This paper explores the transparent programmability of communicating parallel tasks in a Network of, Workstations (NOW). Programs which are tied up with specific machines will not be resilient to the changing conditions of a NOW. The Distributed Pipes (DP) model enables location independent intertask communication among processes' across machines. This approach enables migration of communicating parallel tasks according to runtime conditions. A transparent programming model for a parallel solution to Iterative Grid Computations using DP is also proposed. Programs written using the model are resilient to the heterogeneity of nodes and changing conditions in the NOW. They are also devoid of any network related code. The design of runtime support and function library support are presented. An engineering problem, namely, the Steady State Equilibrium Problem, is studied over the model. The performance analysis shows the speedup due to parallel execution and scaled down memory requirements. We present a case where the effect of communication overhead can be nullified to achieve a linear to super-linear speedup. The analysis discusses performance resilience of Iterative Grid Computations and characterizes synchronization delay among subtasks and the effect of network overhead and load fluctuations on performance. The performance saturation characteristics of such applications are also studied.