Case study - tumour growth assignment

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Reference no: EM132438821

Case Study - Tumour growth

Heat flux and thermal resistance. Suppose we have two different materials with widths d₁ and d₂, conductivities k₁ and k₂, and which are joined together at x = 0. The equilibrium temperatures U₁(x) and U₂(x) both satisfy the basic equilibrium heat equations

d²U₁/dx² = 0, d²U₂/dx² = 0.

The temperature on the inside (x = -d₁) is held (by a thermostat) at a temperature u_i and the temperature on the outside (x = d₂) is held (by a thermostat) at a temperature u_o.

(a) Assuming the temperature and heat flux are continuous where the materials join at x = 0, what are the boundary conditions?

(b) Show that the heat flux is given by

J = u_i - u₀ /(d₁/k₁ + d₂k₂)

Textbook: MATHEMATICAL MODELLING WITH CASE STUDIES - Using Maple and MATLAB - Third Edition by B. Barnes and G. R. Fulford

Reference no: EM132438821

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