Question

Chenical reaction, Figure 1: Two end of the rods are maintained at different temperatures A chemically reacting mixture is stored in a thin-walled spherical container of radius 1 200 mm, and the exothermic reaction generates heat at a uniform, but temperature-dependent volumetric rate of q exp( A/T ), where如= 500 W/m3. A = 75 K. and To IS the mixture teinperature in kelvins. The vessel is enclosed by an insulating material of outer radius r2, thermal conductivity k, and emissivity . The outer surface of the insulation experiences convection heat transfer and net radiation exchange with the adjoining air and large surromdings, respectively 1. (10 Pts) Write the steady-state form of the heat diffusion equation for the insulation in spherical coordinates. Verify that this equation is satisfied by the temperature distribution 1- (ri/r) (/r2 T(r)-Ti (Ti T2) 2. (10 Pts) Plot the temperature distribution as function of radius 3. (10 Pts) Applying Fourier's law, show that the rate of heat transfer by conduction through the insu lation may be expressed as Applying an energy balance to a control surface about the container, obtain an alternative expression for r, expressing your results in terns of q and r 4. (10 Pts) Applying an energy balance to a control surface placed around the outer surface of the insulation, obtain an expression from which T2 may be determined as a function of q,ri.h, Tooe and

Answer 1

2- 51 co pr

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ohaleuer the heat ge nerated in undes steady st 5を 3

typer bolte Protfle 32
we don't need values here. That is the reason I am deriving all formulae. Still you have any doubt ask me. I am there to help you