Ratio of temperature difference for given time elapsed Solution

STEP 0: Pre-Calculation Summary
Formula Used
Temperature Ratio = exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Volume*Specific Heat Capacity))
Tratio = exp(-(h*SA*t)/(ρ*VT*c))
This formula uses 1 Constants, 1 Functions, 7 Variables
Constants Used
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Functions Used
exp - Exponential function, exp(Number)
Variables Used
Temperature Ratio - Temperature ratio is the ratio of temperatures at different instances of any process or environment.
Convection Heat Transfer Coefficient - (Measured in Watt per Meter² per K) - Convection Heat Transfer Coefficient is the rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature.
Surface Area - (Measured in Square Meter) - The Surface Area of a three-dimensional shape is the sum of all of the surface areas of each of the sides.
Time Elapsed - (Measured in Second) - Time elapsed after a particular task is started.
Density - (Measured in Kilogram per Meter³) - Density is the degree of compactness of a substance.
Volume - (Measured in Cubic Meter) - Volume is the amount of space that a substance or object occupies or that is enclosed within a container.
Specific Heat Capacity - (Measured in Joule per Kilogram per K) - Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.
STEP 1: Convert Input(s) to Base Unit
Convection Heat Transfer Coefficient: 2.2 Watt per Meter² per K --> 2.2 Watt per Meter² per K No Conversion Required
Surface Area: 50 Square Meter --> 50 Square Meter No Conversion Required
Time Elapsed: 12 Second --> 12 Second No Conversion Required
Density: 5.51 Kilogram per Meter³ --> 5.51 Kilogram per Meter³ No Conversion Required
Volume: 63 Cubic Meter --> 63 Cubic Meter No Conversion Required
Specific Heat Capacity: 4.184 Kilojoule per Kilogram per K --> 4184 Joule per Kilogram per K (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tratio = exp(-(h*SA*t)/(ρ*VT*c)) --> exp(-(2.2*50*12)/(5.51*63*4184))
Evaluating ... ...
Tratio = 0.999091567279178
STEP 3: Convert Result to Output's Unit
0.999091567279178 --> No Conversion Required
FINAL ANSWER
0.999091567279178 <-- Temperature Ratio
(Calculation completed in 00.031 seconds)

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Shri Govindram Seksaria Institute of Technology and Science (SGSITS), Indore
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10+ Transient Heat Conduction Calculators

Instantaneous heat transfer rate
Heat Rate = Convection Heat Transfer Coefficient*Surface Area*(Initial Temperature-Fluid temperature)*(exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Volume*Specific Heat Capacity))) Go
Temperature after given time elapsed
Temperature = ((Initial Temperature-Fluid temperature)*(exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Volume*Specific Heat Capacity))))+Fluid temperature Go
Total heat transfer during a time interval
Heat transfer = Density*Specific Heat*Volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot Number*Fourier Number)))) Go
Ratio of temperature difference for given time elapsed
Temperature Ratio = exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Volume*Specific Heat Capacity)) Go
Power on exponential of temperature-time relation
Constant = -(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Volume*Specific Heat Capacity) Go
Product of Biot and Fourier Number in terms of system properties
Constant = (Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Volume*Specific Heat Capacity) Go
Time Constant in unsteady state heat transfer
Time Constant = (Density*Specific Heat Capacity*Volume)/(Convection Heat Transfer Coefficient*Surface Area) Go
Thermal Capacitance
Thermal capacitance = Density*Specific Heat Capacity*Volume Go
Ratio of temperature difference for given time elapsed in terms of Biot and Fourier Number
Temperature Ratio = exp(-(Biot Number*Fourier Number)) Go
Power on exponential of temperature-time relation in terms of Biot and Fourier Number
Constant = -(Biot Number*Fourier Number) Go

Ratio of temperature difference for given time elapsed Formula

Temperature Ratio = exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Volume*Specific Heat Capacity))
Tratio = exp(-(h*SA*t)/(ρ*VT*c))

What is Temperature-Time relation?

The temperature-time relationship of unsteady-state heat transfer helps to determine the rate of heat transfer that has been conducted in the lumped system in a given time period.

How to Calculate Ratio of temperature difference for given time elapsed?

Ratio of temperature difference for given time elapsed calculator uses Temperature Ratio = exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Volume*Specific Heat Capacity)) to calculate the Temperature Ratio, Ratio of temperature difference for given time elapsed formula calculates the exponential term given in the temperature-time relationship for a lumped body. Temperature Ratio is denoted by Tratio symbol.

How to calculate Ratio of temperature difference for given time elapsed using this online calculator? To use this online calculator for Ratio of temperature difference for given time elapsed, enter Convection Heat Transfer Coefficient (h), Surface Area (SA), Time Elapsed (t), Density (ρ), Volume (VT) & Specific Heat Capacity (c) and hit the calculate button. Here is how the Ratio of temperature difference for given time elapsed calculation can be explained with given input values -> 0.999092 = exp(-(2.2*50*12)/(5.51*63*4184)).

FAQ

What is Ratio of temperature difference for given time elapsed?
Ratio of temperature difference for given time elapsed formula calculates the exponential term given in the temperature-time relationship for a lumped body and is represented as Tratio = exp(-(h*SA*t)/(ρ*VT*c)) or Temperature Ratio = exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Volume*Specific Heat Capacity)). Convection Heat Transfer Coefficient is the rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature, The Surface Area of a three-dimensional shape is the sum of all of the surface areas of each of the sides, Time elapsed after a particular task is started, Density is the degree of compactness of a substance, Volume is the amount of space that a substance or object occupies or that is enclosed within a container & Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.
How to calculate Ratio of temperature difference for given time elapsed?
Ratio of temperature difference for given time elapsed formula calculates the exponential term given in the temperature-time relationship for a lumped body is calculated using Temperature Ratio = exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Volume*Specific Heat Capacity)). To calculate Ratio of temperature difference for given time elapsed, you need Convection Heat Transfer Coefficient (h), Surface Area (SA), Time Elapsed (t), Density (ρ), Volume (VT) & Specific Heat Capacity (c). With our tool, you need to enter the respective value for Convection Heat Transfer Coefficient, Surface Area, Time Elapsed, Density, Volume & Specific Heat Capacity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Temperature Ratio?
In this formula, Temperature Ratio uses Convection Heat Transfer Coefficient, Surface Area, Time Elapsed, Density, Volume & Specific Heat Capacity. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Temperature Ratio = exp(-(Biot Number*Fourier Number))
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