile ◽  
Special Cases ◽  
Scs Model

Abstract The energy pile technology has been widely used, and the solid cylindrical heat source (SCS) model is usually adopted to describe the heat transfer process between the energy pile and the surrounding soil. This paper investigates the SCS model with a convective boundary condition (SCS-3 model), and realistic conditions such as transversely isotropic ground and groundwater flow are all included in the model. An analytical solution for the problem is established using Green's function method and the theory of moving heat sources. Solutions for the SCS model with a boundary condition of the first kind (SCS-1 model) and for the line source (LS) model with a convective boundary condition (LS-3 model) are recovered as special cases of the solution in this paper. Computational examples are presented, and comparisons between different models are made. First, the SCS-1 model is compared with the SCS-3 model, showing the error caused by neglecting the surface convective effect. Second, the LS-3 model is compared with the SCS-3 model, showing the error associated with neglecting the size of heat source. The effects of groundwater flow velocity and convective heat transfer coefficient on the temporal and spatial variations of these errors are also investigated.

Numerical investigation of laminar forced convection for a non-Newtonian nanofluids flowing inside an elliptical duct under convective boundary condition

2019 ◽  
Vol 29 (1) ◽  
pp. 334-364 ◽  
Author(s):  
Haroun Ragueb ◽  
Kacem Mansouri
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Fluid Flow ◽  
Transfer Coefficient ◽  
Convective Boundary Condition ◽  
Bulk Temperature ◽  
Convective Boundary ◽  
Content Type ◽  
The Heat Transfer Coefficient

PurposeThe purpose of this study is to investigate the thermal response of the laminar non-Newtonian fluid flow in elliptical duct subjected to a third-kind boundary condition with a particular interest to a non-Newtonian nanofluid case. The effects of Biot number, aspect ratio and fluid flow behavior index on the heat transfer have been examined carefully.Design/methodology/approachFirst, the mathematical problem has been formulated in dimensionless form, and then the curvilinear elliptical coordinates transform is applied to transform the original elliptical shape of the duct to an equivalent rectangular numerical domain. This transformation has been adopted to overcome the inherent mathematical deficiency due to the dependence of the ellipsis contour on the variables x and y. The yielded problem has been successfully solved using the dynamic alternating direction implicit method. With the available temperature field, several parameters have been computed for the analysis purpose such as bulk temperature, Nusselt number and heat transfer coefficient.FindingsThe results showed that the use of elliptical duct enhances significantly the heat transfer coefficient and reduces the duct’s length needed to achieve the thermal equilibrium. For some cases, the reduction in the duct’s length can reach almost 50 per cent compared to the circular pipe. In addition, the analysis of the non-Newtonian nanofluid case showed that the addition of nanoparticles to the base fluid improves the heat transfer coefficient up to 25 per cent. The combination of using an elliptical duct and the addition of nanoparticles has a spectacular effect on the overall heat transfer coefficient with an enhancement of 50-70 per cent. From the engineering applications view, the results demonstrate the potential of elliptical duct in building light-weighted compact shell-and-tube heat exchangers.Originality/valueA complete investigation of the heat transfer of a fully developed laminar flow of power law fluids in elliptical ducts subject to the convective boundary condition with application to non-Newtonian nanofluids is addressed.

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