In this paper, we examine the flow of a convective Maxwell fluid through a channel with a sensor surface placed between two parallel plates, for applications in cooling electronic devices, microfluidics, environmental monitoring, and the oil and gas industries. The flow is squeezed from one side, and the channel surface is instrumented with a microcantilever sensor. The heat- and mass-transfer equations are formulated using the Cattaneo-Christov model, to incorporate heat absorption and a chemical reaction. Boundary-layer approximations are considered, and similarity transforms convert the partial differential equations into linear ordinary differential equations, which are solved numerically. The effects of various parameters on velocity, concentration, and temperature gradients are analyzed. Results show that the velocity of the Maxwell fluid decreases with higher thermal and solutal Grashof numbers and the Maxwell fluid parameter. The thermal-relaxation parameter and heat-absorption coefficient contribute to a reduced temperature distribution. The concentration decreases with variations in the solutal relaxation coefficient and reaction parameter. Physical quantities, such as skin friction, decline due to the Maxwell fluid parameter. A comparison with previously published results is also included.