Question

Two large parallel plates with surface conditions approximating those of a blackbody are maintained at 800°C and 100°C, respectively. Determine the rate of heal transfer by radiation between the plates in Wim and the radiative heat transfer coefficient in W/m K ) 12 Write down the one-dimensional sent heal conduction equation for a plane wall with constant thermal conductivity and heat generation in its simplest form, and indicate what each variable represents 13 Write down the one-dimensional transient heat conduction equation for a long cylinder with constant thermal conductivity and heat generation, and indicate what cach variable 14 Starting with an energy balance on a rectangular volume element, derive the one dimensional transient heat conduction equation for a plane wall with constant thermal conductivity and no heat generation 15 Starting with an energy balance on a cylindrical shell volume clement, derive the steady one-dimensional heat conduction equation for a long cylinder with constant thermal conductivity in which heat is generated at a rate of 16 Starting with an energy balance on a spherical shell volume element, derive the one- dimensional transient heat codaction equation for a sphere with constant thermal conductivity and no heat generation 17 Consider a medium in which the heat conduction equation is given in its simplest form от 1 от yed (a) is heat transferendy or transient? (b) Is heat transfer one two or three-dimensional? (c) Is there heat generation in the medium? (d) is the thermal conductivity of the medium constant or variable? 18 Consider a medium in which the heat conduction equation is given in its simplest form IddT. 0 (a) is heat transfer steady or transient? (b) Is heat transfer one-two or three-dimensional? (c) Is there heat generation in the medium? (d) Is the thermal conductivity of the medium constant or variable? 19 Consider a medium in which the heat conduction equation is given in its simplest form laar 1 ar ar (a) Is heat transfer steady or transient? () is heat transfer one two or three-dimensional? (c) Is there heat generation in the medium? () is the thermal conductivity of the medium constant or variable? 110 Consider a medium in which the heat conduction equation is given in its simplest form a'r a'T IT (a) Is heat transfer tady or transient" () is heat transfer one two or three-dimensional (c) is there heat generation in the medium? Is the thermal cor

Answer 1

Soi). Dr Given two large plates are at 8000 and 100°c. In question it is said that plates are very lange so we can take shape faclo7 as 1 T - 908c = 1073k , T = 10oC = 343 K * Net Tradiative heat transfer. - A soc % = o[titz"] - 5.64 *18* [1679" (9730"} ( 65.65x16 74,061-63 WA Icoc. * we can write a = UA (AT) = 0 [01] = 0 [11-Tz] 7406163 = 1073 – 373] heat transfer coefficient Cu} = 105-502 fmasc. Pediative en aith. Constant thermal 2) one dimensional conductivity and transient. beat conduction heat generation, cohere T. temperature Wen- K - per unit Voilume. conductivity. Heat generated Constant thermal thermal diffusivity - t - time.

for a long cylinder with 2 I one-dimensional constant thermal transient Conductivity heat and conduction Ean heat generation, * * (T) + pengene where r - &gen - T - t a - radial direction, Heat generated per unit volume. constant thermal conductivity. Temperature time Thermal diffusivity - Peci 4)

Grenenclized ennot conction in Cartesian Coodinates Cordinates in differential in diter Qytdy งศา - - * Ein + Egen - Eout = Estated, Oxtda - - - xx Oy From tayla's expansion Senies ! we have Que+ @y+ Qz + Qgen - Qxtox - Qytdy - @z+dz = Estded. > 0 Quiz - Ky dydz e , - Ky dx dzelten, = K dedy Qua Qxt ol = Qx- [out on the day q- artes - E-kazdy de made. Qy - Cytoly = - og [-xy dx dz ef} dy. Q4 - Qztaz - Foto [- Ky dady doza let agen = bene Qgen algen - volume Qgen = Ngen • draudz . Igen & Heat generated per unit volume.

Eelded mcpe . m=f-vol = pdxdydz Estried & Pdedydz ap a to sti from ☺ digde - dute as Jody - [ty tady } dz! + argen dedy dz = pdxdydz ce e non As x,y,z' are independent Coordinates. (te re dxdgdz + going (ang dedydz + (x23x]dxdydz e e dxdy dz cette (v + [may se [ + Yen PC option 1): 36 se the given Syse x = ky kz affumed to be isotropic then K (bul k is changing with temp. ef i is changing with x5,2] k il- (+$2) + ${1*]**(188Pesona Pop 2):- 36 k is independent of temp. Cier position] RCS + esta e agent des i kleep a

no heat generation If o argento f => Diffusion con.