Temperature Inside Plane Wall at given Thickness x with Symmetrical Boundary Conditions Calculator

✖Internal Heat Generation is defined as the conversion of electrical, chemical, or nuclear energy into heat (or thermal) energy which leads to a rise in temperature throughout the medium.ⓘ Internal Heat Generation [q_G]			+10% -10%
✖Wall Thickness is simply the width of the wall that we are taking under consideration.ⓘ Wall Thickness [b]			+10% -10%
✖Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance.ⓘ Thermal Conductivity [k]			+10% -10%
✖Thickness is the distance from one end to the desired end of the body or object.ⓘ Thickness [x]			+10% -10%
✖Surface Temperature is the temperature at or near a surface. Specifically, it may refer to as Surface air temperature, the temperature of the air near the surface of the earth.ⓘ Surface Temperature [T₁]			+10% -10%

✖Temperature 1 is the degree or intensity of heat present in a substance or object.ⓘ Temperature Inside Plane Wall at given Thickness x with Symmetrical Boundary Conditions [t₁]

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Formula

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Temperature Inside Plane Wall at given Thickness x with Symmetrical Boundary Conditions

Formula

`"t"_{"1"} = -("q"_{"G"}*"b"^2)/(2*"k")*("x"/"b"-("x"/"b")^2)+"T"_{"1"}`

Example

`"130.3241K"=-("100W/m³"*("12.601905m")^2)/(2*"10.18W/(m*K)")*("4.266748m"/"12.601905m"-("4.266748m"/"12.601905m")^2)+"305K"`

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Download Steady State Heat Conduction with Heat Generation Formulas PDF

Temperature Inside Plane Wall at given Thickness x with Symmetrical Boundary Conditions Solution

STEP 0: Pre-Calculation Summary

Formula Used

Temperature 1 = -(Internal Heat Generation*Wall Thickness^2)/(2*Thermal Conductivity)*(Thickness/Wall Thickness-(Thickness/Wall Thickness)^2)+Surface Temperature
t₁ = -(q_G*b^2)/(2*k)*(x/b-(x/b)^2)+T₁
This formula uses 6 Variables

Variables Used

Temperature 1 - (Measured in Kelvin) - Temperature 1 is the degree or intensity of heat present in a substance or object.
Internal Heat Generation - (Measured in Watt Per Cubic Meter) - Internal Heat Generation is defined as the conversion of electrical, chemical, or nuclear energy into heat (or thermal) energy which leads to a rise in temperature throughout the medium.
Wall Thickness - (Measured in Meter) - Wall Thickness is simply the width of the wall that we are taking under consideration.
Thermal Conductivity - (Measured in Watt per Meter per K) - Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance.
Thickness - (Measured in Meter) - Thickness is the distance from one end to the desired end of the body or object.
Surface Temperature - (Measured in Kelvin) - Surface Temperature is the temperature at or near a surface. Specifically, it may refer to as Surface air temperature, the temperature of the air near the surface of the earth.

STEP 1: Convert Input(s) to Base Unit

Internal Heat Generation: 100 Watt Per Cubic Meter --> 100 Watt Per Cubic Meter No Conversion Required
Wall Thickness: 12.601905 Meter --> 12.601905 Meter No Conversion Required
Thermal Conductivity: 10.18 Watt per Meter per K --> 10.18 Watt per Meter per K No Conversion Required
Thickness: 4.266748 Meter --> 4.266748 Meter No Conversion Required
Surface Temperature: 305 Kelvin --> 305 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t₁ = -(q_G*b^2)/(2*k)*(x/b-(x/b)^2)+T₁ --> -(100*12.601905^2)/(2*10.18)*(4.266748/12.601905-(4.266748/12.601905)^2)+305

Evaluating ... ...

t₁ = 130.324094010629

STEP 3: Convert Result to Output's Unit

130.324094010629 Kelvin --> No Conversion Required

FINAL ANSWER

130.324094010629 ≈ 130.3241 Kelvin <-- Temperature 1

(Calculation completed in 00.004 seconds)

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Home » Physics » Heat and Mass Transfer » Conduction » Steady State Heat Conduction with Heat Generation » Temperature Inside Plane Wall at given Thickness x with Symmetrical Boundary Conditions

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Shri Govindram Seksaria Institute of Technology and Science (SGSITS), Indore

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< 14 Steady State Heat Conduction with Heat Generation Calculators

Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius

Go Temperature = Internal Heat Generation/(4*Thermal Conductivity)*(Outer Radius of Cylinder^2-Radius^2)+Outer Surface Temperature+ln(Radius/Outer Radius of Cylinder)/ln(Outer Radius of Cylinder/Inner Radius of Cylinder)*(Internal Heat Generation/(4*Thermal Conductivity)*(Outer Radius of Cylinder^2-Inner Radius of Cylinder^2)+(Outer Surface Temperature-Inner Surface Temperature))

Temperature Inside Hollow Sphere at given Radius between Inner and Outer Radius

Go Temperature = Surface Temperature of wall+Internal Heat Generation/(6*Thermal Conductivity)*(Outer Radius of Sphere^2-Radius^2)+(Internal Heat Generation*Inner Radius of Sphere^3)/(3*Thermal Conductivity)*(1/Outer Radius of Sphere-1/Radius)

Temperature Inside Solid Cylinder at given Radius Immersed in Fluid

Go Temperature Solid Cylinder = Internal Heat Generation/(4*Thermal Conductivity)*(Radius of Cylinder^2-Radius^2)+Fluid Temperature+(Internal Heat Generation*Radius of Cylinder)/(2*Convection Heat Transfer Coefficient)

Temperature at given Thickness x Inside Plane Wall Surrounded by Fluid

Go Temperature = Internal Heat Generation/(8*Thermal Conductivity)*(Wall Thickness^2-4*Thickness^2)+(Internal Heat Generation*Wall Thickness)/(2*Convection Heat Transfer Coefficient)+Fluid Temperature

Maximum Temperature Inside Solid Cylinder Immersed in Fluid

Go Maximum Temperature = Fluid Temperature+(Internal Heat Generation*Radius of Cylinder*(2+(Convection Heat Transfer Coefficient*Radius of Cylinder)/Thermal Conductivity))/(4*Convection Heat Transfer Coefficient)

Maximum Temperature in Plane Wall Surrounded by Fluid with Symmetrical Boundary Conditions

Go Maximum Temperature of Plain Wall = (Internal Heat Generation*Wall Thickness^2)/(8*Thermal Conductivity)+(Internal Heat Generation*Wall Thickness)/(2*Convection Heat Transfer Coefficient)+Fluid Temperature

Temperature Inside Plane Wall at given Thickness x with Symmetrical Boundary Conditions

Go Temperature 1 = -(Internal Heat Generation*Wall Thickness^2)/(2*Thermal Conductivity)*(Thickness/Wall Thickness-(Thickness/Wall Thickness)^2)+Surface Temperature

Temperature Inside Solid Cylinder at given Radius

Go Temperature Solid Cylinder = Internal Heat Generation/(4*Thermal Conductivity)*(Radius of Cylinder^2-Radius^2)+Surface Temperature of wall

Temperature Inside Solid Sphere at given Radius

Go Temperature 2 = Surface Temperature of wall+Internal Heat Generation/(6*Thermal Conductivity)*(Radius of Sphere^2-Radius^2)

Surface Temperature of Solid Cylinder Immersed in Fluid

Go Surface Temperature of wall = Fluid Temperature+(Internal Heat Generation*Radius of Cylinder)/(2*Convection Heat Transfer Coefficient)

Maximum Temperature in Solid Cylinder

Go Maximum Temperature = Surface Temperature of wall+(Internal Heat Generation*Radius of Cylinder^2)/(4*Thermal Conductivity)

Maximum Temperature in Solid Sphere

Go Maximum Temperature = Surface Temperature of wall+(Internal Heat Generation*Radius of Sphere^2)/(6*Thermal Conductivity)

Maximum Temperature in Plane Wall with Symmetrical Boundary Conditions

Go Maximum Temperature = Surface Temperature+(Internal Heat Generation*Wall Thickness^2)/(8*Thermal Conductivity)

Location of Maximum Temperature in Plane Wall with Symmetrical Boundary Conditions

Go Location of Maximum Temperature = Wall Thickness/2

Temperature Inside Plane Wall at given Thickness x with Symmetrical Boundary Conditions Formula

What is steady state conduction?

Steady-state conduction is the form of conduction that happens when the temperature difference(s) driving the conduction are constant.

What is internal heat generation?

Internal heat generation is defined as the conversion of electrical, chemical, or nuclear energy into heat (or thermal) energy which leads to a rise in temperature throughout the medium.

How to Calculate Temperature Inside Plane Wall at given Thickness x with Symmetrical Boundary Conditions?

Temperature Inside Plane Wall at given Thickness x with Symmetrical Boundary Conditions calculator uses Temperature 1 = -(Internal Heat Generation*Wall Thickness^2)/(2*Thermal Conductivity)*(Thickness/Wall Thickness-(Thickness/Wall Thickness)^2)+Surface Temperature to calculate the Temperature 1, The Temperature inside plane wall at given thickness x with symmetrical boundary conditions formula gives the value of temperature at desired thickness inside the plane wall provided with an internal heat generation source. Temperature 1 is denoted by t₁ symbol.

How to calculate Temperature Inside Plane Wall at given Thickness x with Symmetrical Boundary Conditions using this online calculator? To use this online calculator for Temperature Inside Plane Wall at given Thickness x with Symmetrical Boundary Conditions, enter Internal Heat Generation (q_G), Wall Thickness (b), Thermal Conductivity (k), Thickness (x) & Surface Temperature (T₁) and hit the calculate button. Here is how the Temperature Inside Plane Wall at given Thickness x with Symmetrical Boundary Conditions calculation can be explained with given input values -> 130.3241 = -(100*12.601905^2)/(2*10.18)*(4.266748/12.601905-(4.266748/12.601905)^2)+305.

FAQ

What is Temperature Inside Plane Wall at given Thickness x with Symmetrical Boundary Conditions?

The Temperature inside plane wall at given thickness x with symmetrical boundary conditions formula gives the value of temperature at desired thickness inside the plane wall provided with an internal heat generation source and is represented as t₁ = -(q_G*b^2)/(2*k)*(x/b-(x/b)^2)+T₁ or Temperature 1 = -(Internal Heat Generation*Wall Thickness^2)/(2*Thermal Conductivity)*(Thickness/Wall Thickness-(Thickness/Wall Thickness)^2)+Surface Temperature. Internal Heat Generation is defined as the conversion of electrical, chemical, or nuclear energy into heat (or thermal) energy which leads to a rise in temperature throughout the medium, Wall Thickness is simply the width of the wall that we are taking under consideration, Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance, Thickness is the distance from one end to the desired end of the body or object & Surface Temperature is the temperature at or near a surface. Specifically, it may refer to as Surface air temperature, the temperature of the air near the surface of the earth.

How to calculate Temperature Inside Plane Wall at given Thickness x with Symmetrical Boundary Conditions?

The Temperature inside plane wall at given thickness x with symmetrical boundary conditions formula gives the value of temperature at desired thickness inside the plane wall provided with an internal heat generation source is calculated using Temperature 1 = -(Internal Heat Generation*Wall Thickness^2)/(2*Thermal Conductivity)*(Thickness/Wall Thickness-(Thickness/Wall Thickness)^2)+Surface Temperature. To calculate Temperature Inside Plane Wall at given Thickness x with Symmetrical Boundary Conditions, you need Internal Heat Generation (q_G), Wall Thickness (b), Thermal Conductivity (k), Thickness (x) & Surface Temperature (T₁). With our tool, you need to enter the respective value for Internal Heat Generation, Wall Thickness, Thermal Conductivity, Thickness & Surface Temperature and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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