You are asked to estimate the maximum human body temperature if the metabolic heat produced in your body could escape only by tissue conduction and later on the surface by convection. Simplify the human body as a cylinder of L=1.8 m in height and ro= 0.15 m in radius. Further, simplify the heat transfer process inside the human body as a 1-D situation whe the temperature only depends on the radial coordinater from the centerline. The governing d'T +q""=0 dr equation is written as 1 d 4k k- r dr r=0, dT dr =0 d'T r=ro-k =h(T-T) dr (k=0.5 W/m°C), ro is the radius of the cylinder (0.15 m), k is the convection coefficient at the skin surface (15 W/m² °C), Tair is the air temperature (30°C). q"" is the average volumetric heat generation rate in the body (W/m³) and is defined as heat generated per unit volume per second. The 1-D (radial) temperature distribution can be derived as: T(r)= +T 2h 4k , where k is thermal conductivity of tissue (A) q"" can be calculated based on a normal dietary calorie consumption of 2000 Cal/day. You can convert it into J/day and then to J/second. Then, calculate the human body volume (0.15 m in radius and 1.8 m tall). q will then be determined (J/s m³). Write the expressions of the maximal and minimal temperatures in the human body. Calculate the maximal and minimal temperatures of the body. (B) Then use the same expression to calculate the maximal and minimal temperatures when the person is in exercise with a much bigger volumetric heat generation rate as q"-3000 W/m³. (C) Are the calculated results reasonable? Why are the results reasonable or not reasonable?
You are asked to estimate the maximum human body temperature if the metabolic heat produced in your body could escape only by tissue conduction and later on the surface by convection. Simplify the human body as a cylinder of L=1.8 m in height and ro= 0.15 m in radius. Further, simplify the heat transfer process inside the human body as a 1-D situation whe the temperature only depends on the radial coordinater from the centerline. The governing d'T +q""=0 dr equation is written as 1 d 4k k- r dr r=0, dT dr =0 d'T r=ro-k =h(T-T) dr (k=0.5 W/m°C), ro is the radius of the cylinder (0.15 m), k is the convection coefficient at the skin surface (15 W/m² °C), Tair is the air temperature (30°C). q"" is the average volumetric heat generation rate in the body (W/m³) and is defined as heat generated per unit volume per second. The 1-D (radial) temperature distribution can be derived as: T(r)= +T 2h 4k , where k is thermal conductivity of tissue (A) q"" can be calculated based on a normal dietary calorie consumption of 2000 Cal/day. You can convert it into J/day and then to J/second. Then, calculate the human body volume (0.15 m in radius and 1.8 m tall). q will then be determined (J/s m³). Write the expressions of the maximal and minimal temperatures in the human body. Calculate the maximal and minimal temperatures of the body. (B) Then use the same expression to calculate the maximal and minimal temperatures when the person is in exercise with a much bigger volumetric heat generation rate as q"-3000 W/m³. (C) Are the calculated results reasonable? Why are the results reasonable or not reasonable?
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:You are asked to estimate the maximum human body temperature if the metabolic
heat produced in your body could escape only by tissue conduction and later on the surface by
convection. Simplify the human body as a cylinder of L=1.8 m in height and ro= 0.15 m in
radius. Further, simplify the heat transfer process inside the human body as a 1-D situation when
the temperature only depends on the radial coordinater from the centerline. The governing
dT
+q""=0
dr
equation is written as
1 d
k-
r dr
r = 0,
dT
dr
=0
dT
r=ro -k -=h(T-T)
dr
(k-0.5 W/m°C), ro is the radius of the cylinder (0.15 m), h is the convection coefficient at the
skin surface (15 W/m² °C), Tair is the air temperature (30°C). q" is the average volumetric heat
generation rate in the body (W/m³) and is defined as heat generated per unit volume per second.
The 1-D (radial) temperature distribution can be derived as:
T(r) =
q"¹'r² qr qr.
+
4k 2h
+
4k
+T
, where k is thermal conductivity of tissue
air
(A) q" can be calculated based on a normal dietary calorie consumption of 2000 Cal/day.
You can convert it into J/day and then to J/second. Then, calculate the human body volume
(0.15 m in radius and 1.8 m tall). q' will then be determined (J/s m³). Write the expressions of
the maximal and minimal temperatures in the human body. Calculate the maximal and minimal
temperatures of the body.
(B) Then use the same expression to calculate the maximal and minimal temperatures when
the person is in exercise with a much bigger volumetric heat generation rate as q"-3000 W/m².
(C) Are the calculated results reasonable? Why are the results reasonable or not reasonable?
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