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Scientific computation applications often consist of very different components that produce (or take as an input) huge amounts of data. Wrapping such components into Web services to form a combined service for the scientific community has an additional complexity to deal with: how to organize data transfer within the Web service framework efficiently enough to form high quality services that do not suffer in performance. In this paper we propose a method for processing large amounts of data transferred between different components of a compound Web service. For this we develop a full workflow consisting of three separate components around an existing open-source package DOUG, a parallel black-box solver for large sparse systems of linear equations. We demonstrate the feasibility of the concept on an example of solving the steady state heat equations within design problems. The workflow involves a full production cycle, starting with the design of the geometry of the underlying problem domain with appropriate boundary conditions and other parameters, formation of the discretized system to be solved by DOUG and visualization of the heat distribution as a result.