2) Heat and mass transfer . The wall of a building has a surface area, A. The wa

Question

2) Heat and mass transfer

. The wall of a building has a surface area, A. The wall is composed of insulation with an R value of 12 ft2hr0F/BUT, and two other solid layers of thickness L1, and L2, with associated thermal conductivity values of k1 and k2, respectively.

a). If the thickness of solid layers are specified in inches, and the tabulated thermal conductivity data is given in SI units, what are the tabulated dimensional units for thermal conductivity, and how would you allow for thickness in inches?

b). if the outside air temperature id T0, and the inside air temperature is Ti , with the associated combined convection and radiation heat transfer coefficients of h0, and hi , respectively, identify and write down any and all thermal resistance elements, along with the equation for estimating the rate of heat loss or gain through the wall.

c). What is an overall heat transfer coefficient "U0" ?

Explanation / Answer

GIVEN:- Surface area = A, Insulation R value = 12 ft2.hr.F/BTU, Thermal conductivity values k1 & k2 with thickness L1in & L2in respectively.

SOLUTION:-

(a) Dimensional units of thermal conductivity are M1L1T31. These variables are mass (M), length (L), time (T), and temperature (). (ANSWER)

Thickness in inches would have to be converted into ft so that thermal conductivity can be expressed as BTU/(hr·ft°F) (ANSWER)

(b) Outside temperature To and Inside temperature Ti with convection & radiation heat transfer coefficients as ho & hi respectively. Thermal resistance elements are Air, Insulation, Two solid layers.

Heat loss or gain equation for processes connected in series would be 1/Q = 1/Qc + 1/Qr + 1/Qs1 + 1/Qs2 = 1/[ho x A x (To-Ti)] + 1/[hi x A x (To-Ti) + 1/[L1/k1 x A x (To-Ti)] + 1/[L2/k2 x A x (To-Ti)]

i.e. Q = [1/(1/ho + 1/hi + L1/k1 + L2/k2)] x [A x (To-Ti)] where Q is in W (ANSWER)

(c) Overall heat transfer coefficient UO:

UO = 1 / (1/ho + 1/hi + L1/k1 + L2/k2) (ANSWER)

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