Question

proof Transient Heat Transfer in a Semi-infinite region

- 1-cr[

Answer 1

Transient heat conduction in SemiInfinite Soligt. Semi Infinit Solic, characteristics in Idealized body i... : Single plane surface YA ; . . no Region la HEA tipo oni toa Assumptions semi Let consider the os finite body Csemi-infinit body) 0 = a!) Thermal propertly are cum start CK, Picp, 2) @=No Internal generations O Boundaron cuncitin [x=0 , Ti at f=o] [ is at t-o). Ti = Initial body temperature © = heart conductin Only ın 2-direction, f foum Heat equation L froum Assumption potect @g=0, and heat transfer only in a direction.

conditions cencitm # Boundcron , i . - T Colt) =TS # Initial condition I ca, o =Titi . f pour It is to : 7 (4) we need to know Temperature at T (+):? # This .PDE ( 22 7 2 ) can be solved by Cum verting into DDE corclinary differential equation) je, 76244) is conve zeng lonto one variable m. anel 14.at 227 2002 Frams PDE per CD Soins chain Rule. bet pa (0727)

ƏT DAL . dn 40 q2T 227 dx 2 = Әу - + Daciary differential ţ equation with one variable, equation lets, wo en -O put mone, decom --24W. dw --2n-am integrate, I dwa Landa how za m² co] wa cien? Eus incol W Intearate, stom di = 4 en? dm hiteqrate S dr = fu en dan hitearate

T= a stead out. Ce uæ dummy variable. .. Form O Boundum .condition at no o C₂ = TS 2 = T from and Boundary conditions . . . n oo . - by substituting abuve value's Pe ²6 : Cwe can obtain a frumby Substituting in on tem. ibéo T- TQ in a hangt ēdu eof () =ermor Function n - l- esfeccm) La enf (m) = l-eqfccm) Ts-Ti erfc. cimplementary emor Fention. a é ulu - This term canot be solved by Analytically can be solved by . Numers cally. ba - cofomat ]