Question

Electrical analogue for steady state two dimensional heat conduction

Answer 1

So I think it is helpful to you

Answer 2

 mathematical model for multi-dimensional, steady-state heat-conduction is a second-order, elliptic partial-differential equation (a Laplace, Poisson or Helmholtz Equation).  Typical heat transfer textbooks describe several methods to solve this equation for two-dimensional regions with various boundary conditions.  Analytical solutions usually involve an infinite series of transcendental functions. This series must be truncated and evaluated at an array of locations to give an approximate estimate of the temperatures found over the 2-D region.  Some texts also include detailed graphical methods using various paper and pen tools for estimating temperature and heat-flow lines for 2-D problems, but these latter methods have become largely obsolete due to the widespread use of computers and associated numerical algorithms (although the principles on which graphical methods are based are often useful in checking the validity of numerical solutions).

Module Description

In our software module, HTT_2dss, we employ modern numerical methods to solve for the temperature distribution over a user-specified 2-D region. The region is taken as rectangular, with cutouts possible. The user is asked to:

specify the nodalization of the heat-conduction region (dynamic array allocation is used, so the problem size is limited only by the memory available),derive the appropriate heat-balance equations for specified regions of the solution domain (internal points, boundary edges, corners, interfaces, etc.), andinput the resulting numerical coefficients on a special input form: