Analytical Modeling of Advection–Conduction Heat Transfer Outside Borehole Heat Exchangers Under Dirichlet Boundary Conditions

For heat transfer outside borehole heat exchanger (BHE) arrays in aquifers, existing analytical models mostly adopt Neumann or Robin boundary conditions, whereas constant-temperature (Dirichlet) boundaries are more practical and convenient for monitoring in engineering applications. Considering the coupled effects of heat advection and conduction induced by groundwater seepage, and based on the engineering reality that vertical heat flow is much smaller than horizontal heat flow, this study idealized the BHE array as a constant-temperature boundary and established a one-dimensional simplified model. The advection term of the governing equation was removed through the exponential transformation of the dependent variable, and an analytical solution was derived using Fourier transformation. A three-dimensional coupled hydro-thermal numerical model was established in FEFLOW for validation. The results indicate that relative errors between analytical and numerical solutions remain below 3% outside the BHE array; however, the analytical method is inapplicable inside the array due to significant thermal interference, and independent field validation is precluded by prior thermal disturbances. The proposed solution features fast computation and clear physical interpretation, providing a simple and efficient tool for rapid estimation of temperature variations during preliminary feasibility studies of ground-source heat-pump projects.