can you help with parts c,d,e

2.52 A chemically reating mixfure is stoned in a thin-wallod yherical container of rafius ry=200mm, and the exsher" mic neation peracrates heat at a unform, but ieminerafuredepesicnt volumotric rate of q=4, exp (Te, where ature in helvins. The vessel is enckened by an insulating mascrial of outer rallus r3, thermal ceeductivity h, and emissivify . The cuter surface of the insulation expericnees convection heat tramefer and net ratialive eschache with the afpoining air and large surroundings, reygectively. (a) Wrime the steady-stane form of the hear diffusion equation for the insulation. Verify that this quarthon is satistied by the nemperafure disuribution T(r)=Ta,3(Ta,1Tsa)[1(rr(r2)1(rd(r)] Skekb the iemperatare distibulion. Tirl. labeling bey features. (b) Applying Fouricr's law, show that the rale of heat transfer by cenduction through the insulatice may be expressed as qr=(ir1)(1/r2)4aj(T2.1Ts.2) Acplying an encrgy balanee to a conerol surface aboet the container, obtain an alicmative expressice for qe expresing your tesult in terms of q and r1. (c) Applying an eneng bulance to a control surface Fheed around the euter surface of the invulation, ebeain an expression frum which Tk2 may be determined as a function of qFj,hn,Tk,r,andT2 (d) The process engineer wishes to maineain a reactor temperature of Tn=T(r1)=95C under conditions for which k=0.05W/m=K,r7=208mm,h=5 Whin 2K4=0.9.Tn=257C. and T==35C. What is the actual reacter temperature and the euter surfice iemperabure Tn of the invulation? (e) Compute and plot the variation of T3,2 with r2 for 201r2210mm. The kngincer is ceecerned about peecenial bun injuries to personnel who may some into seetact with the exposed surface of the insulation. Is increasing the insulation thicksess a pratical solutioe to maintaining T22457C. What edher parameter could be variedl to redace Tk21