Consider a square channel shown as blue color in the sketch operating under steady state conditions. The inner surface of the square channel is at a uniform temperature of 600 K, while the outer surface is exposed to convection with a fluid at 300 K and a heat transfer coefficient of 50 W/m2-K. From a symmetrical element of the channel, a two-dimensional grid has been constructed and the nodes are labeled. (A) Based on the schematic diagram, write the rate equation for each node of unknown temperature. (Hint: try to use symbols in the rate equations, you can substitute the values of the parameters later in your calculation. This helps check whether the equations are correct.) (B) Using direct method write a Mat Lab code (or any other code) to solve the temperature field. Or using an iterative method write a Mat lab code (or any other code including excel) to solve for the temperature field (let ? =0.1°C). (C) Calculate heat transfer rate passing from the inner surface (along line 8-9). Calculate heat transfer rate from the outer surface (along line 1-2-3-4). Do you think that the heat transfer rates should be equal to each other? Why? Evaluate whether your results are consistent with your prediction. Explain why they are consistent (or inconsistent)?