Question

please provide the complete code for python

Problem 2 (11 pts) From heat transfer, you should recall that Fourier's law of conduction states where λ is the thermal conductivity and q is the heat flux (a vector. Recall that can be written in Cartesian coordinates as v- + is the gradient operator, which In addition, for constant λ. aT where is the thermal diffusivity and V2 is the Laplacian, which in Cartesian coordinates is ▽2 + 하륜 Recall that V represents the slope while V2 represents curture . (5 pts) Complete the following table, assuming a one-dimensional temperature profile: T profile Constant Linear, slope> 0 Linear, slape< o Concave up, centered at origin Concave down, centered at origin Heat Flux 2. (6 pts) For each of the following temperature profiles, plot the coresponding temperature gradient (VT) and scaled time rate of change,滒 (a) T(x) (b) T(x)-sin(2πτ) Put T(x) on the left axis and ▽T {or )on the right axis. Consider the range x [O, 1]. Don't worry about units on any of

Answer 1

1) Below table shows answer to question1 Heat flux is proportional to negative slope of T profile (Spatial gradient) dT/dt or temporal (time based) gradient is proportional to curvature of T profile or derivative of spatial gradient. T profile Constant Linear, slope>0 Linear, slope<0 Concave up (centered Positive for Negative at o) Heat flux 0 Negative constant Positive constant dT/dt 0 0 0 Positive constant side of axis Approaching to zero at origin. Negative on positive side of axis Negative for Negative side of axis Approaching to zero at origin. Positive on positive side of axis Concave down Negative constant (centered at O)

1. 
   2) Below curves show answer to question2. Note that here delta(T) is dT/dx or spatial gradient in one dimension x. Profile for T-x2 1.2 2.5 T 0.8 0.6 04 0.2 0.5 0.2 04 0.6 08 1.2 Profile for T-x2 1.2 2.5 0.8 0.6 0.4 0.2 1.5 0.5 02 04 0.6 0.8 1.2
   
   Profile for T-sin(2pi*x) 0.4 0.6 0.8 112 0.2 Profile for T-sin(2pi x) 50 10 02 04 0.8 112 0.6 -20
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