In this paper, we study the frost formation and growth at the walls of a duct with uniform wall temperature variation. The simulation is performed for laminar flow regime considering suitable semi-empirical models incorporated with computational fluid dynamics (CFD) method. The frost growth is considered to be normal to the duct surface. Since the duct aspect ratio is high, we perform our simulations in two-dimensional zones. To simulate the frost layer properly, we solve both the energy and mass balance equations implementing some semi-empirical correlations on the frost side. At this stage, we suitably predict the required heat flux value at the solid boundary and the heat transfer coefficient, which are required to be used in the CFD calculations in the next stage. So, next is to use the CFD tool to calculate the required heat transfer parameters at the air side. Since the frost growth is performed locally along the wall, the achieved frost growth rate can be applied at any specific location independently. We also investigate the effects of various environmental parameters on the frost growth rate. The current achieved results are verified by comparing them with previous available experimental data. After verification the numerical algorithm, we investigate the frost growth in a duct with uniform wall temperature variation. We assume that the variation of temperature would be gradually and uniform with time. We eventually present the effects of different parameters affecting the frost growth along the duct surface. One significant contribution of this work is to address the effects of inlet boundary location on the frost growth. In this regard, the inlet boundary is placed initially at real entrance and then at a location far upstream of the real entrance. We evaluate the effect of this boundary location on frost thickness. The use of CFD is unavoidable in this study because we need its capability to compute the required wall heat flux condition, which is an input to our semi-empirical analysis in this problem with an unsteady thermal boundary condition situation, in which the wall temperature continuously varies with time. It should be noted that, our chosen empirical method estimate the wall heat flux based on the Nusselt number value. Therefore, CFD largely helps to correct the actual heat flux at the airside. Another contribution of this work is to study frost formation in confined flow cases, in which the flow is developing both hydrodynamically and thermally. Evidently this is in contrast to the frost growth over a simple flat plate like geometry.

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