Transient state
Hi, I am making a simulation of in transient state of the response of a cylinder immersed in a stagnant medium (fluid) subject to a constant heat generation inside it. Actually, using finite difference discretization scheme, fully implicite and TDMA I succeeded to obtain the steady state with very high accuracy. However, the transient state is not good at all since the comparison of the numerical results with the experimental ones give an absolute deviation of almost 10 %. My question is simply, what are the parameters that improve the accuracy of the model beside the 3D(now its only a 2 Dimensional one). What are the parameters that influence the transient state shape and curvature??? respectfully yours

Re: Transient state
You haven't given us enough information.
How big is the cylinder compared to the fluid container? What is the fluid? What is the solid material? Is it hollow, solid, or composite cylinder? How is it heated? Is the heating likely to be volumetric (uniform) or surface? Are you solving the temperature distribution in the solid at the same time as the heat flow in the fluid (conjugate heat transfeer)? What are you measuring? Where? How often? What instrument(s)/technique(s)? After all of this is resolved (I almost certainly have forgotten something!), you need to move on to questions of mesh resolution in the solid and in the fluid, the possibility of turbulence in the fluid, etc. I thought (you experimentalists might help here) that a 10% agreement between experiment and theory in heat transfer work is often regarded as good. Good luck! Jim Park PS: Your question is/was "What are the parameters that influence the transient state shape and curvature?" Among other things, consider the thermal mass(?) of the solid, density x specific x volume and compare to the same quantity for the fluid. Lots of other things for other folks to describe. 
Re: Transient state
I think, you have to give us enough information about this system studied. Also, you give the method of discretization, order of discretization, and etc. I think, the method of linearization of source term of the equation is important for accuration in computation.
What's form of the source term in PD equation solved? You have to use second order discretization. Please use the finite volume method, as describe by Patankar, S.V. (1980). In this book, he describe completely about the rule of discretization, so you get the stable solution and accurately. Thanks Istadi Dept. of Chemical Engineering Diponegoro University Jl. Prof. Sudarto, Semarang. 
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